Legendre, A. M. (Adrien Marie), 1752-1833, Brewster, David, Sir, 1781-1868, Davies, Charles, 1798-1876 · New York, Wiley & Long · leaf 113
es of the diagonals AC~ + BO^ is equivalent to the sum ofthe squares of the sides, that is, to 4AB-, or 4B0^ (Book IV.Prop XIV. Cor.) : and taking away BO- from both, there willremain AC2=3BO^ hence AC^ : BO- : : 3 : 1, or AC : BO: : \^3 : 1 ; hence the side of the inscribed equilateral triangleis… … DiMile the raJius AO inextreme and mean ratio atthe point M (Book IV. Prob.ÎV.) ; take the eliord AB equalto OM the greater segment ;AB will be the side of theregular decagon, and will re-quire to be applied ten timesto the circumference. For, drawing MB, we haveby construction, AO : OM: : OM : AiM…
Trigonometry · Geometry
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