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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. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C'...
An Elementary Treatise on Plane and Solid Geometry - Page 146
by Benjamin Peirce - 1871 - 150 pages

Elements of Geometry: With Practical Applications, for the Use of Schools

Timothy Walker - Geometry - 1829 - 158 pages
...vertices by the space of a quadrant, the sides will become parallel each to each. 3. — When they have an angle of the one equal to an angle of the other, and the sides including these angles proportional. Thus if the angle A = A (fig. 45), and if AB : AD : : AC : AF,...

Elements of Geometry Upon the Inductive Method: To which is Added an ...

James Hayward - Geometry - 1829 - 218 pages
...and suppress , BD . ... ABC ABXAC the common factor =-, we snail have —AE~V~AF' That is — If two triangles have an angle of the one equal to an angle of the other, their areas will be as the products of the sides containing the equal angles. Fig. 94. 17o if we take...

Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - Geometry - 1830 - 584 pages
...side (r). 3. The three sides (/). 4. Two angles, and a side opposite to one of them . »r. 14 5. Au angle of the one equal to an angle of the other, and the sides about two other angles, each to each, and the remaining an;;!« of the same affection, or one of them...

Library of Useful Knowledge: Geometry, plane, solid, and spherical [by ...

Mathematics - 1835
...interjacent side (c). 3. The three sides (/). 4. Two angles, and a side opposite to one of them . cor. 14 5. An angle of the one equal to an angle of the other, and the sides about two other angles, each to each, and the remaining angles of the same affection, or one of them...

First Part of an Elementary Treatise on Spherical Trigonometry

Benjamin Peirce - Spherical trigonometry - 1836 - 84 pages
...(fig. 8.) is the difference between DER and the surn of the other two triangles. 86. Lemma. If two triangles have an angle of the one equal to an angle...supplements of those which include it in the other triangle ; the sum of the surfaces of the two triangles is measured by double the included angle. Demonstration....

First Part of an Elementary Treatise on Spherical Trigonometry

Benjamin Peirce - Spherical trigonometry - 1836 - 92 pages
...in (fig. 8.) is the difference between DER and the sum of the other two triangles. 86. Lemma. If two triangles have an angle of the one equal to an angle...sides which include the angle in one triangle are supple- 1887) ments of those which include it in the other triangle ; the sum of the surfaces of the...

Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1836 - 359 pages
...triangles include, by implication, those of all figures. 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, In the two triangles ABC, DEF, let the angles A and...

The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid - Geometry - 1837 - 410 pages
...which exhibits the subject in a different, and in some respects, a preferable light. Triangles which have an angle of the one equal to an angle of the other, are proportional to the rectangles contained by the sides about those angles : and (2.) equiangular...