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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... "
Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ... - Page 80
by George Roberts Perkins - 1856 - 235 pages
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Manual of Euclid. Books IV. V. VI.

Euclid - 1859 - 136 pages
...rpiywvwv, 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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The Elements of Euclid with Many Additional Propositions and Explanatory Notes

Eucleides - 1860 - 396 pages
...If equal parallelograms have an angle of the one equal to an angle of the other. If parallelograms have an angle of the one equal to an angle of the other, and their sides about the equal angles reciprocally proportional. If parallelograms are about the diameter...
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Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ...

George Roberts Perkins - Geometry - 1860 - 474 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 Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1862 - 532 pages
...properties of triangles include, by implication, those of all figures. PROPOSITION XXIV . — THEOREM. 264. Two triangles, which have an angle of the one equal...containing these angles proportional, are similar. Let the two triangles ABC, DEF have the angle A equal to KD \ E the angle D, and the sides containing...
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Elements of Geometry and Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1862 - 518 pages
...properties of triangles include, by implication, those of all figures. PROPOSITION XXIV. — THEOREM. 264. Two triangles, which have an angle of the one equal...containing. these angles proportional, are similar. Let the two triangles ABC, DEF have the angle A equal to the angle D, and the sides containing these...
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Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - Geometry - 1863 - 504 pages
...properties of triangles include, by implication, those of all f1gures. PROPOSITION XXIV. — THEOREM. 264. Two triangles, which have an angle of the one equal...containing these angles proportional, are similar. Let the two triangles ABC, DEF have the angle A equal to the angle D, and the sides containing these...
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The elements of plane geometry; or, The first six books of Euclid, ed. by W ...

Euclides - 1863 - 122 pages
...angles 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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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 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 - 340 pages
...properties of triangles include, by implication, those of all figures. PROPOSITION XXIV. — THEOREM. 264. Two triangles, which have an angle of the one equal...containing these angles proportional, are similar. Let the two triangles ABC, PEF have the angle A equal to the angle D, and the sides containing these...
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