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34 he informed noble Lords that "in Easy Prussia the situation has undergone but little change.... In the Caucasus, the end of November [six weeks ago] the Turkish Army was being pushed back towards Erzerum." Later, the House heard with startled amazement that "On our own coasts, on the morning of December 16, German battle cruisers bombarded for half-an-hour Harlepool, Scarborough, and Whitby."

As to progress of recruiting, with respect to which information was looked forward to with exceptional interest, he went so far as to say, "Recruiting has proceeded on normal lines."

"The noble lord," said the, amid a murmur of assent from the dumbfounded Peers, "had been very economical in his information," a really delicate way of stating the fact.

Business done.—None.

Friday.—Lords adjourned.

The following extracts from official despatches exchanged between General von Funkinstein and the German Great General Staff have been communicated to us by a wholly impeachable authority, and are published with no reserve whatever:—

(1) From the General Officer Commanding, &c.:—

"... with regard to various recent regrettable incidents in which sections of the Imperial trenches have been captured by native troops from British India (which, according to the German official programme, ought to have been in revolt long since) some light has now been cast upon the probable reason for this. Used as we now are to the contempt for every rule of civilized warfare displayed by our detestable and cowardly adversary, this new revelation of his cunning and brutality will nevertheless come as a shock.

"Aircraft observation has now made it clear that the force immediately opposed to my comand is not the Horse, as was believed, but a picked body of the First Indian Jugglers, specially recruited for this campaign. On the occasion of the last attack we were startled about 5.30 A.M. by a prodigious and ear-splitting noise proceeding from the trenches occupied by these troops—or troupes. Perhaps no soldiers in the world save our own incomparable warriors, trained to withstand modern German music, could have endured this ghastly din without flinching. Before long we observed a confused and stealthy movement on our front; but what was our emotion to see advancing out of the mist not the expected native charge, but a double line of trained cobras. Despite the inevitable shock produced by this discovery, energetic steps were at once taken to deal with the attack, and a brisk fire was opened with hand grenades. The results were however negligible, from the fact that the reptiles, apparently mistaking the hissing of the fuses for a challenge from others of their own species, instantly and savagely bit them off, thus rendering the grenades ineffective. Under these circumstances I had no alternative but to evacuate my position, a movement that was accomplished in fair oder and very creditable time, myself leading..."

(2) Extract from copy of reply by Chief of Great General Staff, Berlin:—

"I am commanded by H.I.M. to inform you that you must retake trenches at once, regardless of loss. Reports of scandalous breach of all civilised laws forwarded to Presidents Geneva Convention and Hague Tribunal. Two reserve battalions of Guards leave Potsdam to-night. Hope that an accentuated mongoose-step movement may crush the new enemy. Please report at once."

(3) From Same as No. 1:—

"Regret to convey further unfavourable development with regard to our operations against the Jugglers' Corps. Having tempted a large body of these into open country some distance to the rear of our original lines, I ordered an attack in what should have been overwhelming force. The enemy was at this stage entirely exposed to our fire, being without any possibility of cover. Unfortunately, just as we had them at our mercy, a concerted movement by their entire strength, known (I believe) as the Mango Trick, resulted in the appearance of a dense grove of these trees, behind which the enemy is at present effectually screened."

(4) From the same:—

"Our treacherous foe has again escaped us. An heroic attack by the bayonet upon the Mango Grove mentioned in previous despatch was successful in capturing the position, but only in time to see the last unit of the defending force vanishing up a rope, which with a large number of others was dangling without visible attachment. The effect of this renewed failure upon the moral of the Imperial army has unfortunately been considerable. I learn from my agents that the enemy is now bringing up a number of heavy hypnotists for use against me personally. Please wire instructions."

(5) From the same as (2):—

"Your resignation on the ground of ill-health regretfully accepted. Return at once."

"'THE SEED OF THE WAR

Freeman's Journal."

But why suddenly break into Flemish?

Routine order issued by the Q.M.G.'s department:—

"'Fuel for general and other headquarter offices and signalling offices with the troops, is authorised at the scale of sixteen kilometres of coal per fireplace per day.

Dec. 20th. B. E. F."

Theirs not to reason why. If the order is "Ten miles of coal per fireplace" then ten miles it is.

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RV 9 (BUDDENBROOKS) so I’ve come, yer honour ’n’ ladies ’n’ gentlemen, to congratulate the Herr Consul ’n’ the Frau Consul, ’n’ the whole respected family, from a full hairt, ’n’ that the child may prosper, for that they desarve fr’m God ’n’ man, for such a master as Consul Buddenbrook there aren’t so many, he’s a noble gentleman, ’n’ our Lord will reward him for all. . . .”

“Splendid, Grobleben! That was a beautiful speech. Thank you very much, Grobleben. What are the roses for?”

But Grobleben has not nearly done. He strains his whining voice and drowns the Consul out.

“. . . ’n’ I say th’ Lord will reward him, him and the whole respected family; ’n’ when his time has come to stan’ before His throne, for stan’ we all must, rich and poor, ’n’ one’ll have a fine polished hard-wood coffin ’n’ ’tother ’n’ old box, yet all on us must come to mother earth at th’ last, yes, we must all come to her at th’ last—to mother earth—to mother—”

“Oh, come, come, Grobleben! This isn’t a funeral, it’s a christening. Get along with your mother earth!”

“. . . ’n’ these be a few flowers,” concludes Grobleben.

“Thank you, Grobleben, thank you. This is too much—what did you pay for them, man? But I haven’t heard such a speech as that for a long time! Wait a minute—here, go out and give yourself a treat, in honour of the day!” And the Consul puts his hand on the old man’s shoulder and gives him a thaler.

“Here, my good man,” says the Frau Consul. “And I hope you love our blessed Lord?”

“I be lovin’ him from my hairt, Frau Consul, thet’s the holy truth!” And Gobleben gets another thaler from her, and a third from Frau Permaneder, and retires with a bow and a scrape, taking the roses with him by mistake, except for those already fallen on the carpet.

The Burgomaster takes his leave now, and the Consul accompanies him down to his carriage. This is the signal for

RV 9 (9)

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/


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'''150 wave the sheaf before the LORD so that it may be accepted on your behalf; the priest is to wave it on the day after the Sabbath.

On the day you wave the sheaf, you shall offer a year-old lamb without blemish as a burnt offering to the LORD, along with its grain offering of two-tenths of an ephah of fine flour mixed with oil—an offering made by fire to the LORD, a pleasing aroma—and its drink offering of a quarter hin of wine.

You must not eat any bread or roasted or new grain until the very day you have brought this offering to your God. This is to be a permanent statute for the generations to come, wherever you live.

The Feast of Weeks (Acts 2:1–13)

From the day after the Sabbath, the day you brought the sheaf of the wave offering, you are to count off seven full weeks. You shall count off fifty days until the day after the seventh Sabbath, and then present an offering of new grain to the LORD.

Bring two loaves of bread from your dwellings as a wave offering, each made from two-tenths of an ephah of fine flour, baked with leaven, as the firstfruits to the LORD.

Along with the bread you are to present seven unblemished male lambs a year old, one young bull, and two rams. They will be a burnt offering to the LORD, together with their grain offerings and drink offerings—an offering made by fire, a pleasing aroma to the LORD.

You shall also prepare one male goat as a sin offering and two male lambs a year old as a peace offering. The priest is to wave the lambs as a wave offering before the LORD, together with the bread of the firstfruits. The bread and the two lambs shall be holy to the LORD for the priest.

On that same day you are to proclaim a sacred assembly, and you must not do any regular work. This is to be a permanent statute wherever you live for the generations to come.

When you reap the harvest of your land, do not reap all the way to the edges of your field or gather the gleanings of your harvest. Leave them for the poor and the foreign resident. I am the LORD your God.’”

The Feast of Trumpets (Numbers 29:1–6)

The LORD also said to Moses, “Speak to the Israelites and say, ‘On the first day of the seventh month you are to have a day of rest, a sacred assembly announced by trumpet blasts. You must not do any regular work, but you are to present an offering made by fire to the LORD.’”

The Day of Atonement (Leviticus 16:1–34; Numbers 29:7–11)

Again the LORD said to Moses, “The tenth day of this seventh month is the Day of Atonement. You shall hold a sacred assembly and humble yourselves, and present an offering made by fire to the LORD.

On this day you are not to do any work, for it is the Day of Atonement, when atonement is made for you before the LORD your God. If anyone does not humble himself on this day, he must be cut off from his people. I will destroy from among his people anyone who does any work on this day.

You are not to do any work at all. This is a permanent statute for the generations to come, wherever you live. It will be a Sabbath


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is the word used by Muhammadan writers to express the corruption of the sacred Scriptures of the Jews and Christians, as asserted in the Qurán.

Imám Fakhar-ud-dín Rází, in his commentary, explains "Tahríf" to mean, to change, alter, or turn aside anything from the truth. Muslim divines say there are two kinds of Tahríf, namely, Tahríf-i-Mʾanawí, a corruption of the meaning; and Tahríf-i-Lafzí, a corruption of the words.

Muhammadan controversialists, when they become acquainted with the nature of the contents of our sacred books, and of the impossibility of reconciling the contents of the Qurán with those of the sacred Scriptures,


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RV 10 (BUDDENBROOKS) the party to break up—for Gerda Buddenbrook must rest. The old Frau Consul, Tony, Erica, and Mamsell JugmannJungmann [sic] are the last to go.

“Well, Ida,” says the Consul, “I have been thinking it over: you took care of us all, and when little Johann gets a bit older—He still has the monthly nurse now, and after that he will still need a day-nurse, I suppose—but will you be willing to move over to us when the time comes?”

“Yes, indeed, Herr Consul, if your wife is satisfied.”

Gerda is content to have it so, and thus it is settled.

In the act of leaving, however, and already at the door, Frau Permaneder turns. She comes back to her brother and kisses him on both cheeks, and says: “It has been a lovely day, Tom. I am happier than I have been for years. We Buddenbrooks aren’t quite at the last gasp yet, thank God, and whoever thinks we are is mightily mistaken. Now that we have little Johann—it is so beautiful that he is christened Johann—it looks to me as if quite a new day will dawn for us all!”

RV 10 (10)


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'''Leviticus 24:7 of complete rest for you, and you shall humble yourselves. From the evening of the ninth day of the month until the following evening you are to keep your Sabbath.”

The Feast of Tabernacles (Nehemiah 8:13–18; Zechariah 14:16–21)

And the LORD said to Moses, “Speak to the Israelites and say, ‘On the fifteenth day of the seventh month the Feast of Tabernacles to the LORD begins, and it continues for seven days. On the first day there shall be a sacred assembly. You must not do any regular work. For seven days you are to present an offering made by fire to the LORD. On the eighth day you are to hold a sacred assembly and present an offering made by fire to the LORD. It is a solemn assembly; you must not do any regular work.

