 | 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
...right, the remaining angles will be right angles. FIRST BOOK. COR. 2. — If two parallelograms have an angle of the one equal to an angle of the other, the remaining angles will be also equal ; for the angles which are opposite to these equal angles are... | |
 | William Frothingham Bradbury - Geometry - 1872 - 262 pages
...bisecting line meets AC produced, the segments of the base (59) are AE and CE. (I. 17.) (1. 45.) (16.) 61 i Two triangles having an angle of the one equal to an angle in the other are to each other as the rectangles of the sides containing the equal angles ; or ABC:ADE—ABXAC:AD... | |
 | William Frothingham Bradbury - Geometry - 1872 - 124 pages
...line meets AC produced, the segments of the base (59) are AE and CJEL (I. 17.) (1. 45.) (16.) 61 1 Two triangles having an angle of the one equal to an angle in the other are to each other as the rectangles of the sides containing the equal angles ; or ABC:... | |
 | William Chauvenet - Mathematics - 1872 - 382 pages
...are to each other as the products of the sides including the equal angles. Two triangles which have an angle of the one equal to an angle of the other may be placed with their equal angles in coincidence. Let ABC, ADE, be the two triangles having the... | |
 | Thomas Steadman Aldis - 1872 - 84 pages
...of "proportional compasses." 2. Two triangles have their altitudes proportional to their bases, and an angle of the one equal to an angle of the other, adjacent to the bases; prove that they are similar. 3. Prove that two quadrilateral figures are similar... | |
 | David Munn - 1873 - 160 pages
...opposite angles 42 VII. 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,...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... | |
 | Benjamin Greenleaf - Geometry - 1873 - 202 pages
...the triangles DEF, ABC are also equiangular and similar. THEOREM XV. 208. 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... | |
 | L J V. Gerard - 1874 - 428 pages
...are not reciprocally proportional. THEOREM 18. (Eucl. VI. 16.) Two equivalent triangles which have an angle of the one equal to an angle of the other, have the sides of these angles reciprocally proportional. Let there be two equivalent triangles, ABC... | |
 | Euclid, James Bryce, David Munn (F.R.S.E.) - Geometry - 1874 - 236 pages
...equal PKOP. XI— THEOREM. (Euc. VI. 14, 15.) Equal parallelograms and 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. Let MB and BN be... | |
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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. 
