text:
User talk:16ronaldlai

Hello, welcome to Wikipedia. The article you created at The Film Services Office appears to be copied from http://www.fso-tela.gov.hk/about_us.cfm. Unless you are the author of the original information and you are able to release it under the GFDL then the page will need to be deleted. Please see Copyrights for further information. Even if this is a copyright violation, we would still welcome any original contributions from you. See the instructions on how to edit a page for more info. Thanks. Angela. 20:47, Feb 25, 2004 (UTC)

Sorry for that.
Sorry about that, I have read the Wikipedia:Copyrights for detail after your remind. Thank you very much, I will delete that artical and I am sure i will not do this anymore.

 * No problem. It'll be deleted in a few days. If you have any questions, see the help pages, add a question to the village pump or ask me on my talk page. I hope you enjoy editing here and being a Wikipedian! Angela. 04:06, Feb 29, 2004 (UTC)

title: User talk:16ronaldlai


text:
User talk:Hylaride

Hello, welcome to Wikipedia. Here's some tips:
 * You can introduce yourself on the new users page
 * If you made any edits before you got an account, you might be interested in assigning those to your username.
 * You can sign your name using three tildes, like . If you use four, you can add a datestamp too.
 * If you ever think a page or image should be deleted, please list it at the votes for deletion page. There is also a votes for undeletion page if you want to retrieve something that you think should not have been deleted.
 * If you have any questions, see the help pages, add a question to the village pump or ask me on my talk page.

Other useful pages are: how to edit, how to write a great article, naming conventions, manual of style and the Wikipedia policies.

I hope you enjoy editing here and being a Wikipedian! Angela. 20:48, Feb 25, 2004 (UTC)

Speedy deletion nomination of Kingston community credit union
A tag has been placed on Kingston community credit union requesting that it be speedily deleted from Wikipedia. This has been done under section A7 of the criteria for speedy deletion, because the article appears to be about an organization or company, but it does not indicate how or why the subject is important or significant: that is, why an article about that subject should be included in an encyclopedia. Under the criteria for speedy deletion, such articles may be deleted at any time. Please see the guidelines for what is generally accepted as notable, as well as our subject-specific notability guideline for organizations and companies. You may also wish to consider using a Wizard to help you create articles - see the Article Wizard.

If you think that this notice was placed here in error, you may contest the deletion by adding  to the top of the page that has been nominated for deletion (just below the existing speedy deletion or "db" tag), coupled with adding a note on the talk page explaining your position, but be aware that once tagged for speedy deletion, if the page meets the criterion it may be deleted without delay. Please do not remove the speedy deletion tag yourself, but don't hesitate to add information to the page that would render it more in conformance with Wikipedia's policies and guidelines. Lastly, please note that if the page does get deleted, you can contact one of these admins to request that they userfy the page or have a copy emailed to you. RadioFan (talk) 15:20, 15 November 2009 (UTC)

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

title: User talk:Hylaride


text:
Klezmorim

Klezmorim can refer to:

 * Musicians who play klezmer, a style of music originating with the Ashkenazi Jews of Central and Eastern Europe
 * The Klezmorim, a klezmer band

title: Klezmorim


text:
Baron de Saumarez

Baron de Saumarez, on the Island of Guernsey, is a title in the Peerage of the United Kingdom. It was created on 15 September 1831 for the prominent naval commander Admiral Sir James Saumarez, 1st Baronet. He had already been created a Baronet, of Guernsey, on 13 June 1801. Lord de Saumarez was succeeded by his eldest son James, the second Baron, a clergyman. James was succeeded by his younger brother, John, the third Baron, whose son, the fourth Baron, was a career diplomat who bought the family estate at Castel, Guernsey, from his father, the third Baron, who wished to sell it. However, by marrying an heiress, the fourth Baron also brought estates in Suffolk into the family.

The family seat was at Castel in Guernsey from the time of the first baron until the fourth Baron died there in 1937. After the German occupation of the Channel Islands during the Second World War, the later barons lived mostly at their Shrubland Park estate, near Ipswich, in Suffolk. the titles are held by the fourth Baron's great-grandson, the seventh Baron, who succeeded his father the sixth Baron in 1991. Although born and brought up in Suffolk, in April 2006, after the death of his mother, the present Lord de Saumarez sold Shrubland Park and settled in Guernsey.

Not be confused with Saumarez Park at Castel, the Sausmarez Manor estate at Saint Martin in Guernsey belongs to the senior line of the Sausmarez family, from which the Barons de Saumarez are descended. Matthew de Sausmarez (1718–1778), father of the first baron, was a younger brother of John de Sausmarez (1706–1774), of Sausmarez Manor.

Barons de Saumarez (1831)

 * James Saumarez, 1st Baron de Saumarez (1757–1836)
 * James Saumarez, 2nd Baron de Saumarez (1789–1863)
 * John St Vincent Saumarez, 3rd Baron de Saumarez (1806–1891)
 * James St Vincent Saumarez, 4th Baron de Saumarez (1843–1937)
 * James St Vincent Broke Saumarez, 5th Baron de Saumarez (1889–1969)
 * James Victor Broke Saumarez, 6th Baron de Saumarez (1924–1991)
 * Eric Douglas Saumarez, 7th Baron de Saumarez (b. 1956)

title: Baron de Saumarez


text:
ETLA

ETLA can refer to:

 * Research Institute of the Finnish Economy, a major Finnish think tank for economic, policy and social studies
 * Extended three-letter acronym, four-letter acronym, four-letter abbreviation
 * Enterprise Term License Agreement, a type of license agreement for organizations for Adobe Inc. products.

Etla can refer to:
 * Etla District, part of the Valles Centrales region of the state of Oaxaca, Mexico.
 * The town and municipality officially known as Villa de Etla in Oaxaca, Mexico.
 * The town and municipality officially known as San Agustín Etla in Oaxaca, Mexico.

title: ETLA


text:
Middlebury College

Middlebury College is a private liberal arts college in Middlebury, Vermont. Founded in 1800 by Congregationalists, Middlebury was the first operating college or university in Vermont.

In the fall of 2020, the college enrolled 2,773 undergraduates from all 50 states and 74 countries and offers 45 majors in the arts and humanities as well as joint engineering programs. In addition to its undergraduate liberal arts program, the school also has graduate schools, the Middlebury College Language Schools, the Bread Loaf School of English, and the Middlebury Institute of International Studies at Monterey, as well as its C.V. Starr-Middlebury Schools Abroad international programs. Middlebury's 31 varsity teams are the Middlebury Panthers and compete in the NCAA Division III's NESCAC.

19th century
Middlebury received its founding charter on November 1, 1800, as an outgrowth of the Addison County Grammar School, which had been founded three years earlier in 1797. The college's first president—Jeremiah Atwater—began classes a few days later, making Middlebury the first operating college or university in Vermont. One student named Aaron Petty graduated at the first commencement held in August 1802. The college's founding religious affiliation was loosely Congregationalist. Yet the idea for a college was that of town fathers rather than clergymen, and Middlebury was clearly "the Town's College" rather than the Church's. Chief among its founders were Seth Storrs and Gamaliel Painter, the former credited with the idea for a college and the latter as its greatest early benefactor. In addition to receiving a diploma upon graduation, Middlebury graduates also receive a replica of Gamaliel Painter's cane. Painter bequeathed his original cane to the college and it is carried by the college President at official occasions including first-year convocation and graduation. Alexander Twilight, class of 1823, was the first black graduate of any college or university in the United States; he also became the first African American elected to public office, joining the Vermont House of Representatives in 1836. At its second commencement in 1804, Middlebury granted Lemuel Haynes an honorary master's degree, the first advanced degree ever bestowed upon an African American.