These are the LORD’s appointed feasts, which you are to proclaim as sacred assemblies for presenting offerings by fire to the LORD—burnt offerings and grain offerings, sacrifices and drink offerings, each on its designated day. These offerings are in addition to the offerings for the LORD’s Sabbaths, and in addition to your gifts, to all your vow offerings, and to all the freewill offerings you give to the LORD.

On the fifteenth day of the seventh month, after you have gathered the produce of the land, you are to celebrate a feast to the LORD for seven days. There shall be complete rest on the first day and also on the eighth day.

On the first day you are to gather the fruit of majestic trees, the branches of palm trees, and the boughs of leafy trees and of willows of the brook. And you are to rejoice before the LORD your God for seven days. You are to celebrate this as a feast to the LORD for seven days each year. This is a permanent statute for the generations to come; you are to celebrate it in the seventh month.

You are to dwell in booths for seven days. All the native-born of Israel must dwell in booths, so that your descendants may know that I made the Israelites dwell in booths when I brought them out of the land of Egypt. I am the LORD your God.’”

So Moses announced to the Israelites the appointed feasts of the LORD. The Oil for the Lamps (Exodus 27:20–21)

Then the LORD said to Moses, “Command the Israelites to bring you pure oil of pressed olives for the light, to keep the lamps burning continually.

Outside the veil of the Testimony in the Tent of Meeting, Aaron is to tend the lamps continually before the LORD from evening until morning. This is to be a permanent statute for the generations to come. He shall tend the lamps on the pure gold lampstand before the LORD continually.

The Showbread (Exodus 25:23–30; Exodus 37:10–16)

You are also to take fine flour and bake twelve loaves, using two-tenths of an ephah for each loaf, and set them in two rows—six per row—on the table of pure gold before the LORD. And you are to place pure frankincense near each row, so that it may serve as a memorial portion for the bread, an offering made by fire to the LORD.


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 268 charge the Christians with the Tahríf-i-Lafzí. They say the Christians have expunged the word Ahmad from the prophecies, and have inserted the expression "Son of God," and the story of the crucifixion, death, and resurrection of our blessed Lord. This view, however, is not the one held by the most celebrated of the Muslim commentators.

Imám Muhammad Ismaíl Bokhárí, records that Ibn ʿAbbás said that "the word Tahríf (corruption) signifies to change a thing from its original nature; and that there is no man who could corrupt a single word of what proceeded from God, so that the Jews and Christians could corrupt only by misrepresenting the meaning of the words of God."

Ibn-i-Mazar and Ibn Abi Hátim state, in the commentary known as the Tafsír Durr-i-Mansúr, that they have it on the authority of Ibn-i-Munía, that the Taurát (i. e. the books of Moses), and the Injíl (i. e. the Gospels), are in the same state of purity in which they were


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January 13, 1915.

''—A mud puddle in shire, in which are discovered forty yeomen in khaki lying on their backs and flapping their legs like seals. They are not really seals, but men whom their and country needs, doing breathing exercises. The reason they do not get up out of the puddle and walk away is that they would probably be killed by the enormous troop sergeant who is instructing them.''

Troop Sergeant (fiercely). Now then. Work at it. I'm 'ere to do you a bit of good, I am. Finest thing in the world, this is. Some of you fellows don't know a good thing when you see it. What is it that causes tuberckylosis? Why, want of hoxygen. That's what it is. Look at San Stevens—middle-weight champion of the world he was. And what did he die of? Why, drink. And what made him take to drink? Why, want of hoxygen. That's what it was. If a man can't breathe hoxygen he'll drink it. How many cells do you suppose you 'ave in your lungs, Number Three?

Number Three (inhaling through the mouth). Don't know, Sergeant.

Troop Sergeant. Why, fifty million. Fifty million cells in your lungs you've got.

[Number Three, appalled at this revelation, inhales briskly through the nose in the hope of filling some of them.

Troop Sergeant. And how many do you suppose you generally use? Why, not half of them. Twenty-five million cells you've got doing nothing.

[''Number Three exhales despondently through the mouth, realising the vanity of all human endeavour. The Troop Sergeant, satisfied that he has disposed of Number Three, glares contentedly at the troop in silence.''

Troop (exhaling through the mouth). F-s-s-s-s-h.

Troop Sergeant (with sudden emotion). Look at your neck, Number Ten. I ask you, look at the back of your neck.

[Number Ten, feeling that this is a difficult feat to perform at any time and quite impossible when lying on his back, continues to gaze upwards, conscious of insubordination.

Troop Sergeant. Why is it twisted like that? A bone out of place, the doctors will tell you. But (solemnly) is it out of place, I ask you? Tell me that. Want of hoxygen—that's what it is. It's as plain as day.

[Enter Troop Officer.

Troop Officer (explosively). A-tssh! Code id by head, Sergeadt.

Troop Sergeant. Ah, Sir, if you was to do these breathing exercises you wouldn't 'ave no colds, Sir. If everyone was to do these exercises there wouldn't by no doctors, Sir. It's only want of hoxygen that makes people ill. There isn't a man in this troop's 'ad a cold since we began, Sir.

Numbers Five, Seven and Nine (surreptitiously). A-tissh!

[The Troop Sergeant is about to ignore this breach of discipline when Number Three, who has been trying to repress a sneeze while inhaling through the nose and at the same time carrying the legs to a vertical position above the body, explodes violently.

Troop Sergeant (ominously). Number Three!

Number Three (weakly). Yes, Sergeant.

Troop Sergeant. Have you got a cold?

Number Three (ingratiatingly). Only a very little one, Sergeant.

Troop Sergeant (appealing to Officer). Isn't it enough to break one's 'eart, Sir? 'Ere am I trying to do them a bit o' good and 'ere's this man lies there with his 'ead tucked into 'is chest, and doesn't even try to breath. There's only one thing that causes a cold. Want of hox A-tissh! A-tissh!

[''A painful silence ensues. The Officer walks away, leaving the Sergeant to his grief. The forty seals continue to flap in the mud puddle in shire.''

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Page:General Investigations of Curved Surfaces, by Carl Friedrich Gauss, translated into English by Adam Miller Hiltebeitel and James Caddall Morehead.djvu/112

 $$ d. \frac{\frac{dx}{dw}} {\sqrt{\left(\frac{dx}{dw}\right)^{2} + \left(\frac{dy}{dw}\right)^{2} + \left(\frac{dz}{dw}\right)^{2}}}, \qquad d. \frac{\frac{dy}{dw}} {\sqrt{\left(\frac{dx}{dw}\right)^{2} + \left(\frac{dy}{dw}\right)^{2} + \left(\frac{dz}{dw}\right)^{2}}}, $$

$$ d. \frac{\frac{dz}{dw}} {\sqrt{\left(\frac{dx}{dw}\right)^{2} + \left(\frac{dy}{dw}\right)^{2} + \left(\frac{dz}{dw}\right)^{2}}} $$

must be proportional to the quantities $P,$  $Q,$  $R$ respectively. If $ds$  is an element of the curve; $\lambda$  the point upon the auxiliary sphere, which represents the direction of this element; $L$  the point giving the direction of the normal as above; and $\xi,$  $\eta,$  $\zeta;$ $X,$  $Y,$  $Z$  the coordinates of the points $\lambda,$  $L$  referred to the centre of the auxiliary sphere, then we have

$$\begin{array}{c} dx = \xi\, ds,\qquad dy = \eta\, ds,\qquad dz = \zeta\, ds, \\ \xi^{2} + \eta^{2} + \zeta^{2} = 1. \end{array}$$

Therefore we see that the above differentials will be equal to $d\xi,$  $d\eta,$  $d\zeta.$ And since $P,$  $Q,$  $R$  are proportional to the quantities $X,$  $Y,$  $Z,$  the character of the shortest line is such that

$$\frac{d\xi}{X} = \frac{d\eta}{Y} = \frac{d\zeta}{Z}.$$

13.

To every point of a curved line upon a curved surface there correspond two points on the sphere, according to our point of view; namely, the point $\lambda,$ which represents the direction of the linear element, and the point $L,$  which represents the direction of the normal to the surface. The two are evidently $90^{\circ}$  apart. In our former investigation (Art. 9 ), where [we] supposed the curved line to lie in a plane, we had two other points upon the sphere; namely, $\mathfrak{L},$ which represents the direction of the normal to the plane, and $\lambda',$  which represents the direction of the normal to the element of the curve in the plane. In this case, therefore, $\mathfrak{L}$  was a fixed point and $\lambda,$  $\lambda'$ were always in a great circle whose pole was $\mathfrak{L}.$  In generalizing these considerations, we shall retain the notation $\mathfrak{L},$  $\lambda',$  but we must define the meaning of these symbols from a more general point of view. When the curve $s$ is described, the points $L,$  $\lambda$  also describe curved lines upon the auxiliary sphere, which, generally speaking, are no longer great circles. Parallel to the element of the second line,


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 future master of Rome was now coming home, after nearly ten years' absence, at the head of the victorious legions with which he had struck terror into the Germans, overrun all Spain, left his mark upon Britain, and "pacified" Gaul. But Cicero, in common with most of the senatorial party, failed to see in Julius Cæsar the great man that he was. He hesitated a little—Cæsar would gladly have had his support, and made him fair offers; but when the Rubicon was crossed, he threw in his lot with Pompey. He was certainly influenced in part by personal attachment: Pompey seems to have exercised a degree of fascination over his weakness. He knew Pompey's indecision of character, and confessed that Cæsar was "a prodigy of energy;" but though the former showed little liking for him, he clung to him nevertheless. He foreboded that, let the contest end which way it would, "the result would certainly be a despotism." He foresaw that Pompey's real designs were as dangerous to the liberties of Rome as any of which Cæsar could be suspected. "Sullaturit

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Page:General Investigations of Curved Surfaces, by Carl Friedrich Gauss, translated into English by Adam Miller Hiltebeitel and James Caddall Morehead.djvu/113

 we draw a radius of the auxiliary sphere to the point $\lambda',$ but instead of this point we take the point opposite when $\lambda'$  is more than $90^{\circ}$  from $L.$  In the first case, we regard the element at $\lambda$  as positive, and in the other as negative. Finally, let $\mathfrak{L}$ be the point on the auxiliary sphere, which is $90^{\circ}$  from both $\lambda$  and $\lambda',$  and which is so taken that $\lambda,$  $\lambda',$  $\mathfrak{L}$  lie in the same order as $(1),$  $(2),$  $(3).$

The coordinates of the four points of the auxiliary sphere, referred to its centre, are for

$$\begin{alignedat}{4} &L\qquad &&X\quad &&Y\quad &&Z \\ &\lambda &&\xi   &&\eta   &&\zeta \\ &\lambda'&&\xi'  &&\eta'  &&\zeta' \\ &\mathfrak{L}     &&\alpha &&\beta  &&\gamma. \end{alignedat}$$

Hence each of these $4$  points describes a line upon the auxiliary sphere, whose elements we shall express by $dL,$  $d\lambda,$  $d\lambda',$  $d\mathfrak{L}.$ We have, therefore,

$$\begin{aligned} d\xi  &= \xi'\, d\lambda, \\ d\eta &= \eta'\, d\lambda, \\ d\zeta &= \zeta'\, d\lambda. \end{aligned}$$

In an analogous way we now call

$$\frac{d\lambda}{ds}$$

the measure of curvature of the curved line upon the curved surface, and its reciprocal

$$\frac{ds}{d\lambda}$$

the radius of curvature. If we denote the latter by $\rho,$ then

$$\begin{aligned} \rho\, d\xi  &= \xi'\, ds, \\ \rho\, d\eta &= \eta'\, ds, \\ \rho\, d\zeta &= \zeta'\, ds. \end{aligned}$$

If, therefore, our line be a shortest line, $\xi',$  $\eta',$  $\zeta'$ must be proportional to the quantities $X,$  $Y,$  $Z.$  But, since at the same time

$$\xi'^{2} + \eta'^{2} + \zeta'^{2} = X^{2} + Y^{2} + Z^{2} = 1,$$

we have

$$\xi'  = \pm X,\quad \eta' = \pm Y,\quad \zeta' = \pm Z,$$

and since, further,

$$\begin{aligned} \xi'X + \eta'Y + \zeta'Z &= \cos \lambda'L \\ &= \pm (X^{2} + Y^{2} + Z^{2}) \\ &= \pm 1, \end{aligned}$$


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'''152  Every Sabbath day the bread is to be set out before the LORD on behalf of the Israelites as a permanent covenant. It belongs to Aaron and his sons, who are to eat it in a holy place; for it is to him a most holy part of the offerings made by fire to the LORD—his portion forever.”

