 | Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...equal to the angle GFL (1 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...proportionals, the triangle ABE is equiangular (6. vi.), and therefore similar, to the triangle FGL (4. vi.) ; wherefore the angle ABE is equal to the... | |
 | Euclides - Geometry - 1853 - 176 pages
...(vi. 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,...angles proportionals, the triangle abe is equiangular (vi. 6), and therefore similar, to the triangle fgl (vi. 4) ; wherefore the angle abe is equal to the... | |
 | William Somerville Orr - Science - 1854 - 534 pages
...the diagonals. Because the 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... | |
 | Euclides - 1855 - 270 pages
...and BA is to AE, as GF is to FL (VI. Def. 1). Because the triangles ABE and FGL have an angle in the one, equal to an angle in the other, and their sides about the equal angles proportionals. Therefore the triangle AUK is equiangular and similar to the triangle... | |
 | Euclides - 1855 - 230 pages
...triangles have an angle of the one equal to an angle of the other. If triangles have an angle in the one equal to an angle in the other, and their sides about the equal angles reciprocally proportional. If three straight lines be proportionals. CONSEQUENcES.... | |
 | Euclid - 1859 - 150 pages
...their sides about the equal angle* reciprocally proportional ; and triangles which have an angle in the one equal to an angle in the other, and their sides about the equal angles reciprocally proportional, are equal to one another. PART L Statement — Let the... | |
 | Robert Potts - Geometry, Plane - 1860 - 380 pages
...equal to the angle GFL, (vi. 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...angles proportionals, the triangle ABE is equiangular to the triangle FGL : (vi. 6.) and therefore similar to it ; (vi. 4.) wherefore the angle ABE is equal... | |
 | Euclides - 1860 - 288 pages
...the angle GFL ; and BA is to AE as GF to FL (VI. Dcf. 9) ; wherefore, because the triangles ABE and FGL have an angle in one equal to an angle in the...angles proportionals, the triangle ABE is equiangular (VI. 6), and therefore similar to the triangle FGL (VI. 4) ; wherefore the angle ABE is equal to the... | |
 | Eucleides - 1860 - 396 pages
...the angle GFL (a), and as BA is to AE, BO is GF to FL : therefore the two triangles BAE, GFL having an angle in one, equal to an angle in the other, and the sides about the equal angles proportionals, are equiangular ; and therefore the angle AEB is equal... | |
 | Horatio Nelson Robinson - Geometry - 1860 - 470 pages
...BC And in like manner it may be shown that AE : ED :: AC : CB BOOK II. Cor. 2. Two triangles having an angle in one equal to an angle in the other, and the sides about these equal angles proportional, are equiangular and similar. For, if the smaller triangle... | |
| |
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. 
