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The elements of Euclid : viz, the first six books, together with the eleventh and twelfth : the errors, by which Theon, or others, have long ago vitiated these books, are corrected, and some of Euclid's demonstrations are restored : also, The book of Euclid's data, in like manner corrected (1834)

Euclid, Euclid, Simson, Robert, 1687-1768 · Philadelphia : Desilver & Thomas · leaf 145

An illustration from The elements of Euclid : viz, the first six books, together with the eleventh and twelfth : the errors, by which Theon, or others, have long ago vitiated these books, are corrected, and some of Euclid's demonstrations are restored : also, The book of Euclid's data, in like manner corrected, 1834, leaf 145
trian-gle LHK; but it has been proved that the triangle EBC is like-wise to the triangle LGH, as the triangle ABE to the triangleFGL. Therefore as the triangle ABE is to the triangle FGL, sois triangle EBC to triangle LGH, and triangle ECD to triangleLHK: and therefore as one of the antecedents to… … BOOK VI. THE ELEMENTS OF EUCLID. 143 has to the triangle FGL, the duplicate ratio of that which the sideAB has to the homologous side FG. Therefore also the polygonABCDE has to the polygon FGHKL the duplicate ratio of thatwhich AB has to the homologous side FG. Wherefore, similarpolygons, Sec. Q.…

Mathematics, Greek · Geometry · Trigonometry

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