The elements of Euclid for the use of schools and colleges; comprising the first six books and portions of the eleventh and twelfth books; (1903)
Euclid, Todhunter, I. (Isaac), 1820-1884, ed. edt, Simson, Robert, 1687-1768, ed. edt · London; New York, Macmillan · leaf 252
aken in order, about each of theirangles^ he proportionals, the triangles shall he equiangular to oneanother, and shall have those angles equal which are opposite to thehomologous sides. Let the triangles ABC, DEF have their sides proportional,so that AB is to BC as DE to EF; and BC to CA as EFto… … Construction. At E make the z.FEGr equal to the Z.ABC,the points D and G being on opposite sides of EF; and at Fmake the ^EFG- equal to the ^BCA. [I. 23. Proof. The remaining ^EGrF = the remaining Z.BAC ;the /\ABC is equiangular to the AGtEF ; .-. AB :BC ::GE : EF.But AB :BC ::DE:EF; .-. DE :EF…
Euclid's Elements · Geometry · Mathematics, Greek
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