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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 65
by Adrien Marie Legendre - 1841 - 235 pages
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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 a right...
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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...
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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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First Part of an Elementary Treatise on Spherical Trigonometry

Benjamin Peirce - Spherical trigonometry - 1836 - 71 pages
...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 the other triangle...
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An Elementary Treatise on Plane and Solid Geometry

Benjamin Peirce - Geometry - 1837 - 159 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 the other triangle...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1837 - 390 pages
...proportional DB is found : which was to be done.* PROP. XIV. THEOR. EQUAL parallelograms which have an angle of the one equal to an angle of the other, have their sides about those angles reciprocally proportional : and (2.) parallelograms which have...
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Euclid's Elements of plane geometry [book 1-6] with explanatory appendix ...

Euclides - 1840
...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. Let the triangles be so placed that the equal angles may be vertically...
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The figures of Euclid with the enunciations, as printed in Euclid's Elements ...

Euclides - 1840
...the equal angles reciprocally proportional, are equal. PROP. XV. THEOR. Equal triangles which have an angle of the one equal to an angle of the other, have the sides about the equal angles reciprocally proportional : and triangles which have an angle...
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Elements of Plane Geometry: For the Use of Schools

Nicholas Tillinghast - Geometry, Plane - 1844 - 108 pages
...(by -the Corollary to the last Proposition) similar. PROP. XVII. THEOREM. Two triangles, which have an angle of the one. equal to an angle of the other,...about the equal angles proportional, are similar. In the triangles ABC, DEF, let the angles, C, F,be equal, and AC : CB : : c Fig. 74. DF : FE, then...
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The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1845 - 352 pages
...proportional DB is found : which was to be done.* PROP. XIV. THEOR. — Equal parallelograms which have an angle of the one equal to an angle of the other, have their sides about those angles reciprocally proportional : and (2) parallelograms which have an...
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