Punishment for Blasphemy

Now the son of an Israelite mother and an Egyptian father went out among the Israelites, and a fight broke out in the camp between him and an Israelite. The son of the Israelite woman blasphemed the Name with a curse. So they brought him to Moses. (His mother’s name was Shelomith daughter of Dibri, of the tribe of Dan.)

They placed him in custody until the will of the LORD should be made clear to them.

Then the LORD said to Moses, “Take the blasphemer outside the camp, and have all who heard him lay their hands on his head; then have the whole assembly stone him.

And you are to tell the Israelites, ‘If anyone curses his God, he shall bear the consequences of his sin. Whoever blasphemes the name of the LORD must surely be put to death; the whole assembly must surely stone him, whether he is a foreign resident or native; if he blasphemes the Name, he must be put to death.

An Eye for an Eye (Matthew 5:38–48)

And if a man takes the life of anyone else, he must surely be put to death. Whoever kills an animal must make restitution—life for life. If anyone injures his neighbor, whatever he has done must be done to him: fracture for fracture, eye for eye, tooth for tooth. Just as he injured the other person, the same must be inflicted on him.

Whoever kills an animal must make restitution, but whoever kills a man must be put to death. You are to have the same standard of law for the foreign resident and the native; for I am the LORD your God.’”

Then Moses spoke to the Israelites, and they took the blasphemer outside the camp and stoned him. So the Israelites did as the LORD had commanded Moses. The Seventh Year (Exodus 23:10–13; Deuteronomy 15:1–6)

Then the LORD said to Moses on Mount Sinai, “Speak to the Israelites and say to them: When you enter the land that I am giving you, the land itself must observe a Sabbath to the LORD.

For six years you may sow your field and prune your vineyard and gather its crops. But in the seventh year there shall be a Sabbath of complete rest for the land—a Sabbath to the LORD.

You are not to sow your field or prune your vineyard. You are not to reap the aftergrowth of your harvest or gather the grapes of your untended vines. The land must have a year of complete rest. Whatever the land yields during the Sabbath year shall be food for you—for yourself, your manservant and maidservant, the hired hand or foreigner who stays with you, and for your livestock and the wild animals in your land. All its growth may serve as food.

The Year of Jubilee

And you shall count off seven Sabbaths of years—seven times seven years—so that the seven Sabbaths of years amount to forty-nine


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 and since we always choose the point $\lambda'$ so that

$$\lambda'L < 90^{\circ},$$

then for the shortest line

$$\lambda'L = 0,$$

or $\lambda'$  and $L$ must coincide. Therefore

$$\begin{aligned} \rho\, d\xi  &= X\, ds, \\ \rho\, d\eta &= Y\, ds, \\ \rho\, d\zeta &= Z\, ds, \end{aligned}$$

and we have here, instead of $4$  curved lines upon the auxiliary sphere, only $3$  to consider. Every element of the second line is therefore to be regarded as lying in the great circle $L\lambda.$ And the positive or negative value of $\rho$  refers to the concavity or the convexity of the curve in the direction of the normal.

14.

We shall now investigate the spherical angle upon the auxiliary sphere, which the great circle going from $L$ toward $\lambda$  makes with that one going from $L$  toward one of the fixed points $(1),$  $(2),$  $(3);$   e.g. , toward $(3).$  In order to have something definite here, we shall consider the sense from $L(3)$  to $L\lambda$  the same as that in which $(1),$  $(2),$  and $(3)$  lie. If we call this angle $\phi,$ then it follows from the theorem of Art. 7 that

$$\sin L(3). \sin L\lambda. \sin\phi = Y\xi - X\eta,$$

or, since $L\lambda = 90^{\circ}$ and

$$\sin L(3) = \sqrt{X^{2} + Y^{2}} = \sqrt{1 - Z^{2}},$$

we have

$$\sin\phi = \frac{Y\xi - X\eta}{\sqrt{X^{2} + Y^{2}}}.$$

Furthermore,

$$\sin L(3). \sin L\lambda. \cos\phi = \zeta,$$

or

$$\cos\phi = \frac{\zeta}{\sqrt{X^{2} + Y^{2}}}$$

and

$$\tan\phi = \frac{Y\xi - X\eta}{\zeta} = \frac{\zeta'}{\zeta}.$$


text:
Page:Cicero (Collins 1871).djvu/82

70 animus," he says of him in one of his letters, coining a verb to put his idea strongly—"he wants to be like Sulla." And it was no more than the truth. He found out afterwards, as he tells Atticus, that proscription-lists of all Cæsar's adherents had been prepared by Pompey and his partisans, and that his old friend's name figured as one of the victims. Only this makes it possible to forgive him for the little feeling that he showed when he heard of Pompey's own miserable end.

Cicero's conduct and motives at this eventful crisis have been discussed over and over again. It may be questioned whether at this date we are in any position to pass more than a very cautious and general judgment upon them. We want all the "state papers" and political correspondence of the day—not Cicero's letters only, but those of Cæsar and Pompey and Lentulus, and much information besides that was never trusted to pen or paper—in order to lay down with any accuracy the course which a really unselfish patriot could have taken. But there seems little reason to accuse Cicero of double-dealing or trimming in the worst sense. His policy was unquestionably, from first to last, a policy of expedients. But expediency is, and must be more or less, the watchword of a statesman. If he would practically serve his country, he must do to some extent what Cicero professed to do—make friends with those in power. "Sic vivitur"—"So goes the world;" "Tempori serviendum est"—"We must bend to circumstances"—these are not the noblest mottoes, but they are acted upon continually

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Rh by the most respectable men in public and private life, who do not open their hearts to their friends so unreservedly as Cicero does to his friend Atticus. It seemed to him a choice between Pompey and Cæsar; and he probably hoped to be able so far to influence the former, as to preserve some shadow of a constitution for Rome. What he saw in those "dregs of a Republic," as he himself calls it, that was worth preserving;—how any honest despotism could seem to him more to be dreaded than that prostituted liberty,—this is harder to comprehend. The remark of Abeken seems to go very near the truth—"His devotion to the commonwealth was grounded not so much upon his conviction of its actual merits, as of its fitness for the display of his own abilities."

But that commonwealth was past saving even in name. Within two months of his having been declared a public enemy, all Italy was at Cæsar's feet. Before another year was past, the battle of Pharsalia had been fought, and the great Pompey lay a headless corpse on the sea-shore in Egypt. It was suggested to Cicero, who had hitherto remained constant to the fortunes of his party, and was then in their camp at Dyrrachium, that he should take the chief command, but he had the sense to decline; and though men called him "traitor," and drew their swords upon him, he withdrew from a cause which he saw was lost, and returned to Italy, though not to Rome.

The meeting between him and Cæsar, which came at last, set at rest any personal apprehensions from that

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text:
Page:General Investigations of Curved Surfaces, by Carl Friedrich Gauss, translated into English by Adam Miller Hiltebeitel and James Caddall Morehead.djvu/115

 Hence we have

$$d\phi = \frac{\zeta Y\, d\xi - \zeta X\, d\eta - (Y\xi - X\eta)\, d\zeta + \xi\zeta\, dY - \eta\zeta\, dX} {(Y\xi - X\eta)^{2} + \zeta^{2}}.$$

The denominator of this expression is

$$\begin{aligned} &= Y^{2}\xi^{2} - 2XY\xi\eta - X^{2}\eta^{2} + \zeta^{2} \\ &= -(X\xi + Y\eta)^{2} + (X^{2} + Y^{2})(\xi^{2} + \eta^{2}) + \zeta^{2} \\ &= -Z^{2}\zeta^{2} + (1 - Z^{2})(1 - \zeta^{2}) + \zeta^{2} \\ &= 1 - Z^{2}, \end{aligned}$$

or

$$d\phi = \frac{\zeta Y\, d\xi - \zeta X\, d\eta + (X\eta - Y\xi)\, d\zeta - \eta\zeta\, dX + \xi\zeta\, dY} {1 - Z^{2}}.$$

We verify readily by expansion the identical equation

$$\begin{array}{c} \eta\zeta(X^{2} + Y^{2} + Z^{2}) + YZ(\xi^{2} + \eta^{2} + \zeta^{2}) \\ = (X\xi + Y\eta + Z\zeta)(Z\eta + Y\zeta) + (X\zeta - Z\xi)(X\eta - Y\xi) \end{array}$$

and likewise

$$\begin{array}{c} \xi\zeta(X^{2} + Y^{2} + Z^{2}) + XZ(\xi^{2} + \eta^{2} + \zeta^{2}) \\ = (X\xi + Y\eta + Z\zeta)(X\zeta + Z\xi) + (Y\xi - X\eta)(Y\zeta - Z\eta). \end{array}$$

We have, therefore,

$$\begin{aligned} \eta\zeta &= -YZ + (X\zeta - Z\xi )(X\eta - Y\xi), \\ \xi\zeta &= -XZ + (Y\xi   - X\eta)(Y\zeta - Z\eta). \end{aligned}$$

Substituting these values, we obtain

$$ d\phi = \frac{Z}{1 - Z^{2}}(Y\, dX - X\, dY) + \frac{\zeta Y\, d\xi - \zeta X\, d\eta}{1 - Z^{2}} $$

$$ + \frac{X\eta - Y\xi}{1 - Z^{2}}\bigl\{ d\zeta - (X\zeta - Z\xi)\, dX - (Y\zeta - Z\eta)\, dY\bigr\}. $$

Now

$$\begin{alignedat}{4} & X\, dX &&+    Y\, dY &&+     Z\, dZ &&= 0, \\ &\xi\, dX &&+ \eta\, dY &&+ \zeta\, dZ &&= -X\, d\xi - Y\, d\eta - Z\, d\zeta. \end{alignedat}$$

On substituting we obtain, instead of what stands in the parenthesis,

$$d\zeta - Z(X\, d\xi + Y\, d\eta + Z\, d\zeta).$$

Hence

$$ d\phi = \frac{Z}{1 - Z^{2}}(Y\, dX - X\, dY)+ \frac{d\xi}{1 - Z^{2}}\{\zeta Y - \eta X^{2}Z + \xi XYZ\} $$

$$ \begin{aligned} &- \frac{d\eta}{1 - Z^{2}}\{\zeta X + \eta XYZ - \xi Y^{2}Z\}\\ &+ d\zeta(\eta X - \xi Y). \end{aligned} $$


text: Page:Tirukural - tr. Pope - 1886.djvu/44


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72 quarter. Cicero does not appear to have made any dishonourable submission, and the conqueror's behaviour was nobly forgetful of the past. They gradually became on almost friendly terms. The orator paid the Dictator compliments in the Senate, and found that, in private society, his favourite jokes were repeated to the great man, and were highly appreciated. With such little successes he was obliged now to be content. He had again taken up his residence in Rome; but his political occupation was gone, and his active mind had leisure to employ itself in some of his literary works.