In 1883, the trustees voted to accept women as students in the college, making Middlebury one of the first formerly all-male liberal arts colleges in New England to become a coeducational institution. The first female graduate—May Belle Chellis—received her degree in 1886. As valedictorian of the class of 1899, Mary Annette Anderson became the first African-American woman elected to Phi Beta Kappa.

20th century
The college's centennial in 1900 began a century of physical expansion beyond the three buildings of Old Stone Row. York and Sawyer designed the Egbert Starr Library (1900), a Beaux-Arts edifice later expanded and renamed the Axinn Center, and Warner Hall (1901). Growth in enrollment and the endowment led to continued expansion westward. McCullough Hall (1912) and Voter Hall (1913) featured gymnasium and laboratories, respectively, adopting Georgian Revival styling while confirming the campus standard of grey Vermont limestone, granite, and marble.

In 1914 and subsequent decades, Middlebury College offered courses in eugenics in fields such as pedagogy, biology, and sociology. The college had "extensive involvement in the eugenics movement." The year-long, mandatory "Orientating Course for Freshmen" in 1925 included the subject "Eugenics" and explained that in the previous year this had been taught in this class as "What Has Civilization to Expect from Eugenics." The 1930 Fourth Annual Report of the Eugenics Survey of Vermont noted that Middlebury College President Paul Moody was Chairman of the Committee that supervised the Survey. Middlebury biology supervisor, professor A.E. Lambert lectured outside the college on the "Science of Modern Welfare," based on "heredity and eugenics." Middlebury biology professor Owen Wesley Mills was a member of the Second International Congress of Eugenics.

The national fraternity Kappa Delta Rho was founded in Painter Hall on May 17, 1905. Middlebury College abolished fraternities in the early 1990s, but the organization continued on campus in the less ritualized form of a social house. Due to a policy at the school against single-sex organizations, the house was forced to coeducate during the same period as well. The German Language School, founded in 1915 under the supervision of then-President John Martin Thomas, began the tradition of the Middlebury College Language Schools. These Schools, which take place on campus during the summer, enroll about 1,350 students in the Arabic, Chinese, French, German, Hebrew, Italian, Japanese, Portuguese, Russian, and Spanish Language Schools.

Middlebury President Paul Dwight Moody began the American tradition of a National Christmas Tree in 1923 when the college donated a 48-foot balsam fir for use at the White House. The tree was illuminated when Vermont native Calvin Coolidge flipped an electric switch in the first year of his presidency. The Bread Loaf School of English, Middlebury's graduate school of English, was established at the college's Bread Loaf Mountain campus in 1920. The Bread Loaf Writers' Conference was established in 1926. In 1978, the Bread Loaf School of English expanded to include a campus at Lincoln College, Oxford University. In 1991, the School expanded to include a campus at St. John's College in New Mexico, and to the University of North Carolina, Asheville, in 2006. The C.V. Starr-Middlebury Schools Abroad began in 1949 with the school in Paris; they now host students at 38 sites in Argentina, Brazil, China, Cameroon, Chile, France, Germany, India, Italy, Japan, Jordan, Morocco, Russia, Spain, Uruguay, United Kingdom, and Puerto Rico. The Center for Medieval and Renaissance Studies was founded as an educational charity in 1975 by Drs John and Sandy Feneley in Oxford, England, establishing a facility at St. Michael's Hall in 1978, including the Feneley Library, and close links with Keble College, Oxford; in 2014, CMRS became part of Middlebury College Schools Abroad as Middlebury-CMRS, offering U.S. undergraduates an Oxford Humanities Research Program and Middlebury Museum Studies in Oxford. In 1965, Middlebury established its Environmental Studies program, creating the first undergraduate Environmental Studies program in the U.S. Nationally affiliated fraternities were abolished in 1990; some chose to become co-educational social houses which continue today.

21st century
In May 2004, an anonymous benefactor made a $50 million donation to Middlebury. It is the largest cash gift the school has ever received. The donor asked only that Middlebury name its recently built science building, Bicentennial Hall, after outgoing President John McCardell Jr. As of July 2014, Middlebury's endowment stood at approximately $1 billion.

In 2005, Middlebury signed an affiliation agreement with the Monterey Institute of International Studies, a graduate school in Monterey, California. On June 30, 2010, the Monterey Institute was officially designated as a graduate school of Middlebury College.

In the summer of 2008, Middlebury and the Monterey Institute of International Studies launched a collaborative program to offer summer language immersion programs in Arabic, Chinese, French, German, Italian, and Spanish to middle and high school students through the Middlebury-Monterey Language Academy (MMLA). In January 2014, as part of a new brand identity system, Middlebury announced that the Monterey Institute of International Studies would be renamed the Middlebury Institute of International Studies at Monterey. On March 2, 2017, political scientist Charles Murray was shouted down by students at a campus event, and prevented from speaking at the McCullough Student Center. Murray had been named a white nationalist by the Southern Poverty Law Center, and has been criticized for a teenaged incident in 1960 where he burned a cross on a hill in his hometown of Newton, Iowa, an act which Murray himself later characterized as "incredibly dumb". After the protest, Murray's talk was moved to Wilson Hall and published online; however, after the talk there was a violent attack by protesters who attempted to obstruct and damage the vehicle of Bill Burger (the Vice President of communications at Middlebury College), Murray, and Middlebury professor Allison Stanger; Stanger was injured in the attack, requiring her hospitalization with a neck injury and concussion. Middlebury President Laurie L. Patton responded after the event, saying the school would respond to the clear violations of college policy by students that occurred. Some students (and faculty ) felt that by refusing to allow Murray to speak, and by injuring Stanger, the Middlebury College student community "trod all over the ideas of free speech this country was founded upon". The school took disciplinary action against 74 students for their involvement in the incident.

In the spring of 2017, the college also faced allegations of racial profiling, after a student was faced with disciplinary action despite evidence that they had not been present at the protest. Middlebury released a statement asserting that such allegations had been investigated that the college had determined that no such racial profiling had taken place. The statement also noted than an investigation had refuted the anonymous allegations against Burger.

Academics
Founded in 1800, the college enrolls approximately 2,500 undergraduates from all 50 states and 70 countries. The college offers 40 undergraduate departments and programs. Middlebury was the first institution of higher education in the United States to offer an environmental studies major, establishing the major in 1965. Middlebury College is accredited by the New England Commission of Higher Education.

The most popular undergraduate majors at Middlebury by number of 2021 graduates were:
 * Econometrics & Qualitative Economics (81)
 * Computer Science (47)
 * Political Science & Government (47)
 * Environmental Studies (45)
 * Neuroscience (37)

The academic year follows a 4–1–4 schedule of two four-course semesters in the autumn and spring plus what is known as a "Winter Term" session in January. The Winter Term, often called "J-Term" for January Term, allows students to enroll in one intensive course, pursue independent research, or complete an off-campus internship. Winter Term courses are taught by a mix of traditional faculty and special instructors.

