 Two triangles, which have an angle in the one equal to an angle in the other, are to each other as the rectangles of the sides Fig.  Elements of Solid Geometry - Page xiby William Herschel Bruce, Claude Carr Cody - 1912 - 110 pagesFull view - About this book
 | Charles Hutton - Mathematics - 1812 - 620 pages
...identical (ill. 5) ; which is absurd, since their angles arc unequal. THEOREM LXXXVI. Triangles, which have an Angle in the one Equal to an Angle in the other, and the Sides about these angles Proportional, are Equiangular. LET ABC, DEF, be two triangles, having... | |
 | Adrien Marie Legendre - Geometry - 1819 - 574 pages
...have already been given in articles 189, 190. THEOREM. 216. Two triangles, which have an angle in tlie one equal to an angle in the other, are to each other as the rectangles of tlie sides fig. l28.ru/ucA contain the equal angles ; thus, the triangle ABC (fig. 128)... | |
 | Charles Hutton - Mathematics - 1822 - 616 pages
...identical (th. 5) ; which is absurd, since their angles are unequal. THEOREM LXXXVI. Triangles, which have an Angle in the one Equal to an Angle in the other, and the Sides about these angles Proportional, are Equiangular. LET ABC. DBF, be two triangles, haying... | |
 | Adrien Marie Legendre, John Farrar - Geometry - 1825 - 280 pages
...the hypothenuse have already been given in articles 189, 190. THEOREM. 216. Two triangles, which have an angle in the one equal to an angle in the other, are to each other as the rectangles of the sides Fig. 128. which contain the equal angles; thus, the triangle ABC (fig. 128)... | |
 | Adrien Marie Legendre, John Farrar - Geometry - 1825 - 294 pages
...hypothenuse have already been given in articles 189, 190. THEOREM. 21 6. Two triangles, which have an angle in the one equal to an angle in the other, are to each other as the rectangles of the sides Fig. 128. which contain the equal angles; thus, the triangle ABC (fig. 128)... | |
 | Adrien Marie Legendre - 1825 - 570 pages
...the hypothenuse have already been given in articles 189, 190. THEOREM. 216. Two triangles, which have an angle in the one equal to an angle in the other, arc to each other as the rectangle^ of the sides Fig. 128. which contain the equal angles ; thus, the... | |
 | John Radford Young - Euclid's Elements - 1827 - 228 pages
...rectangles of the sides containing the equal angles be equivalent, the triangles will be equivalent, and if triangles having an angle in the one equal to an angle in the other be equivalent, the rectangles of the sides containing the equal angles will be equivalent ; the same... | |
 | John Radford Young - Euclid's Elements - 1827 - 246 pages
...Scholium. The above proposition is obviously true of rhomboids, that is, rhomboids are similar which have an angle in the one equal to an angle in the other, and the containing sides proportional ,• for such rhomboids must be equiangular, and the opposite... | |
 | Euclid, Dionysius Lardner - Euclid's Elements - 1828 - 542 pages
...ABD from both, and the remainders CAB and CDB are equal. (152) COR. 1. — If two parallelograms have an angle in the one equal to an angle in the other, all the angles must be equal each to each. For the opposite angles are equal by this proposition, and... | |
 | Adrien Marie Legendre - Geometry - 1828 - 346 pages
...of triangles include, by implication, those of all figures. THEOREM. 208. Two triangles which have an angle in the one equal to an angle in the other, and the sides containing those angles proportional, are similar. Let the angles A and D be equal ;... | |
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