| Benjamin Donne - 1796 - 120 pages
...on the other ; the line DF will coincide with AC, and EF with BC. THEOREM 16. If two triangles have three sides of one equal to the three sides of the other, each to each, thefe triangles are equal in every rcfpeft. — 8 E. 1, or 17 D. 1. Ciť For if the triangle DEF be... | |
| Daniel Cresswell - Geometry - 1816 - 338 pages
...Theorem. If two spherical triangles * on the same sphere, or on equal spheres, have the three sides of the one equal to the three sides of the other, each to each, the angles also of the one shall be equal to the angles of the other, each to each, to which thevequal... | |
| Adrien Marie Legendre - Geometry - 1819 - 576 pages
...thus two circles having the same radius arc equal ; and two triangles having the three sides of the one equal to the three sides of the other, each to each, are also equal. 162. Two figures are similar, which have the angles of the one equal to the angles... | |
| Adrien Marie Legendre - Geometry - 1825 - 276 pages
...thus two circles having the same radius are equal ; and two triangles having the three sides of the one equal to the three sides of the other, each to each, are also equal. 162. Two figures are similar, which have the angles of the one equal to the angles... | |
| Adrien Marie Legendre, John Farrar - Geometry - 1825 - 280 pages
...BC : EF : : AC : DF; consequently FG = DF; hence the triangles EOF, DEF, have the three sides of the one equal to the three sides of the other, each to each ; they are therefore equal (43). But, by constr .ction, the triangle EGF is equiangular with the triangle... | |
| George Lees - 1826 - 276 pages
...GEOMETRY. Book I. s Sup. PROP. IV. THEOREM. If two triangles, ABC and DEF, have the three sides of the one equal to the three sides of the other, each to each, viif. AB to DE, AC to DF, and BC to EF, the triangles are equal in every respect. Let AB be that side... | |
| Alexander Ingram - Mathematics - 1830 - 458 pages
...circle, meet in the poles of that circle. PROP. V. If two spherical triangles have the three sides of the one equal to the three sides of the other, each to each, the angles which are opposite to the equal sides are likewise equal ; and conversely. PROP. VI. If... | |
| Pierce Morton - Geometry - 1830 - 584 pages
...equilateral triangles. JoinBD; then because the triangles В FD, В С D have the three sides of the one equal to the three sides of the other, each to each, the angle В FD is equal to the angle В С D (I. 7.), that is, to the angle of a regular pentagon... | |
| Mathematics - 1835 - 684 pages
...last circle in F ; and join FA, F В. Then, because the triangles ECD, FAB have the three sides of the one equal to the three sides of the other, each to each, (7.) they are equal in every respect, and the angle at A is equal to the angle at C. Therefore, &c.... | |
| John Playfair - Geometry - 1836 - 148 pages
...equiangular triangle is also equilateral. PROP. VII. THEOR. If two triangles have the three sides of the one equal to the three sides of the other, each to each ; the angles opposite the equal sides are also equal. Let the two triangles ABC, DEF, have the three... | |
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