Language schools
The Middlebury College Language Schools, which began with the establishment of the School of German in 1915, offer intensive instruction in 10 languages during six-, seven-, or eight-week summer sessions. The schools enroll about 1,350 students every summer. The Schools all use an immersion-based approach to language instruction and acquisition. All students in the Language Schools must sign and abide by Middlebury's "Language Pledge," a pledge to use their target language exclusively during the duration of their time at the school.

Undergraduate instruction, available to undergraduate students, government employees and individuals from professional backgrounds, is offered in Abenaki, Arabic, Chinese, French, German, Hebrew, Italian, Japanese, Portuguese, Russian, Korean, and Spanish.

Associated programs
The Middlebury Institute of International Studies at Monterey, in Monterey, California became an affiliate of Middlebury following the signing of an affiliation agreement between the two in December 2005. The Institute currently enrolls 790 graduate students in the fields of international relations, international business, language teaching, and translation and interpretation.

The Middlebury College Language Schools offers a Doctor of Modern Languages. Unique to Middlebury, the D.M.L. prepares teacher-scholars in two modern foreign languages, helping them develop as teachers of second-language acquisition, literature, linguistics, and language pedagogy. Middlebury also offers summer language immersion programs in Arabic, Chinese, French, German, and Spanish to middle and high school students through the Middlebury-Monterey Language Academy. The Bread Loaf School of English is based at the college's Bread Loaf Mountain campus in Ripton, just outside Middlebury, in sight of the main ridge of the Green Mountains. The poet Robert Frost is credited as a major influence on the school. Frost "first came to the School on the invitation of Dean Wilfred Davison in 1921. Friend and neighbor to Bread Loaf, (he) returned to the School every summer with but three exceptions for 42 years." Every summer since 1920, Bread Loaf has offered students from around the United States and the world intensive courses in literature, creative writing, the teaching of writing, and theater. Many prominent faculty and staff have been associated with the college. The C.V. Starr-Middlebury Schools Abroad, operated by Middlebury College in 17 countries across 5 continents, offer overseas academic programs for undergraduates from various U.S. institutions, as well as graduate-level programs for students from Middlebury College's Language Schools and the Monterey Institute of International Studies.

The Rohatyn Center for Global Affairs, was founded by Felix Rohatyn '49, investment banker, former U.S. Ambassador to France, and founder of Rohatyn Associates. Located at the Robert A. Jones '59 House, the center combines Middlebury's strengths in political, linguistic, and cultural studies to offer internationally focused symposia, lectures, and presentations.

The Center for the Comparative Study of Race and Ethnicity engages in interdisciplinary and comparative approaches for understanding formations of race and ethnicity and their effects on human relations. The Center for Social Entrepreneurship encourages students to develop innovative solutions to address society's most pressing social problems. Programs on Creativity and Innovation (PCI) is a series of initiatives designed to encourage Middlebury students to explore ideas in nonacademic settings.

Bread Loaf Writers' Conference
In addition to the six-week summer program, Middlebury College's Bread Loaf campus is also the site of the Bread Loaf Writers' Conference for established authors, founded in 1926. It was called by The New Yorker "the oldest and most prestigious writers' conference in the country." The conference is administered by director Michael Collier and assistant director Jennifer Grotz. Many prominent members of society have been associated with the Writers' Conference.

Reputation and rankings
In 2023, U.S. News & World Report ranked Middlebury as tied for 11th out of 186 liberal arts college overall in the U.S., tied for 12th out of 36 in "Best Undergraduate Teaching", and 18th out of 93 for "Best Value" among liberal arts colleges for 2023.."

Washington Monthly ranked the school 19th out of 199 in its 2023 liberal arts college rankings.

The 2022 Parchment student choice college ranking, which tracks student college acceptances of students accepted to multiple schools in order to reveal preference for their chosen school compared to other schools, ranks Middlebury as 47th of 1055 colleges.

Admissions
The Carnegie Foundation classifies Middlebury as a "more selective" institution. For the class of 2026, the college offered admission to 1,955 students out of an applicant pool of 13,028, yielding an overall acceptance of 15%.

Middlebury enrolls around 600 students to begin in the fall semester and an additional 100 to begin in the spring. Those accepted for the fall admissions program begin the academic year in September and are referred to as "Regs." Those accepted for the spring admissions program begin the academic year in February and are referred to as "Febs." Students accepted to the Feb program use the fall semester, called a "Febmester," to travel, volunteer, enroll at other universities, or work. Febs graduate in the annual mid-year commencement at the Middlebury College Snow Bowl.

Tuition, room, and board at Middlebury is $79,800 for the 2022–23 academic year. For the class entering in 2022–23, the average financial aid grant award is $57,078. The college is need-blind for incoming domestic students.

Campus
The 350 acre main campus is located in the Champlain Valley between Vermont's Green Mountains to the east and New York's Adirondack Mountains to the west. The campus is situated on a hill to the west of the village of Middlebury, a traditional New England village centered on Otter Creek Falls.

In the fall of 1994 the President and Board of Trustees of Middlebury College adopted a "One Percent for Art" policy. This decision set aside one percent of the cost of any renovation or new construction at the college for the purchase, installation, maintenance, and interpretation of works of art publicly displayed on campus. There are 19 works in Middlebury's campus public art collection, including Frisbee, George Rickey's Two Open Rectangles, Excentric, Variation VI, Tony Smith's Smog, and a version of Robert Indiana's Love series. The collection also includes works by Dan Graham, Scott Burton, Jules Olitski, Joseph Beuys, Matt Mullican, Jenny Holzer, Christian Petersen, Buky Schwartz, George Rickey, Clement Meadmore, and Jonathan Borofsky.

Middlebury College Museum of Art
The museum opened in the Mahaney Arts Center (named after alumni Kevin P. Mahaney, '84) in 1992, designed by Hardy Holzman Pfeiffer's architectural firm. It was accredited by the American Association of Museums in 2005.

Sustainability
Middlebury has incorporated environmental stewardship into its mission statement. The college is a signatory to the American College & University Presidents Climate Commitment and the Talloires Declaration. Additionally, the college has committed to be carbon neutral by 2016. Middlebury was one of six universities to receive a grade of "A−" from the Sustainable Endowments Institute on its College Sustainability Report Card 2008, the highest grade awarded. In 2009, Middlebury opened a state-of-the-art biomass plant on campus that is estimated to cut the college's carbon dioxide output by 40 percent and reduce its use of fuel oil by 50 percent.

In 2010, the Rockefeller Brothers Fund and Middlebury announced the creation of the Sustainable Investments Initiative, a co-mingled fiscal vehicle seeking investments that generate long-term social, environmental, and economic value. The Initiative will seek investments focused on sustainability issues such as clean energy, water, climate science, and green building projects, in an effort to identify businesses positioned to become a part of the worldwide shift to improve energy efficiency, decrease dependence on fossil fuels, and mitigate climate change.

