 | George Washington Hull - Geometry - 1807 - 408 pages
...they are similar to each other. PROPOSITION XVIII. THEOREM. 254. Two triangles are similar when they have an angle of one equal to an angle of the other, ancL the sides including these angles proportional. *BD* Given — The triangles ABC and DEF, with... | |
 | Adrien Marie Legendre - Geometry - 1819 - 574 pages
...GH, so that AB:FG::BC:GH. It follows from this, that the triangles ABC, FGH, having an angle of the one equal to an angle of the other and the sides about the equal angles proportional, are similar (208), consequently the angle ECA — GHF. These equal angles... | |
 | Rev. John Allen - Astronomy - 1822 - 516 pages
...HG, and of PB to BL or HE. Cor. 1. — By a similar reasoning it may be proved, that triangles, which have an angle of one, equal to an angle of the other, are to each other, in a ratio, compounded of the ratios, of the sides including the equal angles. Cor.... | |
 | Peter Nicholson - Architecture - 1823 - 210 pages
...triangles DEF, ABC, are equiangular and similar. THEOREM 60. 158. Two triangles which have an angle of the one equal to an angle of the other, and the sides about them proportionals, are similar. Let the angle A equal D, and suppose that AB : DE : : AC : DF, the... | |
 | Adrien Marie Legendre - Geometry - 1825 - 276 pages
...of triangles involve those of all figures. THEOREM. 208. Two triangles, which have an angle of the one equal to an angle of the other and the sides about these angles proportional, are similar. Demonstration. Let the angle A-=D (fig. 122), and let Fifr 122. ^g . DE ..£C. QF^ the... | |
 | Adrien Marie Legendre, John Farrar - Geometry - 1825 - 280 pages
...CA we shall have CP : CM : : CM : CQ ; consequently the triangles CPM, CQM, having an angle of the one equal to an angle of the other and the sides about the equal angles proportional, are similar (203) ; therefore MP : MQ : : CP : CM or CA. But the proportion... | |
 | Adrien Marie Legendre, John Farrar - Geometry - 1825 - 294 pages
...that AB : FG : : BC : GH. It follows from this, that the triangles ABC, FGH, having an angle of the one equal to an angle of the other and the sides about the equal angles proportional, are similar (208), consequently the angle BCA = GHF. These equal angles... | |
 | Pierce Morton - Geometry - 1830 - 584 pages
...The three sides (/). 4. Two angles, and a side opposite to one of them . »r. 14 5. Au angle of the one equal to an angle of the other, and the sides about two other angles, each to each, and the remaining an;;!« of the same affection, or one of them a right... | |
 | Mathematics - 1835 - 684 pages
...The three sides (/). 4. Two angles, and a side opposite to one of them . cor. 14 5. An angle of the one equal to an angle of the other, and the sides about two other angles, each to each, and the remaining angles of the same affection, or one of them a right... | |
 | Euclid, James Thomson - Geometry - 1837 - 410 pages
...sides about those angles reciprocally proportional : and (2.) triangles which have an angle of the one equal to an angle of the other, and the sides about those angles reciprocally proportional, are equal to one another. 1. Let ABC, ADE be equal triangles,... | |
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... they have an angle of one equal to an angle of the other and the including sides are proportional; (c) their sides are respectively proportional. 
