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 201
y described from four straight lines be propor-tionals, the straight lines shall be proportionals.^ * See Note. 198 THE ELEMENTS OF EUCLID. BOOK XI. Let the four straight lines AB, CD, EF, GH be proportion-als, viz. as AB to CD, so EF to GH; and let the similar paral-lelopipeds AK, CL, EM, GN be… … that CD is (11. 5.) to O, as GH to Q, and O to P, as Q to R;therefore, ex sequali (22. 5.), AB is to P, as EF to R: but as ABto P, so (Cor. 33. 11.) is the solid AK to the solid CL; and asEF to R, so (Cor. 33. 11.) is the solid EM to the solid GN; there-fore (11. 5.) as the solid AK to the solid…
Mathematics, Greek · Geometry · Trigonometry
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