Also in 2010, Middlebury College and Integrated Energy Solutions, a Vermont developer of farm-based methane energy, agreed to explore a bio-methane gas collection and delivery system that could help Middlebury further reduce its use of fossil fuels. Middlebury has agreed to purchase bio-methane gas from IES over a 10-year period, with the agreement contingent on the college raising money to build storage facilities for the gas on campus and retrofit its current heating plant to burn the new fuel.

Student life
In 2013, Princeton Review ranked Middlebury as one of the top 20 schools in the US for "best quality of life." There are over 140 registered student organizations at Middlebury. Students register for organizations of interest during the Fall Activities Fair in September.

The Middlebury Campus is the student weekly of Middlebury College. The Campus was founded in 1900, and is entirely student-run. In 2019, the Middlebury Independent, a monthly journal, was established. The Local Noodle, a satirical student publication founded in 2016, publishes multiple times a semester and maintains a consistent online presence.

WRMC-FM is Middlebury's student-volunteer-run radio station.

Student body
The median family income of Middlebury students is $244,300, with 53% of students coming from the top 5% highest-earning families and 14.2% from the bottom 60%. Middlebury College is the ranked 5th in the country for the most share (23%) of students coming from the top 1% of family income ($630,000 or more per year).

As of the 2019 school year, the student body consisted of 53% women and 47% men.

Traditions
Middlebury's Winter Carnival is the oldest student-run winter carnival in the country, started in 1923. The Winter Carnival is a weekend-long event and traditionally includes a bonfire and fireworks on the opening night, ski races at the Middlebury College Snow Bowl on Friday and Saturday, and the Winter Ball on Saturday night.

Middlebury offers a mid-year graduation for those students who complete coursework at the end of January. These students are usually "Febs," students who began their Middlebury careers as February first-years. The mid-year graduation tradition is for all graduating seniors to ski down the Middlebury College Snow Bowl in their caps and gowns to receive their diplomas.

Middlebury Outdoor Programs organizes outdoor orientations for incoming students in September and February. These orientations involve several days of hiking, rock climbing, kayaking, snowshoeing, and other activities in the wilderness around Middlebury.

Following the New Traditions Contest initiated by President Laurie Patton in the spring of 2018, Middlebury held its first Panther Day on October 20, 2018. The new tradition was held during Homecoming Weekend and included a parade of student clubs and organizations, in an effort to build school spirit. A group of student protesters lined the side of the parade route to call attention to the lack of support by the college for survivors of sexual assault.

New England Review
The New England Review (NER) is a quarterly literary journal published by Middlebury College.

NER publishes poetry, fiction, translations, and a wide variety of non-fiction in each issue. It has published work by many who have gone on to win major awards such as the Pulitzer Prize, the National Book Award, and the National Book Critics Circle Award.

Athletics
Middlebury competes in the New England Small College Athletic Conference. The Panthers lead the NESCAC in total number of National Championships, having won 33 team championships since the conference lifted its ban on NCAA play in 1994.

In the early 20th century, Middlebury's traditional athletic rivals included the University of Vermont and Norwich University. In football, Middlebury is rivals with Hamilton College; the rivalry dates to 1911 and since 1980 the game between the two schools has been called the "Rocking Chair Classic," with the Mack-Jack Rocking Chair going to the winner (Middlebury has historically dominated the rivalry).

The real-life version of Quidditch was brought to life in 2005 at Middlebury College, by Xander Manshel and Alex Benepe, who later became the first commissioner of quidditch. It has grown into a distinct sport after 15 publications of rulebooks.

In 2016, Princeton Review ranked Middlebury's athletic facilities as 18th-best in the United States.

Presidents

 * 1) Jeremiah Atwater, 1800–09
 * 2) Henry Davis, 1809–18
 * 3) Joshua Bates, 1818–40
 * 4) Benjamin Labaree, 1840–66
 * 5) Harvey Denison Kitchel, 1866–75
 * 6) Calvin Butler Hulbert, 1875–80
 * 7) Cyrus Hamlin, 1880–85
 * 8) Ezra Brainerd, 1885–1908
 * 9) John Martin Thomas, 1908–21
 * 10) Paul Dwight Moody, 1921–43
 * 11) Samuel Somerville Stratton, 1943–63
 * 12) James Isbell Armstrong, 1963–75
 * 13) Olin Clyde Robison, 1975–90
 * 14) Timothy Light, 1990–91
 * 15) John McCardell Jr., 1991–2004
 * 16) Ronald D. Liebowitz, 2004–15
 * 17) Laurie L. Patton, 2015–present

title: Middlebury College


text:
Baron Denman

Baron Denman, of Dovedale in the County of Derby, is a title in the Peerage of the United Kingdom. It was created in 1834 for the prominent lawyer, judge and Whig politician Thomas Denman. He served as Lord Chief Justice of the King's Bench from 1832 to 1850. His son, the second Baron, assumed in 1876 by royal licence the additional surname of Aitchison, which was that of his father-in-law. He was succeeded by his grandnephew, the third Baron. He was the grandson of the Hon. Richard Denman, younger son of the first Baron. Lord Denman notably served as Governor-General of Australia from 1911 to 1914. He was succeeded by his eldest son, the fourth Baron. On his death in 1971, the title passed to his first cousin, Sir Charles Denman, 2nd Baronet, of Staffield (see below), who became the fifth holder of the title.

The Denman baronetcy, of Staffield in the County Cumberland, was created in the Baronetage of the United Kingdom in 1945 for the Hon. Richard Denman, younger brother of the third Baron Denman. He had represented Carlisle in the House of Commons as a Liberal from January 1910 until 1918 and Leeds Central as Labour from 1929, and National Labour from 1931 to 1945. He was succeeded by his son, the aforementioned second Baronet, who succeeded as fifth Baron Denman in 1971. He had unsuccessfully contested Leeds Central in the 1945 general election for the Conservatives. He was succeeded by his son, who succeeded as sixth Baron Denman in 2012.

Barons Denman (1834)

 * Thomas Denman, 1st Baron Denman (1779–1854)
 * Thomas Aitchison-Denman, 2nd Baron Denman (1805–1894)
 * Thomas Denman, 3rd Baron Denman (1874–1954)
 * Thomas Denman, 4th Baron Denman (1905–1971)
 * Charles Spencer Denman, 5th Baron Denman, CBE, MC (1916–2012)
 * Richard Thomas Stewart Denman, 6th Baron Denman (b. 1946)

The heir apparent is the present holder's son, the Hon. Robert Denman (b. 1995).

Denman baronets, of Staffield (1945)

 * Sir Richard Douglas Denman, 1st Baronet (1876–1957)
 * Sir Charles Spencer Denman, 2nd Baronet (1916–2012), succeeded as Baron Denman in 1971 (see above for earlier history of this title)

title: Baron Denman


text: User talk:205.213.111.54

title: User talk:205.213.111.54


text:
Twins' Love

Twins' Love is an EP by the Cantopop group Twins. Since the first EP Twins (AVEP) was a great success, the Twins released this second CD just 3 months later, in November 2001. It contained 8 songs and 1 music video, "Oi Ching Dong Yap Jun" (愛情當入樽).

