 | Charles Davies - Geometry - 1854 - 436 pages
...of triangles include, by implication, those of all f1gures. BOOK IY. 109 D PROPOSITION XX. THEOREM. Two triangles, which have an angle of the one equal...to an angle of the other, and the sides containing those angles proportional, are similar. Let ABC, DEF, be two triangles, having the angle A equal to... | |
 | William Somerville Orr - Science - 1854 - 534 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... | |
 | Euclides - 1855 - 270 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... | |
 | Euclides - 1855 - 230 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.]... | |
 | Peter Nicholson - Cabinetwork - 1856 - 518 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,... | |
 | George Roberts Perkins - Geometry - 1856 - 460 pages
...other, and the sides containing the equal angles proportional. Two rhombuses are similar, when they have an angle of the one equal to an angle of the other. All squares are similar figures. All regular polygons of the same number of sides are similar figures.... | |
 | Euclid - 1859 - 150 pages
...rpiywvwv, àvriirtirèvQaaiv at ir\tvpai, ai irepi ràç; îffaç ywviaç, laa iariv iKtlva. Equal triangles which have an angle of the one equal to an angle of the other have their sides about the equal angle* reciprocally proportional ; and triangles which have an angle... | |
 | Eucleides - 1860 - 396 pages
...If equal parallelograms have an angle of the one equal to an angle of the other. If parallelograms have an angle of the one equal to an angle of the other, and their sides about the equal angles reciprocally proportional. If parallelograms are about the diameter... | |
 | George Roberts Perkins - Geometry - 1860 - 472 pages
...other, and the sides containing the equal angles proportional. Two rhombuses are similar, when they have an angle of the one equal to an angle of the other. All squares are similar figures. All regular polygons of the same number of sides are similar figures.... | |
 | William Grier - Mechanical engineering - 1861 - 316 pages
...angle C equal to the angle F ; then will the two triangles be identical, or equal in all respects. 2. Let the two triangles ABC, DEF, have the angle A equal to the angle D, the angle B equal to the angle E, and the side AB equal to the side DE ; then these two triangle* will... | |
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Two triangles, which have an angle of the one equal to an angle of the other, and the sides containing these angles proportional, are similar. 
