 | Elias Loomis - Conic sections - 1849 - 252 pages
...(Def. 3), and AB : BC : : FG : GH. And, because the triangles ABC, FGH have an angle in the one equrJ to an angle in the other, and the sides about these equal angles proportional, they are similar (Prop. XX.); therefore the angle BCA is equal to the angle GHF. Also, because the... | |
 | George Roberts Perkins - Geometry - 1850 - 332 pages
...the parallelogram mentioned in Cor. 1. PROPOSITION XIV. THEOREM. Triangles which have an angle in the one equal to an angle in the other, and the sides about these angles proportional, are equiangular. Let ABC, DFG be two triangles, having the angle A equal to the... | |
 | Euclides - Geometry - 1853 - 176 pages
...def. 1). and ba is to ae, as gf to fl (vi. def. 1) : wherefore, because the triangles abe, f gl have an angle in one equal to an angle in the other, and their sides about these equal angles proportionals, the triangle abe is equiangular (vi. 6), and therefore... | |
 | Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...Def. vi.), and BA is to AE, as GF to FL (1 Def. vi.) : Wherefore, because the triangles ABE, FGL have an angle in one equal to an angle in the other, and their sides about these equal angles proportionals, the triangle ABE is equiangular (6. vi.), and therefore... | |
 | William Somerville Orr - Science - 1854 - 534 pages
...polygons are similar, the angle BAE = GFL, and ВЛ : AE : : GF : FL; .-. the triangles ABE, FGL have an angle in one equal to an angle in the other, and the sides ahout those equal angles proportionals, .'. * 6 & 4 VI. the triangles are equiangular and similar,*... | |
 | Euclides - 1855 - 230 pages
...equal to the angle F, and BA is to AE, as GF is to FL (a); and because the triangles ABE, FGL have an angle in one equal to an angle in the other, and their sides about these equal angles proportionals, the triangles are equiangular (b), and therefore... | |
 | Elias Loomis - Conic sections - 1858 - 256 pages
...(Dei. 3), and AB : BC : : FG : GH. And, because the triangles ABC, FGH have an angle in the one equr.l to an angle in the other, and the sides about these equal angles proportional, they are similar (Prop. XX.) ; therefore the angle BCA is equal to the angle GHF. Also, because the... | |
 | Eucleides - 1860 - 396 pages
...v. 11. (3) V. 12. F, and BA is to AE, as GF is to FL (a) ; and because tho triangles ABE, FGL have an angle in one equal to an angle in the other, and their sides about these equal angles proportionals, the triangles are equiangular (b), and therefore... | |
 | Robert Potts - Geometry, Plane - 1860 - 380 pages
...def. 1.) and BA is to AE, as GFto FL : (vi. def. 1.) therefore, because the triangles ABE, FGL have an angle in one, equal to an angle in the other, and their sides about these equal angles proportionals, the triangle ABE is equiangular to the triangle... | |
 | Robert Potts - 1865 - 528 pages
...def. 1.) and BA is to AE, as GF to FL: (vi. def. 1.) therefore, because the triangles ABE, FGL have an angle in one, equal to an angle in the other, and their sides about these equal angles proportionals, the triangle ABE is equiangular to the triangle... | |
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FGL ; (vi. 6.) and therefore similar to it ; (vi. 4.) wherefore the angle ABE is equal to the angle FGL: and, because the polygons are similar, the whole angle ABC is equal to the whole angle FGH ; (vi. 
