Books Books
The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw...
Elements of Geometry and Trigonometry Translated from the French of A.M ... - Page 82
by Charles Davies - 1849 - 359 pages

## Elements of Geometry: With, Practical Applications

George Roberts Perkins - Geometry - 1850 - 332 pages
...also be proportional to the sides GH, HK, (B. IV, Def. III.) Therefore, the two triangles ABC, GHK have an angle of the one equal to an angle of the other, and the sides about those angles proportional, and consequently these triangles are similar; and being similar, we...

## Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1852 - 436 pages
...properties of triangles include, by implication, those of all figures. B 109 D DF., PROPOSITION XX. THEOEEM. Two triangles, which have an angle of the one equal...containing those angles proportional, are similar. Let ABC, DEF, be two triangles, having the angle A equal to D ; then, if AB : DE :: AC : DF, the two...

## The Elements of Euclid: With Many Additional Propositions ..., Part 1

Euclid - Geometry - 1853 - 176 pages
...(a) Hypoth. (41 I.29. (c) I. 26. fa) I. 29. (6) Hypoth. (c) I. 34. COROLLARY 2. If two parallelograms have an angle of the one equal to an angle of the other, the remaining angles shall be respectively equal. For the angles opposite the equal angles are equal...

## Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - Geometry - 1854 - 436 pages
...triangles. Thus, the properties of triangles include, by implication, those of all f1gures. BOOK IY. 109 D PROPOSITION XX. THEOREM. Two triangles, which have...containing those angles proportional, are similar. Let ABC, DEF, be two triangles, having the angle A equal to D ; then, if AB : DE : : AC : DF, the two...

## Orr's Circle of the Sciences: The mathematical sciences

William Somerville Orr - Science - 1854 - 532 pages
...equal to au angle of the other, have their sides about the equal angles reciprocally proportional ; and triangles which have an angle of the one equal to an angle of the other, and their sides about those angles reciprocally proportional, are equal to one another. Let the triangles...

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

Euclides - 1855 - 258 pages
...and hare their sides reciprocally proportional, they are equiangular. PROP. XV. ТНЕORЕМ. Equal triangles which have an angle of the one equal to an angle of the other, have their sides about the equal angles reciprocally proportional; and conversely, triangles which...

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

Euclides - 1855 - 226 pages
...BC the segments of the base (c). PROPOSITION XIV. THEOREM [1.]—If equal parallelograms (AB and BC) have an angle of the one equal to an angle of the other, their sides about the equal angles are reciprocally proportional (DB is to BE, as GB is to BF). [3.]...

## Practical carpentry, joinery, and cabinet-making [by P. Nicholson. by P ...

Peter Nicholson - Cabinetwork - 1856 - 482 pages
...but, since AB is equal to the sum of the two lines AD, DB, therefore AB'=AC*+BC9. THEOREM 54,. 125. Two triangles, which have an angle of the one equal to an angle of the other, are to each other as the rectangle of the sides about the equal angles. Suppose the two triangles joined,...