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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 329

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 329
the straightline EA to AD. But the ratio of EA to AD is given, thereforethe ratio of the triangle ACB to the triangle ADB is given. PROBLEM. To find the ratio of two triangles ABC, ABD given in species,and which are described upon the same straight line AB. Take a straight line FG given in position… … EUCLID S DATA. 327 FGK equal to the angles ABC, ABD, each to each. Thereforethe triangles ABC, ABD are equiangular to the triangles FGH,FGK, each to each. Through the point H draw HL parallel toFG, meeting KF produced in L. And because the angles BAG,BAD are equal to the angles GFH,GFK, each to…

Mathematics, Greek · Geometry · Trigonometry

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