| 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 the angle A = the... | |
| 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 the angle A = the... | |
| 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... | |
| 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... | |
| 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... | |
| 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 sides of... | |
| John Radford Young - Euclid's Elements - 1827 - 228 pages
...be divided into two scalene triangles that shall be similar to each other. PROPOSITION XVI. THEOREM. Triangles having an angle in the one equal to an angle in the other, are to each other as the rectangles of their containing sides. Let the triangles ABC, DEF have the... | |
| 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 ; if we have AB... | |
| 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... | |
| George Darley - Euclid's Elements - 1836 - 172 pages
...the halves of the pa- AGCDHF rallelograms AI, DK. This, &c. ART. 106. Equal triangles which have also an angle in the one equal to an angle in the other, have the sides about these equal angles reciprocally proportional. Let ABC, DEF, be two equal triangles,... | |
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