 | William Chauvenet - Geometry - 1871 - 380 pages
...THEOREM. , -•. ,." 57. Two tetraedrons which have a triedral angle of the one equal to a triedral angle of the other, are to each other as the products of the three edges of the equal triedral angles. Let ABCD, AB'C'D', be the given tetraedrons, placed with... | |
 | William Chauvenet - Mathematics - 1872 - 382 pages
...GEOMETRY.— BOOK IV. THEOREMS. 219. Two triangles which have an angle of the one equal to the supplement of an angle of the other are to each other as the products of the sides including the supplementary angles. (IV. 22. ) 220. Prove, geometrically, that the square described upon the sum... | |
 | William Chauvenet - Geometry - 1872 - 382 pages
...PROPOSITION XX.—THEOREM. 57. Two tetraedrons which have a triedral angle of the one equal to a triedral angle of the other, are to each other as the products of the three edges of the equal triedral angles. Let AB CD, AB'C'D', be the given tetraedrons, placed with... | |
 | Euclid - Geometry - 1872 - 284 pages
...equal angles are reciprocally proportional (AB to BC as LB to BD). And if two triangles (ABD and CBL), have an angle of one equal to an angle of the other, and the sides about the equal angles reciprocally proportional, they will be equal to one another.... | |
 | David Munn - 1873 - 160 pages
...To find the area of any polygon 43 EXERCISES (4) 44 VIII. Two triangles which have an angle of the one equal to an angle of the other, are to each other...the products of the sides including the equal angles 47 IX. The areas of similar triangles are to each other as the squares of their like sides 48 X. The... | |
 | William Chauvenet - Geometry - 1875 - 466 pages
...GEOMETRY.—BOOK IV. THEOREMS. 219. Two triangles which have an angle of the one equal to the supplo mcnt of an angle of the other are to each other as the products of the siiitM including the supplementary angles. (IV. 22.) 220. Prove, geometrically, that the square described... | |
 | 1876 - 646 pages
...two triangles are similar when they are mutually equiangular. 2. Two triangles having an angle of the one equal to an angle of the other are to each other...products of the sides including the equal angles. 3. To inscribe A circle in a given triangle. 4. The side of a regular inscribed hexagon is equal to... | |
 | George Albert Wentworth - Geometry - 1877 - 416 pages
...value. Ex. 1. 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. С \j 2. Show, geometrically, that the square described upon the sum of two straight... | |
 | George Albert Wentworth - Geometry - 1877 - 416 pages
...SD* + 4 QED GEOMETRY. BOOK IV. PROPOSITION XIII. THEOREM. 341. Two triangles having an angle of the one equal to an angle of the other are to each other as the products cf t he sides including the equal angles. Let the triangles ABC and ADE have the common angle A. We... | |
 | 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,... | |
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Two triangles which have an angle of one equal to the supplement of an angle of the other are to each other as the products of the sides including the supplementary angles. 