It was at this time that the blow fell upon him which prostrated him for the time, as his exile had done, and under which he claims our far more natural sympathy. His dear daughter Tullia—again married, but unhappily, and just divorced—died at his Tusculan villa. Their loving intercourse had undergone no change from her childhood, and his grief was for a while inconsolable. He shut himself up for thirty days. The letters of condolence from well-meaning friends were to him—as they so often are—as the speeches of the three comforters to Job. He turned in vain, as he pathetically says, to philosophy for consolation.

It was at this time that he wrote two of his philosophical treatises, known to us as 'The True Ends of Life,' and the 'Tusculan Disputations,' of which more will be said hereafter. In this latter, which he named from his favourite country-house, he addressed himself to the subjects which suited best with his own

title: Page:Cicero (Collins 1871).djvu/84


text: Page:The Philippine Islands, 1493-1803 (Volume 10).djvu/323


text: Buddenbrooks/Volume 2

title: Buddenbrooks/Volume 2


text:
Page:Punch Vol 148.djvu/82

36

,—When you have witnessed a military inspection, have seen the Great Man going round the companies and have heard his few kind words to the victims of his scrutiny, no doubt you have told yourself that a soldier's life must be very smooth and comfortable and his work as easy as kiss-my-hand. If further you assume, from the clock-like regularity of the parade, that we must all be on very good terms and intimate understanding with each other, I feel bound to disclose the dismal facts.

The information that we were to be inspected by our Great Man on the Friday was handed to me, with the soup, at Thursday's mess. I did not appreciate its horrible significance and, wondering why it should put the older hands off their ration beef, I ate my dinner in the usual manner, cracked a jest or two with the slightly preoccupied Adjutant and C.O., and later on strolled down to my company's billet to inform them that they would be inspected on the morrow. I supposed they would say to each other, "Oh! indeed," and turn in to sleep; but I am credibly informed that they had no bed that night.

On the following morning I was dumbfounded by their dazzling appearance and could not help remarking that here at last was the Perfect Thing. I was just sufficiently soldierlike, however, to examine them with an icy disdain before we set out. En route to the rendezvous, I pictured to myself the Great Man's delight at beholding us, his superlative admiration expressed in a voice choked with affectionate emotion, and his final jocular farewell to myself—"As for your company, my dear Henry, it's marvellous."

I cannot record the actual event in all its details, which were mostly bootlaces and whiskers. The first I knew of the trouble was a face so ominous as to divert attention even from a splendid uniform. Such was the look in the inspecting eye that, had I been my own master, I should have bowed as lowly as to Allah, and said, "Your Highness, I regret that urgent business at the Bank compels the instant departure of myself (with my company)," and we should have been gone at the double before he had gathered the gist of my remark. As it was, I had to stand fast and pretend that we were all very glad to see him and hoped he would make a long stay with us.

At about the third man he stopped dead, very dead, and called my attention to the fact that this private was all whiskers and no boot-laces. What had I to say to that? I might have said, "So he is, Sir, now I come to look at him. He should, of course, have been all boot-laces and no whisker," or merely, " Well, I never!" or, again, with some truth, "As to his laces, Sir, they were there a minute ago but have just fallen out of his boots; and the hair has all grown on his face while you and I were saluting each other just now." Instead I was mute by the visitation of Heaven and we passed on, to pause at No. 8, whose feet and face also were by now all that they should not be.

Again I was called upon for a speech—in vain. You will notice, Charles, that Brigadiers and Colonels are poltroons at these times; they push the company-commander into the forefront of the battle and skulk behind his back.

The Great Man interrupted his examination to chat with his A.D.C., mainly, I fancy, about whiskers and bootlaces. Being also interested in the subject, I took the opportunity to look along my company and see (believe me or not, as you please) the whiskers coming into existence and the laces going out.... I gathered later that things were much the same with every company in the brigade. The Brigadier gathered this also, but at once and from the Great Man.

That night the Brigadier sent for our C.O. The next morning our C.O. sent for us. In due sequence we sent for our section-commanders, and what was left of them, when we had finished, went to interview the private. The last-named, having no one to whom to express his contempt, utter loathing and devilish intentions for the future, adopted the only alternative and took the necessary action.

The news of a second inspection reached me a week in advance, during which I took no food because I was left no time and had no appetite. It was a gloomy period, which was relieved only by two small incidents. The one took place at the C.O.'s inspection, and I will call it "The Private and the Toothbrush." Asked why it was so black, he replied that he cleaned his teeth with permanganate of potash, thus defeating the little crowd inspecting him, since none knew whether that chemical could be used for cleaning teeth and, if it could, whether it would turn the brush black. The other I will call The Memo. of the Transport Officer," who was so upset by what was said to him that he "begged to certify that he had that day purchased 3 new altars for his Transport service." This was officially passed on to me to cheer me up a little, and I am authorised to divulge it to you.

The week elapsed in a hurricane of harsh oaths, and again I paraded my company. Upon examination it now appeared to me to be the most revoltingly untidy and deficient sight I had ever seen, an opinion heartily endorsed by the Adjutant, C.O. and Brigadier. En route to the rendezvous this time I pictured nothing to myself; I merely shifted my service revolver to a position from which I could more easily destroy myself in an emergency..... And when the Great Mun approached he smiled at me, and no sooner had he remarked to his A.D.C. that the buttons and bayonets of the brigade did credit to all concerned than those stolidly dull buttons of mine brightened up and bayonets grew where before there had been empty and depressed scabbards.

I don't know exactly what the Great Man said to the Brigadier, but expect it was much the same as the C.O. said to us and wo to the section-commanders. I doubt if the section-commanders said anything nice to the private, but no doubt the latter knew by instinct that this was an occasion upon which he might with impunity, but only once in a way, step slightly aside from the straight and narrow path. I guess, my dear Charles, that it is only the second inspection to which you, as representing the ignorant public, are invited.

The forty-eight hours' leave (by way of reward or for convalescence) which ensued I spent with my wife. With feminine perversity she at once started inspecting my moustache, one of the most astonishing productions of these astonishing times. "Say what you please now," said I, quite imperturbable. "At the next inspection you'll find yourself remarking that it is the best disciplined and equipped moustache you have ever seen." And so it is.

Yours ever,

"'There is a curious discrepancy in the reports of the Kaiser's New Year message to his forces that have reached London.' Irish Times."

The has been misled. They have not reached London.

title: Page:Punch Vol 148.djvu/82


text:
Swarb v. Lennox

Appellants (hereafter plaintiffs), purporting to act on behalf of a class consisting of all Pennsylvania residents who signed documents containing cognovit provisions leading, or that could lead, to confessed judgments in Philadelphia, brought this action challenging the Pennsylvania system as unconstitutional on its face as violative of due process. The three-judge District Court held that: the Pennsylvania system leading to confessed judgments and execution complies with due process only if "there has been an understanding and voluntary consent of the debtor in signing the document"; plaintiffs did not sustain their burden of proof with respect to lack of valid consent in the execution of bonds and warrants of attorney accompanying mortgages; the record did not establish that the action could be maintained on behalf of natural persons with incomes over $10,000, but an action could be maintained for those who earn less than $10,000 and who signed consumer financing or lease contracts containing cognovit provisions; there was no intentional waiver of known rights by members of that class in executing confession-of-judgment clauses; and no judgment by confession might be entered after November 1, 1970, as to a member of the recognized class unless it is shown that the debtor "intentionally, understandingly, and voluntarily waived" his rights; and the court declared the Pennsylvania practice of confessing judgments to be unconstitutional, prospectively effective as noted, as applied to the designated class, and enjoined entry of any confessed judgment against a member of the class absent a showing of the required waiver. The plaintiffs appealed, claiming that the entire Pennsylvania scheme is unconstitutional on its face.

Held:

 * 1. The Pennsylvania rules and statutes relating to cognovit provisions are not unconstitutional on its face, as under appropriate circumstances, a cognovit debtor may be held effectively and legally to have waived the rights he would possess if the document he signed had contained no cognovit provision. D.H. Overmyer Co. v. Frick Co., ante, p. 174. P. 200.

 * 2. In light of the fact that the named defendants and the intervenors have taken no cross appeal, the affirmance of the judgment below does not mean that the District Court's opinion and judgment are approved as to other aspects and details that were not before this Court. P. 201.

314 F. Supp. 1091, affirmed.

BLACKMUN, J., delivered the opinion of the Court, in which BURGER, C.J., and BRENNAN, STEWART, WHITE, and MARSHALL, JJ., joined. WHITE, J., filed a concurring opinion, post, p. 202. DOUGLAS, J., filed an opinion dissenting in part, post, p. 203. POWELL and REHNQUIST, JJ., took no part in the consideration or decision of the case.

David A. Scholl argued the cause for appellants pro hac vice. With him on the briefs was Harvey N. Schmidt.

Philip C. Patterson argued the cause for appellees. With him on the brief for appellees Middle Atlantic Finance Assn. et al. was ''Marvin Comisky. J. Shane Creamer, Attorney General, and Barry A. Roth'', Assistant Deputy Attorney General, filed a brief for appellee the Commonwealth of Pennsylvania.

William L. Matz argued the cause for the Pennsylvania Savings & Loan League as amicus curiae urging affirmance. With him on the brief was Herbert Bass.

Briefs of amici curiae urging reversal were filed by Don B. Kates, Jr., Martin R. Glick, and Carol Ruth Silver for California Rural Legal Assistance et al.; by John J. Brennan and Gordon W. Gerber for the Pennsylvania Bankers Assn.; by David M. Jones for the Pennsylvania Credit Union League; and by Edward Donald Foster and Blair C. Shick for the National Consumer Law Center.

