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" 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. "
Elements of Geometry: Containing the First Six Books of Euclid, with a ... - Σελίδα 136
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Royal Military Academy, Woolwich - 1853 - 400 σελίδες
...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...

The first six books of the Elements of Euclid, with numerous exercises

Euclides - 1853 - 178 σελίδες
...(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...

Orr's Circle of the Sciences: Organic nature, vols. 1-3 (1854-1856)

William Somerville Orr - 1854 - 534 σελίδες
...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...

The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1855 - 262 σελίδες
...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...

The Elements of Euclid, with many additional propositions, and explanatory ...

Euclides - 1855 - 230 σελίδες
...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....

Manual of Euclid. Books IV. V. VI.

Euclid - 1859 - 136 σελίδες
...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...

Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1860 - 380 σελίδες
...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...

Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ...

Euclides - 1860 - 288 σελίδες
...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...

The Elements of Euclid with Many Additional Propositions and Explanatory Notes

Eucleides - 1860 - 396 σελίδες
...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...

Elements of Geometry, and Plane and Spherical Trigonometry: With Numerous ...

Horatio Nelson Robinson - 1860 - 468 σελίδες
...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...




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