| 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... | |
| Thomas Keith - Navigation - 1810 - 478 pages
...construetion, also AB is common to the two triangles ABC and ADB, therefore the three sides of the one are **equal to the three sides of the other, each to each. The** angles -which are opposite to the equal sides in each triangle are equal. For, Produce the sides BC... | |
| Daniel Cresswell - Geometry - 1816 - 352 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 - 574 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, 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... | |
| 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... | |
| Thomas Keith - Navigation - 1826 - 504 pages
...equally obtuse. PROPOSITION Til. (B) In any two spherical triangles, if the three sides of the one be **equal to the three sides of the other, each to each, the** angles which are opposite to the equal sides will be equal. Let ABC be any triangle on the surface... | |
| 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 two... | |
| Pierce Morton - Geometry - 1830 - 584 pages
...each. For, if the polar triangles A' B' C', D' E' F be described, they will have the three sides of the **one equal to the three sides of the other, each to each,** because every two corresponding sides, as A' B' and D' E' are (7.) supplements of the measures of equal... | |
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