 | George Albert Wentworth - Geometry - 1877 - 426 pages
...then Iff + Ж? + m? + DA2 = 4 2 + * 2 + 4 4 QED GEOMETRY. BOOK IV. PROPOSITION XIII. THEOREM. 341. Two triangles having an angle of the one equal to an angle of the oiher are to each other as the products of the sides including the equal angles. Д Let the triangles... | |
 | George Albert Wentworth - Geometry - 1877 - 436 pages
...PROPOSITION XIX. THEOREM. 577. Two tetrahedrons having a trihedral angle of the one equal to a trihedral angle of the other are to each other as the products of the three edges of these trihedral angles. Let V and V denote the volumes oî the two tetrahedrons D-ABC,... | |
 | William Frothingham Bradbury - Geometry - 1877 - 262 pages
...are respectively similar. 112. Two tetraedrons having a triedral angle of the one equal to a triedral angle of the other are to each other as the products of the edges of the equal triedral angles. (70 ; II. 116, 55.) 113. State and prove the converse of Theorem... | |
 | Elias Loomis - Conic sections - 1877 - 458 pages
...point D toward B, or from it. D2 PROPOSITION XXI. THEOREM. Two triangles are similar when they have an angle of the one equal to an angle of the other, and the sides including those angles proportional. Let the triangles ABC, DEF have the angle A of the... | |
 | Āryabhaṭa - 1878 - 100 pages
...sides about th« equal angles, reciprocally proportional. And conversely triangles and parallelograms having an angle of the one equal to an angle of the other and their sides about the equal angles reciprocally proportional, are equal to one another. First,... | |
 | William Henry Harrison Phillips - Geometry - 1878 - 236 pages
...3). ABE BE .. . ABC ABD The same is true of parallelograms. BE BF' VI. Theorem. If two triangles have an angle of the one equal to an angle of the other, the ratio of their areas is equal to that of the products of the sides which contain those angles.... | |
 | James Maurice Wilson - 1878 - 450 pages
...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. Part. En. Let A BCD, EFGH be two parallelograms which have... | |
 | J. G - 1878 - 408 pages
...contained between the point and the parallels. 14. // two parallelograms are equal in area, and have an angle of the one equal to an angle of the other, then tfie sides which contain Vie angle of the first are the extremes of a proportion of which the... | |
 | James McDowell - 1878 - 310 pages
...form a rectangle, then shall the triangles be equiangular (VI. 5, 16) 54 81. If two triangles have an angle of the one equal to an angle of the other and the rectangle under the sides about the equal angles equal, a side of each triangle being taken... | |
 | George Albert Wentworth - 1879 - 196 pages
...PAGE 217. Ex. i. Show that two triangles which have an angle of the one equal to the supplement of the angle of the other are to each other as the products of the sides including the supplementary angles. Let A ABC and CDE have AACB and DCE supplements of each other. Place these A... | |
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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. 