Briefs of amici curiae urging affirmance were filed by Matthew Hale for the American Bankers Assn., and by Gilbert Nurick and Moses K. Rosenberg for the Pennsylvania Land Title Assn.

title: Swarb v. Lennox


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Page:Cicero (Collins 1871).djvu/85

Rh sorrowful mood under his recent bereavement. How men might learn to shake off the terrors of death—nay, to look upon it rather as a release from pain and evil; how pain, mental and bodily, may best be borne; how we may moderate our passions; and, lastly, whether the practice of virtue be not all-sufficient for our happiness.

A philosopher does not always find in himself a ready pupil. It was hardly so in Cicero's case. His arguments were incontrovertible; but he found them fail him sadly in their practical application to life. He never could shake off from himself that dread of death which he felt in a degree unusually vivid for a Roman. He sought his own happiness afterwards, as he had done before, rather in the exciting struggle of public life than in the special cultivation of any form of virtue; and he did not even find the remedy for his present domestic sorrow in any of those general moral reflections which philosophy, Christian as well as pagan, is so ready to produce upon such occasions; which are all so undeniable, and all so utterly unendurable to the mourner.

Cicero found his consolation, or that diversion of thought which so mercifully serves the purpose of consolation, where most men of active minds like his seek for it and find it—in hard work. The literary effort of writing and completing the works which have been just mentioned probably did more to soothe his mind than all the arguments which they contained. He resumed his practice as an advocate so far as to plead a cause before Cæsar, now ruling as Dictator at Rome—the last cause, as events happened, that he was

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74 ever to plead. It was a cause of no great importance—a defence of Deiotarus, titulary king of Armenia, who was accused of having entertained designs against the life of Cæsar while entertaining him as a guest in his palace. The Dictator reserved his judgment until he should have made his campaign against the Parthians. That more convenient season never came: for before the spring campaign could open, the fatal "Ides of March" cut short Cæsar's triumphs and his life.

title: Page:Cicero (Collins 1871).djvu/86


text:
Page:Buddenbrooks vol 2 - Mann (IA buddenbrooks0002mann).pdf/21

, proprietor of the firm of H. C. F. Purmeister and Company of Hamburg, came into his brother’s living-room, holding in his hand his modish grey hat and his walking-stick with the nun’s bust. Tom and Gerda sat reading together. It was half past nine on the evening of the christening day.

“Good evening,” said Christian, “Oh, Thomas, I must speak with you at once—Please excuse me, Gerda.—It is urgent, Thomas.”

They went into the dark dining-room, where the Consul lighted a gas-jet on the wall, and looked at his brother. He expected nothing good. Except for the first greeting, he had had no opportunity to speak with Christian, but he had looked at him, during the service, and noted that he seemed unusually serious, and even more restless than common: in the course of Pastor Pringsheim’s discourse he had left the room for several minutes. Thomas had not written him since the day in Hamburg when he had paid over into his brother’s hands an advance of 10,000 marks current on his inheritance, to settle his indebtedness. “Just go on as you are going,” he had said, “and you’ll soon run through all your money. As far as I am concerned, I hope you will cross my path very little in future. You have put my friendship to too hard a test in these three years.” Why was he here now? Something must be driving him.

“Well?” asked the Consul.

“I’m done,” Christian said. He let himself down sidewise on one of the high-backed chairs around the dining-table, and held his hat and stick between his thin knees. RV 11 (11)


text:
Last Sonnet (Keats)

 * "Keats's Last Sonnet", in The Poetical Works of John Keats (1884)
 * "The Last Sonnet", in The complete poetical works and letters of John Keats (1899), edited by Horace Elisha Scudder
 * "Bright star, would I were stedfast as thou art" in The Hundred Best Poems (lyrical) in the English language (1904), edited by Adam Luke Gowans
 * "Last Sonnet" in the Oxford Book of English Verse 1250-1900 (1931), edited by Arthur Quiller-Couch
 * "Last Sonnet" in the Oxford Book of English Verse 1250-1918 (1940), edited by Arthur Quiller-Couch

title: Last Sonnet (Keats)


text:
Page:Buddenbrooks vol 2 - Mann (IA buddenbrooks0002mann).pdf/22

RV 12 (BUDDENBROOKS) “May I ask what it is you are done with, and what brings you to me?” said the Consul. He remained standing.

“I’m done,” repeated Christian, shaking his head from side to side with frightful earnestness and letting his little round eyes stray restlessly back and forth. He was now thirty-three years old, but he looked much older. His reddish-blond hair was grown so thin that nearly all the cranium was bare. His cheeks were sunken, the cheek-bones protruded sharply, and between them, naked, fleshless, and gaunt, stood the huge hooked nose.

“If it were only this—!” he went on, and ran his hand down the whole of his left side, very close, but not touching it. “It isn’t a pain, you know—it is a misery, a continuous, indefinite ache. Dr. Drögemuller in Hamburg tells me that my nerves on this side are all too short. Imagine, on my whole left side, my nerves aren’t long enough! Sometimes I think I shall surely have a stroke here, on this side, a permanent paralysis. You have no idea, I never go to sleep properly. My heart doesn’t beat, and I start up suddenly, in a perfectly terrible fright. That happens not once but ten times before I get to sleep. I don’t know if you know what it is. I’ll tell you about it more precisely. It is—”

“Not now, the Consul said coldly. “Am I to understand that you have come here to tell me this? I suppose not.”

“No, Thomas. If it were only that—but it is not that—alone. It is the business. I can’t go on with it.”

“Your affairs are in confusion again?” The Consul did not start, he did not raise his voice. He asked the question quite calmly, and looked sidewise at his brother, with a cold, weary glance.

“No, Thomas. For to tell you the truth—it is all the same now—I never really was in order, even with the ten thousand, as you know yourself. They only saved me from putting up the shutters at once. The thing is—I had more losses at once, in coffee—and with the failure in Antwerp—That’s the truth. So then I didn’t do any more business; I just sat still.

RV 12 (12)


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RV 13 (BUDDENBROOKS) But one has to live—so now there are notes and other debts—five thousand thaler. You don’t know the hole I’m in. And on top of everything else, this agony—”

“Oh, so you just sat still, did you?” cried the Consul, beside himself. His self-control was gone now. “You let the wagon stick in the mud and went off to enjoy yourself! You think I don’t know the kind of life you’ve been living—theatres and circus and clubs—and women—”

“You mean Aline. Yes, Thomas, you have very little understanding for that sort of thing, and it’s my misfortune, perhaps, that I have so much. You are right when you say it has cost me too much; and it will cost me a goodish bit more, for—I’ll tell you something, just here between two brothers—the third child, the little girl, six months old, she is my child.”

“You fool, you!”

“Don’t say that, Thomas. You should be just, even if you are angry, to her and to—why shouldn’t it be my child? And as for Aline, she isn’t in the least worthless, and you ought not to say she is. She is not at all promiscuous; she broke with Consul Holm on my account, and he has much more money than I have. That’s how decent she is. No, Thomas, you simply can’t understand what a splendid creature she is—and healthy—she is as healthy—!” He repeated the word, and held up one hand before his face with the fingers crooked, in the same gesture as when he used to tell about “Maria” and the depravity of London. “You should see her teeth when she laughs. I’ve never found any other teeth to compare with them, not in Valparaiso, or London, or anywhere else in the world. I'll never forget the evening I first met her, in the oyster-room, at Uhlich’s. She was living with Consul Holm then. Well, I told her a story or so, and was a bit friendly; and when I went home with her afterwards—well, Thomas, that’s a different sort of feeling from the one you have when you do a good stroke of business! But you don’t like to hear about such things—I can see that already—and anyhow, it’s over with. I’m saying good-bye to her, though I shall keep

RV 13 (13)


text:
Page:General Investigations of Curved Surfaces, by Carl Friedrich Gauss, translated into English by Adam Miller Hiltebeitel and James Caddall Morehead.djvu/116

 Since, further,

$$\begin{aligned} \eta X^{2}Z - \xi XYZ &= \eta X^{2}Z + \eta Y^{2}Z + \zeta ZYZ \\ &= \eta Z(1 - Z^{2}) + \zeta YZ^{2}, \\ \eta XYZ - \xi Y^{2}Z &= -\xi X^{2}Z - \zeta XZ^{2} - \xi Y^{2}Z \\ &= - \xi Z(1 - Z^{2}) - \zeta XZ^{2}, \end{aligned}$$

our whole expression becomes

$$\begin{aligned} d\phi &= \frac{Z}{1 - Z^{2}}(Y\, dX - X\, dY) \\ &\quad + (\zeta Y - \eta Z)\, d\xi + (\xi  Z - \zeta X)\, d\eta + (\eta X - \xi   Y)\, d\zeta. \end{aligned}$$

15.

The formula just found is true in general, whatever be the nature of the curve. But if this be a shortest line, then it is clear that the last three terms destroy each other, and consequently

$$d\phi = -\frac{Z}{1 - Z^{2}}(X\, dY - Y\, dX).$$

But we see at once that

$$\frac{Z}{1 - Z^{2}}(X\, dY - Y\, dX)$$

is nothing but the area of the part of the auxiliary sphere, which is formed between the element of the line $L,$ the two great circles drawn through its extremities and

$(3),$ and the element thus intercepted on the great circle through $(1)$  and $(2).$  This surface is considered positive, if $L$  and $(3)$  lie on the same side of $(1)\ (2),$  and if the


text:
Page:Buddenbrooks vol 2 - Mann (IA buddenbrooks0002mann).pdf/24

RV 14 (BUDDENBROOKS) in touch with her on account of the child. I’ll pay up everything I owe in Hamburg, and shut up shop. I can’t go on. I’ve talked with Mother, and she is willing to give me the five thousand thaler to start with, so I can put things in order; and I hope you will agree to it, for it is much better to say quite simply that Christian Buddenbrook is winding up his business and going abroad, than for me to make a failure. You think so too, don’t you? I intend to go to London again, Thomas, and take a position. It isn’t good for me to be independent—I can see that more and more. The responsibility—whereas in a situation one just goes home quite care-free, at the end of the day. And I liked living in London. Do you object?”

During this exposition, the Consul had turned his back on his brother, and stood with his hands in his pockets, describing figures on the floor with his foot.

“Very good, go to London,” he said, shortly, and without turning more than half-way toward his brother, he passed into the living-room.

But Christian followed him. He went up to Gerda, who sat there alone, reading, and put out his hand.

“Good night, Gerda. Weill, Gerda, I’m off for London. Yes, it’s remarkable how one gets tossed about hither and yon. Now it’s again into the unknown, into a great city, you know, where one meets an adventure at every third step, and sees so much of life. Strange—do you know the feeling? One gets it here—sort of in the pit of the stomach—it’s very odd.”

RV 14 (14)


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text:
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] (smelling the bowl). George, it is your medicine!

