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" Assuming that 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... "
SYLLABUS OF PLANE GEOMETRY - Side 17
1876
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1855
...reciprocally proportional, they are equiangular. PROP. XV. ТНЕORЕМ. Equal triangles which have an angle of the one equal to an angle of the other, have their sides about the equal angles reciprocally proportional; and conversely, triangles which...
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The Elements of Euclid, with many additional propositions, and explanatory ...

Euclides - 1855
...angle of the other. If triangles are equiangular . If triangles are similar . . If equal triangles have an angle of the one equal to an angle of the other. If triangles have an angle in the one equal to an angle in the other, and their sides about the equal...
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PLANE AND SOLID GEOMETRY

GEORGE R. PERKINS - 1856
...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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Practical carpentry, joinery, and cabinet-making [by P. Nicholson. by P ...

Peter Nicholson - 1856 - 216 sider
...hypothesis AB : DE :: AC : DF; therefore AH is equal to DF. The two triangles AGH, DEF, have therefore an angle of the one equal to an angle of the other, and the sides containing these angles equal ; therefore they are equal (53) ; but the triangle AGH...
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Manual of Euclid: books iv., v., vi., by J.A. Galbraith and S. Haughton

Euclides - 1859
...àvriirtirèvQaaiv at ir\tvpai, ai irepi ràç; îffaç ywviaç, 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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Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ...

George Roberts Perkins - 1860 - 443 sider
...(T. VI.) : BC : B'C' : : AC : A'C' : : AB : A'B'. GEOMETRY. THEOREM T1ll. 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. In the two triangles ABC, A'B'C',...
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Elements of Geometry and Trigonometry: With Practical Applications

Benjamin Greenleaf - 1862 - 490 sider
...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...
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Elements of Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - 1862 - 490 sider
...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...
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Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - 1863 - 320 sider
...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...
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Primary Elements of Plane and Solid Geometry: For Schools and Academies

Evan Wilhelm Evans - 1862 - 98 sider
...: 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...
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