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" Two triangles having 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. "
Wentworth's Plane Geometry - Page 9
by George Albert Wentworth, David Eugene Smith - 1910 - 287 pages
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Elements of Geometry Upon the Inductive Method: To which is Added an ...

James Hayward - Geometry - 1829 - 218 pages
...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...
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Elements of Geometry: With Practical Applications, for the Use of Schools

Timothy Walker - Geometry - 1829 - 156 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...
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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,...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1836 - 394 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...
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First Part of an Elementary Treatise on Spherical Trigonometry

Benjamin Peirce - Spherical trigonometry - 1836 - 92 pages
...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 of the other ; and the sides which include the angle in one triangle are supple- 1887) ments of those which include...
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First Part of an Elementary Treatise on Spherical Trigonometry

Benjamin Peirce - Spherical trigonometry - 1836 - 84 pages
...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 of the other ; and the sides which include the angle in one triangle are supplements of those which include it in...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1837 - 410 pages
...parallel to AC, MN may be proved in a similar manner to be equal to NO.* Cor. 3. If two parallelograms have an angle of the one equal to an angle of the other, and the sides containing the equal angles respectively equal, the parallelograms are equal to one another....
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An Elementary Treatise on Plane and Solid Geometry

Benjamin Peirce - Geometry - 1837 - 216 pages
...equilateral or equiangular with respect to each other, are equivalent. 467. 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 supplements of those which include it in...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1838 - 382 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 oiher, and the sides containing those angles proportional, are similar. In the two triangles ABC, DEF,...
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The figures of Euclid with the enunciations, as printed in Euclid's Elements ...

Euclides - 1840 - 82 pages
...of the other, have the sides about the equal angles reciprocally proportional : and triangles which have an angle of the one equal to an angle of the other, and the sides about the equal angles reciprocally proportional, are equal. PROP. XVI. THEOR. If four...
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