(The children break into lamentation. He gives his wife an imploring look; he is begging for one smile, but does not get it. In consequence he goes from bad to worse.)

. It was only a joke. Much good my wearing myself to the bone trying to be funny in this house.

(on her knees by the kennel). Father, Nana is crying.

. Coddle her; nobody coddles me. Oh dear no. I am only the bread-winner, why should I be coddled? Why, why, why?

. George, not so loud; the servants will hear you.

(These is only one maid, absurdly small too, but they have got into the way of calling her the servants.)

(defiant). Let them hear me; bring in the whole world. (The desperate man who has not been in fresh air for days, has now lost all self-control.) I refuse to allow that dog to lord it in my nursery for one hour longer.

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the oldest of the merchant senators, died in a grotesque and horrible way. The instinct of self-preservation became very weak in this diabetic old man; and in the last years of his life he fell a victim to a passion for cakes and pastries. Dr. Grabow, as the Möllendorpf family physician, had protested energetically, and the distressed relatives employed gentle constraint to keep the head of the family from committing suicide with sweet bake-stuffs. But the old Senator, mental wreck as he was, rented a room somewhere, in some convenient street, like Little Groping Alley, or Angelswick, or Behind-the-Wall—a little hole of a room, whither he would secretly betake himself to consume sweets. And there they found his lifeless body, the mouth still full of half-masticated cake, the crumbs upon his coat and upon the wretched table. A mortal stroke had supervened, and put a stop to slow dissolution.

The horrid details of the death were kept as much as possible from the family, but they flew about the town, and were discussed at length on the Bourse, in the club, and at the Harmony, in all the business offices, in the Assembly of Burgesses—likewise at all the balls, dinners, and evening parties, for the death occurred in February of the year ’62, and the season was in full swing. Even the Frau Consul’s friends talked about it, on the Jerusalem evenings, in the pauses of Lea Gerhardt’s reading aloud; the little Sunday-school children discussed it in awesome whispers as they crossed the Buddenbrook entry; and Herr Stuht, in Bell-Founders’ Street, went into ample detail over it with his wife, who moved in the highest circles. RV 15 (15)


text:
To Spenser

 * "To Spenser", in The Poetical Works of John Keats (1884)
 * "To Spenser", in The complete poetical works and letters of John Keats (1899), edited by Horace Elisha Scudder

title: To Spenser


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24 ( supplicates him.) In vain, in vain, the proper place for you is the yard, and there you go to be tied up this instant.

( again retreats into the kennel, and the children add their prayers to hers.)

(who knows how contrite he will be for this presently). George, George, remember what I told you about that boy.

. Am I master in this house or is she? (To fiercely) Come along. (He thunders at her, but she indicates that she has reasons not worth troubling him with for remaining where she is. He resorts to a false bonhomie.) There, there, did she think he was angry with her, poor Nana? (She wriggles a response in the affirmative.) Good Nana, pretty Nana. (She has seldom been called pretty, and it has the old effect. She plays rub-a-dub with her paws, which is how a dog blushes.) She will come to her kind master, won’t she? won’t she? (She advances, retreats, waggles her head, her tail, and eventually goes to him. He seizes her collar in an iron grip and amid the cries of his progeny drags her from

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RV 16 (BUDDENBROOKS) But interest could not long remain concentrated upon the past. And even with the first rumour of the old man’s death, the great question had at once sprung up: who was to succeed him?

What suspense, what subterranean activity! A stranger, intent on the sights of the mediaeval town, would have noticed nothing; but beneath the surface there was unimaginable bustle and commotion, as one firm and unassailable honest conviction after another was exploded; and slowly, slowly the while, divergent views approached each other! Passions are stirred, Ambition and Vanity wrestle together in silence. Dead and buried hopes spring once more to life—and again are blasted. Old Kurz, the merchant, in Bakers’ Alley, who gets three or four votes at every election, will sit quaking at home on the fatal day, and listen to the shouting, but he will not be elected this time either. He will continue to take his walks abroad, displaying outwardly his usual mingling of civic pride and self-satisfaction: but he will bear down with him into the grave the secret chagrin of never having been elected Senator.

James Möllendorpf’s death was discussed at the Buddenbrook Thursday dinner-table; and Frau Permaneder, after the proper expressions of sympathy, began to let her tongue play upon her upper lip and look across artfully at her brother. The Buddenbrook ladies marked the look. They exchanged piercing glances, and with one accord shut their eyes and their lips tightly together. The Consul had, for a second, responded to the sly smile his sister gave him, and then given the talk another turn. He knew that the thought which Tony hugged to her breast in secret was being spoken in the street.

Names were suggested and rejected, others came up and were sifted out. Henning Kurz in Bakers’ Alley was too old. They needed new blood. Consul Huneus, the lumber dealer, whose millions would have weighted the scale heavily in his favour, was constitutionally ineligible, as his brother already sat in the Senate. Consul Eduard Kistenmaker, the wine

RV 16 (16)


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RV 17 (BUDDENBROOKS) dealer, and Consul Hermann Hagenström were names that kept their places on the list. But from the very first was heard the name of Thomas Buddenbrook; and as election day approached, it grew constantly plainer that he and Hermann Hagenström were the favoured candidates.

Hermann Hagenström had his admirers and hangers-on—there was no doubt of that. His zeal in public affairs, the spectacular rise of the firm of Strunck and Hagenström, the showy house the Consul kept, the luxurious life he led, the pâtés-de-foie-gras he ate for breakfast—all these could not fail to make an impression. This large, rather over-stout man with the short, full, reddish beard and the snub nose coming down flat on his upper lip, this man whose grandfather nobody knew, not even himself, and whose father had made himself socially impossible by a rich but doubtful marriage; this man had become a brother-in-law of the Huneus’ and the Möllendorpfs, had ranged his name alongside those of the five or six reigning families in the town, and was undeniably a remarkable and a respected figure. The novel and therewith the attractive element in his personality—that which singled him out for a leading position in the eyes of many—was its liberal and tolerant strain. His light, large way of making money and spending it again differed fundamentally from the patient, persistent toil and the inherited principles of his fellow merchants. This man stood on his own feet, free from the fetters of tradition and ancestral piety; and all the old ways were foreign to him. His house was not one of the ancient patrician mansions, built with senseless waste of space, in tall white galleries mounting above a stone-paved ground floor. His home on Sand Street, the southern extension of Broad Street, was a modern dwelling, not conforming to any set style of architecture, with a simple painted façade, but furnished inside with every luxury and planned with the cleverest economy of space. Recently, on the occasion of one of his large evening parties, he had invited a prima donna from the government theatre, to sing after dinner to his guests—among them his

RV 17 (17)


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] ''the room. They listen, for her remonstrances are not inaudible.'')

. Be brave, my dears.

. He is chaining Nana up!

(This unfortunately is what he is doing, though we cannot see him. Let us hope that he then retires to his study, looks up the word ‘temper’ in his Thesaurus, and under the influence of those benign pages becomes a better man. In the meantime the children have been put to bed in unwonted silence, and lights the night-lights over the beds.)

(as the barking below goes on). She is awfully unhappy.

. That is not Nana’s unhappy bark. That is her bark when she smells danger.

(remembering that boy). Danger! Are you sure, Wendy?

(the one of the family, for there is one in every family, who can be trusted to know or not to know). Oh yes.

(Her mother looks this way and that from the window.)

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RV 18 (BUDDENBROOKS) witty, art-loving brother—and had paid her an enormous fee for her services. Hermann Hagenström was not the man to vote in the Assembly for the application of large sums of money to preserve and restore the town’s mediaeval monuments. But it was a fact that he was the first, absolutely the first man in town to light his house and his offices with gas. Yes, if Consul Hagenström could be said to represent any tradition whatever, it was the free, progressive, tolerant, unprejudiced habit of thought which he had inherited from his father, old Hinrich—and on this was based all the admiration people undoubtedly felt for him.

Thomas Buddenbrook’s prestige was of a different kind. People honoured in him not only his own personality, but the personalities of his father, grandfather, and great-grand-father as well: quite apart from his own business and public achievement, he was the representative of a hundred years of honourable tradition. And the easy, charming way, indeed, with which he carried the family standard made no small part of his success. What distinguished him, even among his professional fellow citizens, was an unusual degree of formal culture, which, wherever he went, aroused both wonder and respect in about equal degrees.

On Thursdays at the Buddenbrooks’, the coming election received only brief and passing comment in the presence of the Consul. Whenever it was mentioned, the old Frau Consul discreetly averted her light eyes. But Frau Permaneder, now and then, could not refrain from displaying her astonishing knowledge of the Constitution. She had gone very thoroughly into the decrees touching the election of a member of the Senate, precisely as once she thoroughly informed herself on the laws governing divorce. She talked about voting chambers, ballots, and electors, she weighed all the possible eventualities, she could recite verbatim and glibly the oath taken by the voters. She spoke of the “free and frank discussion” which the Constitution ordains must be held over each name upon the list of candidates, and vivaciously wished

RV 18 (18)


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Rh sent down from heaven, and that no alterations had been made in them, but that the Jews were wont to deceive the people by unsound arguments, and by wresting the sense of Scripture.

Sháh Walí Ullah, in his commentary, the Fauz-ul-Kabír, and also Ibn ʾAbbás, support the same view.

This appears to be the correct interpretation of the various verses of the Qurán charging the Jews with having corrupted the meaning of the sacred Scriptures.

For example, Surat-i-A′l-i-Imrám (iii.), 78: "There are certainly some of them who read the Scriptures perversely, that ye may think what they read to be really in the Scriptures, yet it is not in the Scriptures; and they say this is from God, but it is not from God; and they speak that which is false concerning God against their own knowledge."

Imám Fakhar-ud-dín, in his commentary on this verse, and many others of the same character which occur in the Qurán, says it refers to a Tahríf-i-Mʾanawí, and that it does not mean that the Jews altered the text, but


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RV 19 (BUDDENBROOKS) she might be present when Hermann Hagenström’s character was being pulled to pieces! A moment later she leaned over and began to count the prune-pits on her brother’s dessert-plate: tinker, tailor, soldier, sailor—finishing triumphantly with “senator” when she came to the last pit. But after dinner she could not hold in any longer. She took her brother’s arm and drew him into the bow-window.

“Oh, Tom! Tom! Suppose you are really elected—if our coat-of-arms is put up in the Senate-chamber at the Town Hall I shall just die of joy, I know I shall. I shall fall dead at the news—you'll see!”

“Now, Tony dear! Have a little self-control, a little dignity, I beg of you. You are not usually lacking in dignity. Am I going around like Henning Kurz? We amount to something even without the ‘Senator.’ And I hope you won't die, whichever way it turns out!”

And the agitations, the consultations, the struggles of opinion took their course. Consul Peter Döhlman, the rake with a business now entirely ruined, which existed only in name, and the twenty-seven-year-old daughter whose inheritance he was eating up, played his part by attending two dinners, one given by Thomas Buddenbrook and the other by Herman Hagenström, and both times addressing his host, in his loud, resounding voice, as “Senator.” But Siegismund Gosch, old Gosch the broker, went about like a raging lion, and engaged to throttle anybody, out of hand, who wasn’t minded to vote for Consul Buddenbrook.

