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 Euclid's Elements Book II, Proposition 12: Law of Cosines.

In obtuse-angled triangles (BAC) the square on the side opposite the obtuse angle (BC) is greater than the sum of the squares on the sides containing the obtuse angle (AB and AC) by twice the rectangle contained by one of the sides about the obtuse angle (AC), namely that on which the perpendicular falls, and the straight line cut off outside by the perpendicular towards the obtuse angle (AH). This conclusion is equivalent to the law of cosines.
 
 

Euclid's Elements: Book II, Proposition 12, Law of Cosines

 

 
The Elements: Books I-XIII (Barnes & Noble Library of Essential Reading)

 

by Euclid, Thomas L. Heath (Translator), Andrew Aberdein (Introduction)
(Paperback - Complete and Unabridged)

Euclid's Elements is a fundamental landmark of mathematical achievement. Firstly, it is a compendium of the principal mathematical work undertaken in classical Greece, for which in many cases no other source survives. Secondly, it is a model of organizational clarity which has had a deep influence on the way almost all subsequent mathematical research has been conducted. Thirdly, it is the most successful textbook ever written, only seriously challenged as an account of elementary geometry in the nineteenth century, more than two thousand years after its first publication.

Euclid reportedly lived some time between the death of Plato (427-347 BC) and the birth of Archimedes (287-212 BC). He most likely learned mathematics at Plato's Academy in Athens and taught at Alexandria in Egypt. Scholars believe Euclid was hired as one of the original faculty at a school of advanced study, patterned after those in Athens, and known as the Museum.


 

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