CD Content

 * 1) Computer Data Not Playable
 * 2) Computer Data Not Playable
 * 3) "Oi Ching Dong Yap Jun" (愛情當入樽) - (熱播主打) ( Slam Dunking Love)
 * 4) "Hok Saang Sau Chaak" (學生手冊) (Student Handbook)
 * 5) "Luen Oi Daai Gwoh Tin" (戀愛大過天) - (接力推介) (Love Bigger Than Sky)
 * 6) "Fei Sin" (飛線) (Forwarded Call)
 * 7) "Woh Ping Yat" (和平日) (Peaceful Day)
 * 8) "Yau Soh Bat Ji" (有所不知) - (Disney卡通"Marie"主題曲) (The theme song of the Disney cartoon Marie) (There's Something You Don't Know)
 * 9) "Oi Ching Dong Yap Jun" (愛情當入樽) - (熱播主打) (Air Mix) (Slam Dunking Love)
 * 10) "Woh Ping Yat" (和平日) (We Mix) (The theme song of Fun Fun Show 01) (Peaceful Day)
 * 11) "Nui Haau Naam Sang" (女校男生) - (人氣焦點主打) (Back to School Mix) (Girls` School, Male Student)

title: Twins' Love


text:
Baron de Mauley

Baron de Mauley, of Canford in the County of Dorset, is a title in the Peerage of the United Kingdom. It was created on 10 July 1838 for the Whig politician the Hon. William Ponsonby, who had earlier represented Poole, Knaresborough and Dorset in the House of Commons. He was the third son of the 3rd Earl of Bessborough, an Anglo-Irish peer, and his wife Lady Henrietta Spencer, daughter of the 1st Earl Spencer. He married Lady Barbara Ashley-Cooper, the daughter of Anthony Ashley-Cooper, 5th Earl of Shaftesbury. She was one of the co-heirs to the ancient barony by writ of Mauley (or Maulay), which superseded the feudal barony the caput of which was at Mulgrave Castle, Yorkshire, which barony by writ had become extinct in 1415.

Their son, later the 2nd Baron, sat as Member of Parliament for Poole and Dungarvon. He married his first cousin Lady Maria Ponsonby, daughter of the 4th Earl of Bessborough.

Their eldest son, the 3rd Baron, never married, so the barony was inherited by his brother, who became the 4th Baron. He married the Hon. Madeline Hanbury-Tracy, daughter of the 2nd Baron Sudeley. They had two sons, Capt. Gerald Ponsonby, an officer in the Royal Inniskilling Fusiliers who was killed in the First World War, and Hubert, who became the 5th Baron.

The 5th Baron married Elgiva Margaret Dundas, a great-granddaughter of the 1st Earl of Zetland. They had two sons. The eldest, the 6th Baron, married Helen Alice Douglas, a granddaughter of the 19th Earl of Morton; the marriage was childless. Their second son, Col. Hon. Thomas Ponsonby, an officer of the Wessex Yeomanry who held the offices of Deputy Lieutenant of Gloucestershire and High Sheriff of Gloucestershire, married Maxine Henrietta Thellusson, whose great-great-great-grandfather Charles Thellusson, Member of Parliament for Evesham, was the younger brother of the 1st Baron Rendlesham.

, the title is held by their eldest son, the 7th Baron, who succeeded his uncle in 2002. He is one of the ninety elected hereditary peers that remain in the House of Lords after the passing of the House of Lords Act 1999, and sits as a Conservative. He was elected in 2005 and thereby became the first hereditary peer having succeeded to his title after the House of Lords Act of 1999, to have obtained an elective hereditary peers seat in the House of Lords. In July 2018, the Queen appointed the 7th Baron to succeed the 3rd Baron Vestey as Master of the Horse. The appointment took effect on 1 January 2019.

The Hon. Ashley Ponsonby, younger son of the 1st Baron, was a Liberal politician. Another member of this branch of the Ponsonby family was the Conservative politician Charles Ponsonby, who was created a baronet in 1956. He was the son of the Hon. Edwin Charles William Ponsonby, fifth son of the 2nd Baron.

Former Air Vice Marshal John Ponsonby was the son of officer, diplomat and politician Myles Ponsonby, and a grandson of Victor Coope Ponsonby, the fourth son of the Hon. Edwin Charles William Ponsonby.

Baron de Mauley (1838)

 * William Francis Spencer Ponsonby, 1st Baron de Mauley (1787–1855)
 * Charles Frederick Ashley Cooper Ponsonby, 2nd Baron de Mauley (1815–1896)
 * William Ashley Webb Ponsonby, 3rd Baron de Mauley (1843–1918)
 * Maurice John George Ponsonby, 4th Baron de Mauley (1846–1945)
 * Hubert William Ponsonby, 5th Baron de Mauley (1878–1962)
 * Gerald John Ponsonby, 6th Baron de Mauley (1921–2002)
 * Rupert Charles Ponsonby, 7th Baron de Mauley (born 1957)

The heir presumptive is the present holder's brother, the Hon. (Ashley) George Ponsonby (born 1959). The title next falls to Sir Charles Ponsonby, 3rd Baronet (born 1951), a third cousin of the present holder and his brother. He is the great-grandson of the Hon. Edwin Ponsonby, fifth son of the 2nd Baron.

title: Baron de Mauley


text:
User talk:Ww6q

Hello, welcome to Wikipedia. Here's some tips:
 * You can introduce yourself on the new users page
 * If you made any edits before you got an account, you might be interested in assigning those to your username.
 * You can sign your name using three tildes, like . If you use four, you can add a datestamp too.
 * If you ever think a page or image should be deleted, please list it at the votes for deletion page. There is also a votes for undeletion page if you want to retrieve something that you think should not have been deleted.
 * If you have any questions, see the help pages, add a question to the village pump or ask me on my talk page.

Other useful pages are: how to edit, how to write a great article, naming conventions, manual of style and the Wikipedia policies.

I hope you enjoy editing here and being a Wikipedian! Angela. 20:58, Feb 25, 2004 (UTC)

title: User talk:Ww6q


text:
Talk:Law of cosines

Pythagorean Theorem bit
The bit in the Ptolemy's theorem section references the Pythagorean theorem, citing it as $$a^2+c^2=b^2.\quad$$. I'm no mathematics scholar, but I'm quite sure that isn't the theorem it speaks of. I could be dead wrong, I'm not the most educated fellow, but I think it's worth some speculation. Mason0190 (talk) 13:05, 6 May 2015 (UTC)

 * a²+c²=b² is the Pythagorean theorem. What do you mean? Jam ai qe ju shikoni (talk) 13:41, 24 November 2019 (UTC)

 * Yeesh! don't be obtuse. Standardization (i.e.: Mathematics)— given a right triangle, the square of the length of the hypothenuse c, opposite to the right angle, equals the sum of the squares of the lengths of the two legs a & b, adjacent to, rendering the right angle.
 * $$c^2 = a^2 + b^2 \quad$$  WurmWoode  T   21:40, 3 December 2019 (UTC)

 * I don't see how that puts my argument down, however, I do not think that it is reasonable for me to argue about this. Jam ai qe ju shikoni (talk) 21:45, 22 April 2020 (UTC)

Intended meaning of Euclid's Proposition should be made clear
The text quoted by Euclid concerning the geometric interpretation of the Law of Cosines is helpful but unclear in the sense that Euclid (or possibly Heath) did not name the thing Euclid meant to "namely" identify. In the quote Euclid states 'namely "that" on which the perpendicular falls', but it is unclear if by 'that' he means namely, 'the rectangle' or namely, 'the side about the obtuse angle' which he is describing. It seems to me either Euclid was not expressing himself clearly here or the translation by Heath is at fault but the end of the Euclid quote does not seem to describe a rectangle very well. It might have been clearer if Euclid had stated something closer to the following (CAPS mark my paraphrasing):

"Proposition 12 In obtuse-angled triangles the square on the side subtending the obtuse angle is greater than the EITHER OF THE squares on the sides containing the obtuse angle by twice the rectangle contained by one of the sides about the obtuse angle, namely that RECTANGLE on WHOSE LENGTH the SIDE SUBTENDING the perpendicular falls, and WHOSE WIDTH IS EQUAL TO the straight line SEGMENT cut off outside by the perpendicular towards the obtuse angle."