“Consul Buddenbrook, gentlemen—ah, there’s a man for you! I stood at his father’s side in the ’48, when, with a word, he tamed the unleashed fury of the mob. His father, and his father’s father before him, would have been Senator were there any justice on this earth!”

But at bottom it was not so much Consul Buddenbrook himself whose personality fired Gosch’s soul to its innermost depths. It was rather the young Frau Consul, Gerda Arnoldsen. Not that the broker had ever exchanged a word

RV 19 (19)


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 270 merely that they made alterations in the course of reading.

But whilst all the old commentators, who most probaby had never seen a copy of the sacred Books of the Jews and Christians, only charge us with a Tahríf-i-Mʾanawí, all modern controversialists amongst the Muhammadans contend for a Tahríf-i-Lafzí, as being the only solution of the difficulty.

In dealing with such opponents, the Christian divine will avail himself of the following arguments:—

1. The Qurán does not charge the Jews and Christians with corrupting the text of their sacred books; and all the learned Muslim commentators admit that such is not the case.

2. The Qurán asserts that the Holy Scriptures of the Jews and Christians existed in the days of Muhammad, who invariably speaks of them with reverence and respect.

3. There now exist manuscripts of the Old and New Testaments of an earlier date than that of Muhammad ( 610–632).

4. There are versions of the Old and New Testament now extant, which existed before


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RV 20 (BUDDENBROOKS) with her. He did not belong to her circle of wealthy merchant families, nor sit at their tables, nor pay visits to them. But, as we have seen, Gerda Buddenbrook had but to arrive in the town to be singled out by the roving fancy of the sinister broker, ever on the look-out for the unusual. With unerring instinct he divined that this figure was calculated to add content to his unsatisfied existence, and he made himself the slave of one who had scarcely ever heard his name. Since then he encompassed in his reveries this nervous, exceedingly reserved lady, to whom he had not even been presented: he lifted his Jesuit hat to her, on the street, to her great surprise, and treated her to a pantomime of cringing treachery, gloating over her the while in his thoughts as a tiger might over his trainer. This dull existence would afford him no chance of committing atrocities for this woman’s sake—ah, if it only would, with what devilish indifference would he answer for them! Its stupid conventions prevented him from raising her, by deeds of blood and horror, to an imperial throne!—And thus, nothing was left but for him to go to the Town Hall and cast his vote in favour of her furiously respected husband—and, perhaps, one day, to dedicate to her his forthcoming transitiontranslation?? [sic] of Lope de Vega.

RV 20 (20)


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 Rh Muhammad ; for example, the Septuagint, the Latin Vulgate, the Syriac, the Coptic, and the Armenian versions.

5. The Hexapla, or Octapla of Origen, which dates four centuries before Muhammad, gives various versions of the Old Testament Scriptures in parallel columns.

6. The Syrian Christians of St. Thomas, of Malabar and Travancore, in the south of India, who were separated from the western world for centuries, possess the same Scriptures.

7. In the works of Justin Martyr, who lived from 103 to 167, there are numerous quotations from our sacred books, which prove that they were exactly the same as those we have now. The same may be said of other early Christian writers.

Muhammadan controversialists of the present day urge that the numerous readings which exist in the Christian books are a proof that they have been corrupted. But these do not


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Page:General Investigations of Curved Surfaces, by Carl Friedrich Gauss, translated into English by Adam Miller Hiltebeitel and James Caddall Morehead.djvu/117

 direction from $P$ to $P'$  is the same as that from $(2)$  to $(1);$  negative, if the contrary of one of these conditions hold; positive again, if the contrary of both conditions be true. In other words, the surface is considered positive if we go around the circumference of the figure $LL'P'P$ in the same sense as $(1)\ (2)\ (3);$  negative, if we go in the contrary sense.

If we consider now a finite part of the line from $L$ to $L'$  and denote by $\phi,$  $\phi'$  the values of the angles at the two extremities, then we have

$$\phi' = \phi + \operatorname{Area} LL'P'P,$$

the sign of the area being taken as explained.

Now let us assume further that, from the origin upon the curved surface, infinitely many other shortest lines go out, and denote by $A$ that indefinite angle which the first element, moving counter-clockwise, makes with the first element of the first line; and through the other extremities of the different curved lines let a curved line be drawn, concerning which, first of all, we leave it undecided whether it be a shortest line or not. If we suppose also that those indefinite values, which for the first line were $\phi,$  $\phi',$ be denoted by $\psi,$  $\psi'$  for each of these lines, then $\psi' - \psi$  is capable of being represented in the same manner on the auxiliary sphere by the space $LL'_{1}P'_{1}P.$  Since evidently $\psi = \phi - A,$  the space

$$\begin{aligned} LL'_{1}P'_{1}P'L'L &= \psi' - \psi - \phi' + \phi \\ &= \psi' - \phi' + A \\ &= LL'_{1}L'L + L'L'_{1}P'_{1}P'. \end{aligned}$$

If the bounding line is also a shortest line, and, when prolonged, makes with $LL',$  $LL'_{1}$ the angles $B,$  $B_{1};$  if, further, $\chi,$  $\chi_{1}$  denote the same at the points $L',$  $L'_{1},$  that $\phi$  did at $L$  in the line $LL',$  then we have

$$\begin{aligned} \chi_{1} &= \chi + \operatorname{Area} L'L'_{1}P'_{1}P', \\ \psi' - \phi' + A &= LL'_{1}L'L + \chi_{1} - \chi; \end{aligned}$$

but

$$\begin{aligned} \phi' &= \chi + B, \\ \psi' &= \chi_{1} + B_{1}, \end{aligned}$$

therefore

$$B_{1} - B + A = LL'_{1}L'L.$$

The angles of the triangle $LL'L'_{1}$ evidently are

$$A,\qquad 180^{\circ} - B,\qquad B_{1},$$


text:
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6 First, courts must follow ordinary meaning, not literal meaning. And courts must adhere to the ordinary meaning of phrases, not just the meaning of the words in a phrase.

There is no serious debate about the foundational interpretive principle that courts adhere to ordinary meaning, not literal meaning, when interpreting statutes. As Justice Scalia explained, “the good textualist is not a literalist.” A. Scalia, A Matter of Interpretation 24 (1997). Or as Professor Eskridge stated: The “prime directive in statutory interpretation is to apply the meaning that a reasonable reader would derive from the text of the law,” so that “for hard cases as well as easy ones, the ordinary meaning (or the ‘everyday meaning’ or the ‘commonsense’ reading) of the relevant statutory text is the anchor for statutory interpretation.” W. Eskridge, Interpreting Law 33, 34–35 (2016) (footnote omitted). Or as Professor Manning put it, proper statutory interpretation asks “how a reasonable person, conversant with the relevant social and linguistic conventions, would read the text in context. This approach recognizes that the literal or dictionary definitions of words will often fail to account for settled nuances or background conventions that qualify the literal meaning of language and, in particular, of legal language.” Manning, The Absurdity Doctrine, 116 Harv. L. Rev. 2387, 2392–2393 (2003). Or as Professor Nelson wrote: No “mainstream judge is interested solely in the literal definitions of a statute’s words.” Nelson, What Is Textualism?, 91 Va. L. Rev. 347, 376 (2005). The ordinary meaning that counts is the ordinary public meaning at the time of enactment—although in this case, that temporal principle matters little because the ordinary meaning of “discriminate because of sex” was the same in 1964 as it is now.

Judges adhere to ordinary meaning for two main reasons: rule of law and democratic accountability. A society governed by the rule of law must have laws that are known and understandable to the citizenry. And judicial adherence to


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 therefore their sum is

$$180^{\circ} + LL'_{1}L'L.$$

The form of the proof will require some modification and explanation, if the point $(3)$ falls within the triangle. But, in general, we conclude

 * "The sum of the three angles of a triangle, which is formed of shortest lines upon an arbitrary curved surface, is equal to the sum of $180^{\circ}$ and the area of the triangle upon the auxiliary sphere, the boundary of which is formed by the points $L,$  corresponding to the points in the boundary of the original triangle, and in such a manner that the area of the triangle may be regarded as positive or negative according as it is inclosed by its boundary in the same sense as the original figure or the contrary."

Wherefore we easily conclude also that the sum of all the angles of a polygon of $n$  sides, which are shortest lines upon the curved surface, is [equal to] the sum of $(n - 2)180^{\circ} + $ the area of the polygon upon the sphere etc.

16.

If one curved surface can be completely developed upon another surface, then all lines upon the first surface will evidently retain their magnitudes after the development upon the other surface; likewise the angles which are formed by the intersection of two lines. Evidently, therefore, such lines also as are shortest lines upon one surface remain shortest lines after the development. Whence, if to any arbitrary polygon formed of shortest lines, while it is upon the first surface, there corresponds the figure of the zeniths upon the auxiliary sphere, the area of which is $A,$ and if, on the other hand, there corresponds to the same polygon, after its development upon another surface, a figure of the zeniths upon the auxiliary sphere, the area of which is $A',$  it follows at once that in every case

$$A = A'.$$

Although this proof originally presupposes the boundaries of the figures to be shortest lines, still it is easily seen that it holds generally, whatever the boundary may be. For, in fact, if the theorem is independent of the number of sides, nothing will prevent us from imagining for every polygon, of which some or all of its sides are not shortest lines, another of infinitely many sides all of which are shortest lines.

Further, it is clear that every figure retains also its area after the transformation by development.


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 Rh rationalist; but as Islám is a system of the most positive dogma, it does not admit either of rationalism, or "free thought." Sayyid Ahmad and Ameer ʾAlí no more represent the Muhammadanism of the Qurán and the Traditions, than the opinions of Mr. Voysey represent the teaching of orthodox Christianity.

"Islámism is in itself stationary, and was framed thus to remain; sterile, like its God, lifeless like its first principle in all that constitutes life—for life is love, participation, and progress, and of these the Coranic deity has none. It justly repudiates all change, all development. To borrow the forcible words of Lord Houghton, the written book is there the dead man's hand, stiff and motionless; whatever savours of vitality is by that alone convicted of heresy and defection."


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 We shall here consider 4 figures:

 * 1) an arbitrary figure upon the first surface,
 * 2) the figure on the auxiliary sphere, which corresponds to the zeniths of the previous figure,
 * 3) the figure upon the second surface, which No. 1 forms by the development,
 * 4) the figure upon the auxiliary sphere, which corresponds to the zeniths of No. 3.
 * 1) the figure upon the second surface, which No. 1 forms by the development,
 * 2) the figure upon the auxiliary sphere, which corresponds to the zeniths of No. 3.
 * 1) the figure upon the auxiliary sphere, which corresponds to the zeniths of No. 3.

