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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'... "
First Part of an Elementary Treatise on Spherical Trigonometry - Page 69
by Benjamin Peirce - 1836 - 71 pages
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Manual of Euclid: books iv., v., vi., by J.A. Galbraith and S. Haughton

Euclides - 1859 - 136 pages
...vriirtirvQaaiv at ir\tvpai, ai irepi r; ffa ywvia, 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...
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The Elements of Euclid with Many Additional Propositions and Explanatory Notes

Eucleides - 1860 - 396 pages
...proportional sides are equal. VI. 23, cor. 1. VI. 23, cor. 2. VI. 19. . . VI. 15. VI. 19, cor. HYPOTHESES. If triangles have an angle of the one equal to an angle of the other. If triangles are equiangular . If triangles are similar . . If equal triangles have an angle of the...
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Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ...

George Roberts Perkins - Geometry - 1860 - 470 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....
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Elements of Geometry and Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1862 - 520 pages
...include, by implication, those of all figures. PROPOSITION XXIV. — THEOREM. 264. 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. Let the two triangles ABC, DEF have the angle A...
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Elements of Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1862 - 514 pages
...include, by implication, those of all figures. PROPOSITION XXIV . — THEOREM. 264. 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. Let the two triangles ABC, DEF have the angle A...
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Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - Geometry - 1863 - 504 pages
...include, by implication, those of all f1gures. PROPOSITION XXIV. — THEOREM. 264. 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. Let the two triangles ABC, DEF have the angle A...
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Primary Elements of Plane and Solid Geometry: For Schools and Academies

Evan Wilhelm Evans - Geometry - 1862 - 116 pages
...: hence, it is also similar to DFE. Therefore, two triangles, etc. THEOREM V. Two triangles having an angle of the one equal to an angle of the other, and the sides about those angles proportional, are similar. Let the two triangles ABC, DEF, have the angle A equal...
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The elements of plane geometry; or, The first six books of Euclid, ed. by W ...

Euclides - 1863 - 122 pages
...reciprocalla proportional (tbat is, DB is to BE a GB /stoBF); and, converseln, parallelograms which have an angle of the one equal to an angle of the other, and their sides about the equalangles reciprocallg proportional, are equal to one another. Place the parallelograms...
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The College Euclid: Comprising the First Six and the Parts of the Eleventh ...

Euclides - 1865 - 402 pages
...the three sides of a triangle to the opposite angles meet in the same point. 14. If two trapezinms have an angle of the one equal to an angle of the other, and if, also, the sides of the two figures, about each of their angles, be proportionals, the remaining...
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Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - Geometry - 1868 - 338 pages
...include, by implication, those of all figures. PROPOSITION XXIV. — THEOREM. 264. 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. Let the two triangles ABC, PEF have the angle A...
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