I am not suggesting that the quote be changed but only that a clarification be given by somebody more in the know on this than myself.

P.S. I only place this talk section above the others to more closely align it with the portion of the main article to which it pertains.

132.45.121.6 (talk) 17:48, 27 August 2012 (UTC)

Proof "Using the distance formula" unclear
In "Using the distance formula" the article states as a fact that "We can place this triangle on the coordinate system by plotting..." and then proceeds to use some trigonometry in the coordinates, without any explanation for how those coordinates are derived / where they came from.

Just a comment about the readability- I can't actually see clearly the labels on Figure 2. 67.255.12.129 (talk) 20:52, 19 April 2011 (UTC)

Pythagorean Theorem also Proved by Law of Cosines?
Okay, in the article, it states the since cos 90 is 0 the Law of Cosines is reduced to the Pythagorean Theorem. I don't think that's the case cause if $$a^2=b^2+c^2-2bccosA$$, then wouldn't $$a^2=b^2+c^2$$? —Preceding unsigned comment added by 70.107.165.59 (talk • contribs)

 * Yes, and that's the Pythagorean theorem (in the case where the right angles is the angle between the sides of lengths b and c). Michael Hardy 23:20, 1 March 2007 (UTC)

 * The last time I checked, the Pythagorean theorem is $$a^2+b^2=c^2$$. I put something about this near the top of the page. Mason0190 (talk) 13:08, 6 May 2015 (UTC)

It seems that your answer would technically be correct, Michael, but it's a bit unclear because the variables tend to be such that A and B are the legs and C is the hypotenuse. It's not a correctness issue, it's clarity. Mason0190 (talk) 13:10, 6 May 2015 (UTC)

Circular proof?
In the dot product article, a dot b = a b cos theta is proved using the Law of Cosines. And the Law of Cosines is proved using vector dot products. Shouldn't somebody fix this? --Orborde 07:48, 9 September 2005 (UTC)

 * The dot product proof should be removed. It's circular.  Law of cosines comes first historically and all of vector calculus is assumed to depend on it, not vice versa.  Might as well use vectors to prove the pythagorean theorem.  Pfalstad 10:22, 9 September 2005 (UTC)

 * I have hopefully solved this problem, by stating the law of cosines is equivalent to the dot product formula from theory of vectors. --345Kai 10:45, 30 March 2006 (UTC)

 * "a dot b = a b cos theta" is the definition of a vector dot product. No proof is not required. Jmheneghan (talk) 17:16, 20 May 2016 (UTC)

Jmheneghan (talk) 17:16, 20 May 2016 (UTC)
 * Wow that's pretty darn smart. --M1ss1ontomars2k4 | T | C | @ 04:04, 21 May 2006 (UTC)

 * If you define the dot product (a,b)*(c,d) as ac+bd (so it is linear) and then prove (a,b)*(c,d)=|(a,b)|*|(c,d)|*cos(α) then there is nothing circular. The definition used is a matter of taste, I guess some others are possible. I like the argument with dot product because it gives a different light on the cosine law and I think it deserves a place on this article. Ricardo sandoval 23:20, 12 April 2007 (UTC)

 * I never saw the story of the dot product but I would guess it came from the scalar product of physics (as in the definition of work done in a particle) is that right? Ricardo sandoval 23:20, 12 April 2007 (UTC)

 * I guess we could also define (a,b)*(c,d) as |(a,b)|*|(c,d)|*cos(α) prove the linearity by geometrical arguments and use it to prove the cosine law. right? Ricardo sandoval 23:20, 12 April 2007 (UTC)

Section moving
I removed the following section because this is said in the first paragraph and follows from elementary algebra:

Another use for Law of Cosines
The Law of Cosines can also be used to find the measure of the three angles in a triangle if you know the length of the three sides. This is how you do it: &nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp
 * $$a^2 + b^2 - 2ab\cos C = c^2$$
 * $$         - 2ab\cos C = -a^2 - b^2 + c^2$$
 * $$              \cos C = (-a^2 - b^2 + c^2) / (-2ab)$$
 * $$              \cos C = (a^2 + b^2 - c^2) / (2ab)$$
 * $$                   C = \arccos [(a^2 + b^2 - c^2) / (2ab)]$$

Now you can find the measure of angle C!

— Sverdrup (talk) 21:00, 25 Feb 2004 (UTC)

If noone objects, I'm going to put the vector-based proof first and move the other one down since the former is more simple and universal as opposed to the latter.. or someone else could do it.. or whatever... - Evil saltine 00:33, 22 May 2005 (UTC)

 * As noted above, the vector-based proof is circular: the proof that the dot product of two vectors has a geometric interpretation in Euclidian space is itself based on the law of cosines. So using the geometric interpretation of a dot product to prove the law of cosines is a bit problematic... --Delirium 03:17, 13 November 2005 (UTC)

 * see above --345Kai 10:45, 30 March 2006 (UTC)

We?
Is the usage of "we" throughout this article proper? Shouldn't "we can easily prove" be "can be proved" (wlong with some sentence rearrangement). BrokenSegue 04:00, 30 March 2006 (UTC)

Rewrite
I have rewritten the article and expanded it considerably. I have taken a lot of material from the French article, according to the above suggestion. I hope you like it!!! Please improve further... (and sorry that in the history of this page the big change was signed "Euklid". That was me and and I know we shouldn't use these kinds of names on Wikipedia, so I've changed my login. --345Kai 10:45, 30 March 2006 (UTC)

Great work!! The French article was way better by any standards, I fell bad I can't understand it. I only see the general flow of ideas. Now it is all clear I will read in finer detail, Thanks!!! Ricardo sandoval 23:42, 12 April 2007 (UTC)

Faster demonstrations
The last demonstrations using the power of a point can be simplified, all of them can be worked out with just one application of the power point theorem, and the the first two cases can be made one by considering b<c(always can be done by flipping the sides). Someone willing to make new pictures? Ricardo sandoval 08:02, 16 April 2007 (UTC)

If you need any diagrams drawn, altered, fixed etc. Please post a request at the Graphics Lab. Please read instructions at the top of the page before posting. Thank you! XcepticZP 18:20, 15 November 2007 (UTC)

Alternative proof using Power of a Point Theorem
This proof along with that using Pythagoras theorem are of considerable historical significance since both have their origins in Euclid's Elements and both are referred to in the ground breaking work of Nicolaus Copernicus: "De Revolutionibus Orbium Coelestium". On Page 20 and Page 21 of Book 1 Copernicus describes two techniques for determining angles given all three sides of a triangle. These techniques correspond respectively to the Pythagorean and Power of Points derivations of the Law of Cosines.

