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Elements of geometry : containing the first six books of Euclid, with a supplement on the quadrature of the circle, and the geometry of solids : to which are added, Elements of plane and spherical geometry (1826)

Playfair, John, 1748-1819, Euclid · Philadelphia : Marot & Walter · leaf 54

An illustration from Elements of geometry : containing the first six books of Euclid, with a supplement on the quadrature of the circle, and the geometry of solids : to which are added, Elements of plane and spherical geometry, 1826, leaf 54
raightline which is made up of the half and the part produced. Let the straight line AB be bisected in C,and produced to the pointD; tbe rectangle AD.DB, together with the square of CB, is equal t©the square of CD. Upon CD describe (46. i.) the square CEFD,ioinDE,and throughB draw (31.4 ) FHG… … to CH; M CH is equal (43.1.)to HF; therefore also AL is equal \to HF: To each of these addCM; therefore the whole AM isequal to the gnomon ClViC NowA.M=AD.l)M=AO;DB.beeauseDM=DB. Therefore gnomonCMG=AD.DB, and CMG+LG^AD.DB+CB2. But CMG-fLG=CF=CD% therefore AD.DB + CB^ = CD. Therefore,if a straight…

Euclid's Elements · Geometry · Trigonometry

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