Therefore, according to what we have proved, 2 and 4 have equal areas, as also 1 and 3. Since we assume these figures infinitely small, the quotient obtained by dividing 2 by 1 is the measure of curvature of the first curved surface at this point, and likewise the quotient obtained by dividing 4 by 3, that of the second surface. From this follows the important theorem:

 * "In the transformation of surfaces by development the measure of curvature at every point remains unchanged."

This is true, therefore, of the product of the greatest and smallest radii of curvature.

In the case of the plane, the measure of curvature is evidently everywhere zero. Whence follows therefore the important theorem:

 * "For all surfaces developable upon a plane the measure of curvature everywhere vanishes,"

or

$$\left(\frac{\partial^{2}z}{\partial x\, \partial y}\right)^{2} - \left(\frac{\partial^{2} z}{\partial x^{2}}\right) \left(\frac{\partial^{2} z}{\partial x^{2}}\right) = 0,$$

which criterion is elsewhere derived from other principles, though, as it seems to us, not with the desired rigor. It is clear that in all such surfaces the zeniths of all points can not fill out any space, and therefore they must all lie in a line.

17.

From a given point on a curved surface we shall let an infinite number of shortest lines go out, which shall be distinguished from one another by the angle which their first elements make with the first element of a definite shortest line. This angle we shall call $\theta.$ Further, let $s$  be the length [measured from the given point] of a part of such a shortest line, and let its extremity have the coordinates $x,$  $y,$  $z.$  Since $\theta$  and $s,$  therefore, belong to a perfectly definite point on the curved surface, we can regard $x,$  $y,$  $z$  as functions of $\theta$  and $s.$  The direction of the element of $s$  corresponds to the point $\lambda$  on the sphere, whose coordinates are $\xi,$  $\eta,$  $\zeta.$  Thus we shall have


text: Notes on Muhammadanism/Chapter 54

title: Notes on Muhammadanism/Chapter 54


text: Notes on Muhammadanism/Chapter 55

title: Notes on Muhammadanism/Chapter 55


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 $$\xi = \frac{\partial x}{\partial s},\qquad \eta = \frac{\partial y}{\partial s},\qquad \zeta = \frac{\partial z}{\partial s}.$$

The extremities of all shortest lines of equal lengths $s$ correspond to a curved line whose length we may call $t.$  We can evidently consider $t$  as a function of $s$  and $\theta,$  and if the direction of the element of $t$  corresponds upon the sphere to the point $\lambda'$  whose coordinates are $\xi',$  $\eta',$  $\zeta',$  we shall have

$$\xi'. \frac{\partial t}{\partial \theta} = \frac{\partial x}{\partial \theta},\qquad \eta'. \frac{\partial t}{\partial \theta} = \frac{\partial y}{\partial \theta},\qquad \zeta'. \frac{\partial t}{\partial \theta} = \frac{\partial z}{\partial \theta}.$$

Consequently

$$(\xi\xi' + \eta\eta' + \zeta\zeta')\, \frac{\partial t}{\partial \theta} = \frac{\partial x}{\partial s}. \frac{\partial x}{\partial \theta} + \frac{\partial y}{\partial s}. \frac{\partial y}{\partial \theta} + \frac{\partial z}{\partial s}. \frac{\partial z}{\partial \theta}.$$ This magnitude we shall denote by $u,$ which itself, therefore, will be a function of $\theta$  and $s.$

We find, then, if we differentiate with respect to $s,$

$$\begin{aligned} \frac{\partial u}{\partial s} &= \frac{\partial^{2} x}{\partial s^{2}}. \frac{\partial x}{\partial \theta} + \frac{\partial^{2} y}{\partial s^{2}}. \frac{\partial y}{\partial \theta} + \frac{\partial^{2} z}{\partial s^{2}}. \frac{\partial z}{\partial \theta} + \tfrac{1}{2}\, \frac{\partial \left\{ (\tfrac{\partial x}{\partial s})^{2} + (\tfrac{\partial y}{\partial s})^{2} + (\tfrac{\partial z}{\partial s})^{2}\right\}}{\partial \theta} \\ &= \frac{\partial^{2} x}{\partial s^{2}}. \frac{\partial x}{\partial \theta} + \frac{\partial^{2} y}{\partial s^{2}}. \frac{\partial y}{\partial \theta} + \frac{\partial^{2} z}{\partial s^{2}}. \frac{\partial z}{\partial \theta}, \end{aligned}$$

because

$$\left(\frac{\partial x}{\partial s}\right)^{2} + \left(\frac{\partial y}{\partial s}\right)^{2} + \left(\frac{\partial z}{\partial s}\right)^{2} = 1,$$

and therefore its differential is equal to zero.

But since all points [belonging] to one constant value of $\theta$ lie on a shortest line, if we denote by $L$  the zenith of the point to which $s,$  $\theta$  correspond and by $X,$  $Y,$  $Z$  the coordinates of $L,$  [from the last formulæ of Art. 13 ],

$$\frac{\partial^{2} x}{\partial s^{2}} = \frac{X}{p},\qquad \frac{\partial^{2} y}{\partial s^{2}} = \frac{Y}{p},\qquad \frac{\partial^{2} z}{\partial s^{2}} = \frac{Z}{p},$$

if $p$  is the radius of curvature. We have, therefore,

$$p. \frac{\partial u}{\partial s} = X\, \frac{\partial x}{\partial \theta} + Y\, \frac{\partial y}{\partial \theta} + Z\, \frac{\partial z}{\partial \theta} = \frac{\partial t}{\partial \theta}(X\xi' + Y\eta' + Z\zeta').$$

But

$$X\xi' + Y\eta' + Z\zeta' = \cos L\lambda' = 0,$$

because, evidently, $\lambda'$  lies on the great circle whose pole is $L.$ Therefore we have

$$\frac{\partial u}{\partial s} = 0,$$


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Rh ordinary meaning facilitates the democratic accountability of America’s elected representatives for the laws they enact. Citizens and legislators must be able to ascertain the law by reading the words of the statute. Both the rule of law and democratic accountability badly suffer when a court adopts a hidden or obscure interpretation of the law, and not its ordinary meaning.

Consider a simple example of how ordinary meaning differs from literal meaning. A statutory ban on “vehicles in the park” would literally encompass a baby stroller. But no good judge would interpret the statute that way because the word “vehicle,” in its ordinary meaning, does not encompass baby strollers.

The ordinary meaning principle is longstanding and well settled. Time and again, this Court has rejected literalism in favor of ordinary meaning. Take a few examples:
 * The Court recognized that beans may be seeds “in the language of botany or natural history,” but concluded that beans are not seeds “in commerce” or “in common parlance.” Robertson v. Salomon, 130 U. S. 412, 414 (1889).
 * The Court explained that tomatoes are literally “the fruit of a vine,” but “in the common language of the people,” tomatoes are vegetables. Nix v. Hedden, 149 U. S. 304, 307 (1893).
 * The Court stated that the statutory term “vehicle” does not cover an aircraft: “No doubt etymologically it is possible to use the word to signify a conveyance working on land, water or air .... But in everyday speech ‘vehicle’ calls up the picture of a thing moving on land.” McBoyle v. United States, 283 U. S. 25, 26 (1931).
 * The Court pointed out that “this Court’s interpretation of the three-judge-court statutes has frequently deviated from the path of literalism.” Gonzalez v. Automatic Employees Credit Union, 419 U. S. 90, 96 (1974).


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"Altogether an admirable little book. It combines two excellent qualities, abundance of facts and lack of theories … On every one of the numerous heads (over fifty) into which the book is divided, Mr. Hughes furnishes a large amount of very valuable information, which it would be exceedingly difficult to collect from even a large library of works on the subject. The book might well be called a 'Dictionary of Muhammadan Theology,' for we know of no English work which combines a methodical arrangement (and consequently facility of reference), with fulness of information in so high a degree as the little volume before us."—The Academy. (Review by Mr. Stanley Lane Poole.)

"It contains multum in parvo, and is about the best outlines of the tenets of the Muslim faith which we have seen. It has, moreover, the rare merit of being accurate; and, although it contains a few passages which we would gladly see expunged, it cannot fail to be useful to all Government employés, who have to deal with Muhammadans; whilst to Missionaries, it will be invaluable."—The Times of India. (Review by Colonel W. Nassau Lees, LL.D.)

"This small book is the most luminous, most convenient, and, we think, the most accurate, outline, of the tenets and practices of Islamism that we have met with. It seems exactly the sort of comprehensive and trustworthy book, in small compass, on this subject, that we and many more have of tenlooked for in vain. … The author has evidently studied his subject in a faithful, laborious, and scholarly manner; and has not only studied, but mastered it. The work is of great value for general students, and for men whose work lies among the Musulman population, such as civil servants, and missionaries, it seems to be the very work that is wanted."—The Friend of India.

"It is manifest throughout the work that we have before us the opinions of one thoroughly conversant with the subject, and who is uttering no random notions. … We strongly recommend 'Notes on Muhammadanism.' Our clergy especially, even though they are


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 not missionaries, and have no intention of labouring amongst Muhammadans, or consorting with them, ought to have at least as much knowledge of the system as can be most readily acquired, with a very little careful study, from this useful treatise."—The Record.

"The main object of the work is to reveal the real and practical character of the Islam faith, and in this the author has evidently been successful."—The Standard.

"Its value as a means of correcting the common impressions about Islam will reveal itself to the most cursory reader, while the author's evident scholarship and intimate knowledge of his subject, bespeak for him a patient hearing on points the most open to controversy."—Indian Mail.

"Mr. Hughes has done good service by providing, in the shape of these 'Notes,' a concise, well arranged, and convenient hand-book of Islam; so small that all missionaries can easily find time to master it, yet so comprehensive that the information it gives will be found sufficient—not, indeed, for the curious investigator of the science, but for the ordinary Indian missionary. … Knowledge for which, otherwise, we should be compelled to search through large volumes in many languages, is here brought together in the compass of a small octavo."—Indian Evangelical Review.

"In brief compass it contains a large amount of reliable information. Instead of theories and fancies, facts are placed before us. Muhammadanism is represented as it really is, not as it is supposed that it might possibly be. Instead of retailing the speculations current in literary society at home, Mr. Hughes furnishes us with brief but incisive statements, which, so far as they go, leave nothing to be desired."—The Church Missionary Intelligencer.


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 272 affect, in the least, the main points at issue between the Christian and the Muslim. The Divine Sonship of Christ, the Fatherhood of God, the Crucifixion, Death, and Resurrection of Christ, and the Atonement, are all clearly stated in almost every book of the New Testament, whilst they are rejected by the Qurán.

The most plausible of modern objections urged by Muslim divines is, that the Christians have lost the Injíl which was sent down from heaven to Jesus; and that the New Testament contains merely the Hadís, or Sunna—the traditions handed down by Matthew, Mark, Luke, John, Paul, and others. It is, of course, a mere assertion, unsupported by any proof; but it appears to be a line of argument which commends itself to Sayyid Ahmad Khan, C.S.I., and also to Ameer ʾAlí Maulaví, M.A., LL.B. The latter professes to be a Muhammadan