Fig 1 and Fig 2 are replicas of the diagrams from Page 21 of De Revolutionibus Orbium Coelestium.In Fig 1 triangle ABC is drawn with B an acute angle. With C as centre and BC (=a) as radius semi-circle DBF is constructed with DF a diameter and D a point on AC. The circle meets side AB at E and EC is joined forming isosceles triangle ECB with EB = 2acos(B).Power of Points Theorem (intersecting secants theorem) is applied to point A outside the circle:

$$\begin{array}{lcl} \quad\quad AD \times AF = AB \times AE\\ \Rightarrow (b-a)(b+a)=c(c-2a\cos\hat{B})\\ \Rightarrow \quad b^2-a^2=c^2-2ac.\cos\hat{B}\\ \Rightarrow \quad \quad b^2=a^2+c^2-2ac\cos\hat{B} \end{array}$$

It will be no different in the case of Fig 2 where angle B is obtuse:

$$\begin{array}{lcl} \quad\quad AD \times AF = AB \times AE\\ \Rightarrow (b-a)(b+a)=c(c+2a\cos(180-\hat{B}))\\ \Rightarrow \quad b^2-a^2=c^2-2ac.\cos\hat{B}\\ \Rightarrow \quad \quad b^2=a^2+c^2-2ac\cos\hat{B} \end{array}$$

In addition to the two cases dealt with above, we also need to consider the situation shown in the diagram where Power of Point theorem is applied about point B inside the construction circle.

Triangle ABC is drawn with side AB=c,BC=a and CA=b. With A as centre construct circle DCE with radius b and diameter DE passing through B. CB produced meets the circle at F. Since triangle CAF is isosceles:

$$CF=2b\cos\hat{C}\quad$$.

Now apply the Power of a Point Theorem (intersecting chords theorem) to point B inside the circle:

$$\begin{array}{lcl} \quad\quad BD \times BE = BC \times BF\\ \Rightarrow (b-c)(b+c)=a(2b\cos\hat{C}-a)\\ \Rightarrow \quad b^2-c^2=2ab.\cos\hat{C}-a^2\\ \Rightarrow \quad \quad c^2=b^2+a^2-2ab\cos\hat{C} \end{array}$$ —Preceding unsigned comment added by Neil Parker (talk • contribs) 10:28, 17 December 2007 (UTC)

Distance Proof
I really like this proof, but it seems to be there are multiple cases. All of which work out to the same correct result.

I will ignore cases when any of the angles are right angles, as then the distance formula simply leads to the Pathagorian Theorem, which is a special case of the law of cosines.

The proof given works when angle at vertex C is acute and angle at vertex B is acute. Below are the other cases:

1) The angle at vertex C is acute, and the angle at vertex B is obtuse. a - b*cos(theta) becomes b*cos(theta) - a. (where as in the original theta is the angle at vertex C). Since the term is squared the result is the same since x**2 = (-x)**2

2) The angle at vertex C is obtuse. in this case the side:  a - b*cos(theta)  becomes a + b*cos(180-theta) which is equal to a + b*(-cos(theta)) or a - b*cos(theta).  Again leading to the same result.

Does this seem reasonable to anyone? —Preceding unsigned comment added by NeilAFraser (talk • contribs) 01:30, 12 July 2008 (UTC)

Alternate forms

\begin{align} c^2 & = a^2 + b^2 - 2ab\cos \theta \\ & = (a + b)^2 - 4ab\cos^2 \tfrac{\theta}{2}\\ & = (a - b)^2 + 4ab\sin^2 \tfrac{\theta}{2}\\ \end{align} $$

The alternate forms were found after reading about rounding errors in spherical triangles, as mentioned in the great-circle distance article.

The arithmetic and geometric mean lengths of the known sides are:
 * $$\begin{align}

m_a & = (a+b)/2\\ m_g & = \sqrt{a b}\\ \end{align}$$ And

\begin{align} c^2 & = (a + b)^2 - 4ab\cos^2 \tfrac{\theta}{2}\\ & = 4 m^2_a - 4 m^2_g \cos^2 \tfrac{\theta}{2}\\ & = 4(m_a + m_g \cos\tfrac{\theta}{2}) (m_a - m_g \cos\tfrac{\theta}{2}) \\ & = (2m_a + 2m_g \cos\tfrac{\theta}{2}) (2m_a - 2m_g \cos\tfrac{\theta}{2}) \\ \end{align} $$ Or

\begin{align} (\tfrac{c}{2})^2 & = m^2_a  -  m^2_g \cos^2 \tfrac{\theta}{2}\\ & = (m_a + m_g \cos\tfrac{\theta}{2}) (m_a - m_g \cos\tfrac{\theta}{2}) \\ \end{align} $$ - Ac44ck (talk) 23:40, 10 December 2008 (UTC)

Proof using distance formula moved to talk page.
I moved the following here to the talk page. This proof combines trigonometry and the Pythagorean theorem and quite a bit of algebra of real numbers. It is not nearly as elementary as some of the other proofs presented. I don't see what is gained by including it in the article.--345Kai (talk) 05:40, 8 September 2009 (UTC)

 * Consider a triangle with sides of length a, b, c, where $$\theta$$ is the measurement of the angle opposite the side of length c. We can place this triangle on the coordinate system by plotting

 * $$A = (b\cos \theta ,\ b\sin \theta ),\ B = (a,0),\ \text{and}\ C = (0,0).$$

 * By the distance formula, we have

 * $$c = \sqrt{(b\cos \theta - a)^2+(b\sin \theta - 0)^2}.$$

 * Now, we just work with that equation:

\begin{align} c^2 & {} = (b\cos \theta - a)^2+(b\sin \theta)^2 \\ c^2 & {} = b^2 \cos ^2 \theta - 2ab\cos \theta + a^2 + b^2\sin ^2 \theta \\ c^2 & {} = a^2 + b^2 (\sin ^2 \theta + \cos ^2 \theta ) - 2ab\cos \theta \\ c^2 & {} = a^2 + b^2 - 2ab\cos \theta. \end{align} $$

 * An advantage of this proof is that it does not require the consideration of different cases for when the triangle is acute vs. obtuse.

 * Why banish this one? It sets up one equation and grinds it out. The trig proof that is left requires looking at the triangle in three different ways to come up with three different equations to mash together. It, too, seems to involve "quite a bit of algebra of real numbers."

 * I don't see what is gained by moving it. - Ac44ck (talk) 01:18, 9 September 2009 (UTC)

Law of Cosines is plural, NOT singular
11-03-09: Apparently NorweigianBlue and HambergerRadio don't know their Trigonometry. There are three Cosine formulas, NOT one formula.

