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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... "
The elements of geometry, in eight books; or, First step in applied logic - Pagina 337
door L J V. Gerard - 1874
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The elements of plane geometry, Volume 1

Mathematical association - 1884 - 146 pagina’s
...two adjoining: sides of the one respectively equal to two adjoining sides of the other, and likewise an ang:le of the one equal to an angle of the other ; the parallelograms are identically equal. Let ABCD, EFGH be two parallelograms having the angle ABC...
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The Common Sense of the Exact Sciences

William Kingdon Clifford - 1885 - 310 pagina’s
...proposition about parallel lines.1 The first of these deductions will now show us that if two triangles have an angle of the one equal to an angle of the other and the sides containing these angles respectively equal, they must be equal in all particulars. For...
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Euclid and His Modern Rivals

Lewis Carroll - 1885 - 318 pagina’s
...have two adjacent sides of the one respectively equal to two adjacent sides of the other, and likewise an angle of the one equal to an angle of the other ; the Parallelograms are identically equal.' This might be a useful exercise to set ; but really it...
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Chauvenet's Treatise on Elementary Geometry

William Chauvenet, William Elwood Byerly - 1887 - 331 pagina’s
...B'C' A'B" hence AD BC A'D' X B'C' and we have ABC A' B' C' EXERCISE. Theorem. — 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. Suggestion. Let ADE and...
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A Text-book of Geometry

George Albert Wentworth - 1888 - 272 pagina’s
...proportional, but the homologous angles are not equal. PROPOSITION VII. THEOREM. 326. If two triangles have an angle of the one equal to an angle of the other, and the including sides proportional, they are similar. In the triangles ABC and A'B'C', let ZA=ZA',...
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A Mathematical Solution Book Containing Systematic Solutions to Many of the ...

Benjamin Franklin Finkel - 1888 - 518 pagina’s
...5. Two polygons that are similar to a third polygon ale similar to each other. 6. If two triangles have an angle of the one equal to an angle of the other, their areas are to each other as the rectangles of the sides including those angles. 7. The ratio of...
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Calendar of Dalhousie College and University

Dalhousie University - 1888 - 212 pagina’s
...sides, the solids contained by the alternate segments of these lines are equal. 3. If two triangles have an angle of the one equal to an angle of the other, and have their areas proportional to the squares of the side* opposite these equal angles, they must...
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A Text-book of Geometry

George Albert Wentworth - 1888 - 264 pagina’s
...proportional, but the homologous angles are not equal. PROPOSITION VII. THEOREM. V 326. If two triangles have an angle of the one equal to an angle of the othcr, and the including sides proportional, they are similar. In the triangles ABC and A'B'C ' , let...
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The Elements of Plane and Solid Geometry ...

Edward Albert Bowser - 1890 - 418 pagina’s
...= 12, and AC — 10, find the lengths of the segments BD and CD. Proposition 1 8. Theorem. 314. Two triangles which have an angle of the one equal to an angle of the other, and the sides about these angles proportional, are similar. Hyp. In the A s ABC, A'B'C', let AB AC...
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Euclid Revised: Containing the Essentials of the Elements of Plane Geometry ...

Euclid - 1890 - 442 pagina’s
...their sides about the equal angles reciprocally proportional : (/3) and conversely, if two triangles have an angle of the one equal to an angle of the other, and the sides about the equal angles reciprocally proportional, the triangles have the same area. Let...
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