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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. 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 - Page 63
by Adrien Marie Legendre - 1825 - 224 pages
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Elements of Geometry, Containing the First Six Books of Euclid

Euclid - 1826 - 234 pages
...their «ides, &c. QED PROPOSITION VI. THEOREM. If two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportional, the triangles shall be equiangular, and have those angles equal which subtend the homologous sides....
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Euclid's Elements of geometry, transl. To which are added, algebraic ...

Euclides - 1826 - 226 pages
...their sides, &c. QED PROPOSITION VI. THEOREM. If two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportional, the triangles shall be equiangular, and have those angles equal which subtend the homologous sides,...
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Dialogues on the First Principles of the Newtonian System, Volume 4

Walter Henry Burton - Astronomy - 1828 - 84 pages
...F, are equal; and so, if 'the angles at F had been supposed equal, the triangles would have had each angle of the one equal to an angle of the other, and the side CF lying between correspondent angles in each; whence also DF is equal to FE. Is this sufficiently...
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The Geometrical Companion, in which the Elements of Abstract Geometry are ...

George Darley - Geometry - 1828 - 190 pages
...equal." Here we have a criterion whereby to judge of the equality of two triangular surfaces, which have an angle of the one equal to an angle of the other. For example : ABCD is a road cutting off a triangular field AOB. It is desirable that the line of road...
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Elements of Geometry: With Practical Applications, for the Use of Schools

Timothy Walker - Geometry - 1829 - 138 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 F45 angle A=A (fig. 45), and if AB : AD : : AC...
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Elements of Geometry Upon the Inductive Method: To which is Added an ...

James Hayward - Geometry - 1829 - 218 pages
...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...
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Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry

John Playfair - Geometry - 1829 - 210 pages
...proportional, the triangles will be equiangular. If two triangles have,one angle of one triangle equal to one angle of the other, and the sides about the equal angles proportional, the triangles will be equiangular. Equal parallelograms, and also equal triangles, which have one angle...
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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 a right...
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Library of Useful Knowledge: Geometry plane, solid, and spherical [by Pierce ...

Mathematics - 1835 - 684 pages
...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 a right...
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First Part of an Elementary Treatise on Spherical Trigonometry

Benjamin Peirce - Spherical trigonometry - 1836 - 92 pages
...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 of the other ; and the sides which include the angle in one triangle are supple- 1887) ments of those which include it in the other...
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