 * $$a^2 = b^2 + c^2 - 2bc\cos(\alpha)\,$$
 * $$b^2 = a^2 + c^2 - 2ac\cos(\beta)\,$$
 * $$c^2 = a^2 + b^2 - 2ab\cos(\gamma)\,$$

If you Google "Law of Cosines", you will find the above three formulas, which corresponts to the article's triangle figure.

 * All three are the same formula. Therefore there is just one Cosine Law. Martin 4 5 1  (talk) 23:27, 3 November 2009 (UTC)

All triangles have three Sines, three Cosines, and three Tangents. The same goes for their inverses too. The article's triangular drawing displays three angles, therefore three Cosine identies exists, as I have shown above ... Mike —Preceding unsigned comment added by 169.230.110.161 (talk) 00:54, 4 November 2009 (UTC)
 * In the French Wikipedia, the Law (singular) of cosines, is a featured article. The law is stated there only once, not three times as is it is here after 169.230.110.161 changed the article. I suggest that someone reverts the change, unless there is consensus to do otherwise. I have already reverted a couple of times, but don't want to engage in an edit war, so I'm taking the article off my watchlist. --NorwegianBluetalk 10:49, 4 November 2009 (UTC)

All three say the same thing. Michael Hardy (talk) 17:22, 4 November 2009 (UTC)

The identity
 * $$a^2 = b^2 + c^2 - 2bc\cos(\alpha)\,$$
 * $$a^2 = b^2 + c^2 - 2bc\cos(\alpha)\,$$

applies if a is any of the three sides, and α the angle opposite it, and b and c the other two sides. Thus it can be applied first with one side labeled a, then with a second side labeled a, then with the third side labeled a, so stating the formula just once covers all three sides of the triangle (and also all other triangles). Michael Hardy (talk) 17:34, 4 November 2009 (UTC)

Adjusted line "CH = a cos(π – γ) = −a cos(γ)" in history
I changed the line "CH = a cos(π – γ) = −a cos(γ)" in the history subsection to "CH = (CB) cos(π – γ) = −(CB) cos(γ)". In the equations used in this section and the diagram there is no "a" side. Danshil (talk) 21:39, 19 December 2009 (UTC)

Make consistent with "Law of sines"
The diagram and symbols used for angles on the "Law of cosines" page are not the same as those on the "Law of sines" page. Would it be reasonable to change this page to match those on the "Law of sines" page? — Preceding unsigned comment added by 209.98.145.235 (talk) 14:36, 30 January 2013 (UTC)

relation between the law of sin and cosine

 * $$\arccos\frac{1}{2.5}$$
 * $$\arccos\frac{1}{2.5}$$
 * $$\arccos\frac{4.25}{6.25}$$

consecutive numbers.
 * $$1.5, 2.5, 3.5$$
 * $$4.25, 5.25, 6.25$$
 * $$\frac{1}{2.5}$$
 * $$1.5\times3.5=5.25$$

1-0.68=0.32 change between the law of sin and the law of cosine

 * $$\frac{\sin A}\frac{1}{2.5}=\sqrt5.25$$
 * $$\frac{\sin B}\frac{1}{2.5}\sqrt5.25$$
 * $$\frac{\sin C}\frac{1}{6.25/2}=\sqrt5.25$$

consecutive numbers.
 * $$1.5, 2.5, 3.5$$
 * $$4.25, 5.25, 6.25$$
 * $$\frac{1}{2.5}$$
 * $$1.5\times3.5=5.25$$ — Preceding unsigned comment added by 199.119.233.245 (talk) 19:12, 7 November 2015 (UTC)

199.119.233.215 (talk) 04:21, 16 January 2016 (UTC)

Correction for solving angle-side-side triangles
In the section where you use the quadratic equation to make a form of the law of cosines that solves angle-side-side triangles, there is an error on the bounds checking. You say that if c>=b, there are no solutions. However:

- If c=b, there is one solution. It is an isosceles triangle with b=c, B=C. The triangle itself is twice the size as the right triangle formed by c=b*sin(C) & B = 90. B and C are acute.

- If c>b, there is also one solution. It is a scalene triangle with B and C being acute. — Preceding unsigned comment added by 69.159.12.95 (talk) 01:35, 26 January 2020 (UTC)

 * For future reference, WP:SOFIXIT applies. –Deacon Vorbis (carbon • videos) 01:51, 26 January 2020 (UTC)

Another small addition on the angle-side-side solution
Right now it says, "only one positive solution if c = b sin γ". It should say "only one positive solution if c = b sin γ OR if c>=b" — Preceding unsigned comment added by 69.159.12.95 (talk) 06:06, 26 January 2020 (UTC)

 * WP:SOFIXIT. Also, please place new comments at the end and sign your posts. See Help:Talk for more info. –Deacon Vorbis (carbon • videos) 12:44, 26 January 2020 (UTC)

Demonstration by Chasles relation and scalar product
Will it make sense to add a demonstration with Chasles relation and scalar product? Even if historically it was after, it is a simple and powerful tool to demonstrate it. — Preceding unsigned comment added by 103.139.171.78 (talk) 17:49, 15 July 2020 (UTC)

Proof by application of dot product
Could there be a valid proof using the definition of a dot product. With triangle having side C as the vector A-B, where A,B are the vectors of the triangle legs: then length |C|^2 could be written as |A|^2+|B|^2-2A(dot)B. A(dot)B is defined as |A||B|cos(theta) giving the law of cosines formula. If other editors think this is valid, I could add a formatted proof.  Nik ol ai h ☎📖 21:40, 6 August 2020 (UTC)

 * Absolutely. It should be added --83.56.100.228 (talk) 18:37, 10 October 2020 (UTC)
 * Of course then you have to show why A dot B = |A| |B| cos (theta) is a reasonable definition, since usually dot products are defined by coordinates. Dot product Wqwt (talk) 17:44, 15 June 2024 (UTC)

Requires proof reading?
Perhaps i'm mistaken but angle ABC in Fig 2 appears acute rather than obtuse to me. Proof reading anyone? — Preceding unsigned comment added by 198.24.255.98 (talk) 16:24, 22 September 2020 (UTC)

 * No, it's definitely obtuse (unless there's some issue with it being displayed in a weird aspect ratio). –Deacon Vorbis (carbon • videos) 16:55, 22 September 2020 (UTC)
 * The angle ABC in Fig 2 clearly looks acute on my monitor. Just to be clear an acute angle is smaller than 90 degrees and an obtuse angle is greater than 90 degrees but less than 180 degrees. It makes the whole section unreadable, and brings into question the correctness of articles on the site. — Preceding unsigned comment added by 2605:A601:A706:8700:F91E:CE18:C1EC:7244 (talk) 23:19, 27 September 2020 (UTC)
 * Oh, I think I see the confusion.  ABC is acute, but  ABC is obtuse, because angle ACB is an obtuse angle. –Deacon Vorbis (carbon • videos) 23:28, 27 September 2020 (UTC)
 * Right, ABC is an angle not a triangle. 'Triangle ABC' is confusing if not complete nonsense. — Preceding unsigned comment added by 198.24.255.98 (talk) 23:35, 2 October 2020 (UTC)
 * It's perfectly clear what $$\Delta ABC $$ means: the triangle defined by the vertices A, B, C. Wqwt (talk) 17:45, 15 June 2024 (UTC)

title: Talk:Law of cosines