| Benjamin Peirce - Geometry - 1841 - 186 pages
...AB would by § J5J_and the preceding demonstration, be equal to or less than AC. 63. Theorem. If two **triangles have two sides of the one respectively equal to two sides of the other, and** if the included angle of the first triangle is greater than the included angle of the second triangle,... | |
| James Bates Thomson - Geometry - 1844 - 237 pages
...AG from one side, and its equal AB from the other, there will remain GC<BC, or EF<BC. Hence, If two **triangles have two sides of the one respectively equal to two sides of the other,** while the included angle of the one is greater than the included angle of the other, then will the... | |
| Euclid, James Thomson - Geometry - 1845 - 380 pages
...from the vertex of a triangle to the point of bisection of the base, bisects the triangle ; ana if two **triangles have two sides of the one respectively equal to two sides of the other, and the** contained angles (I. def. 38) supplemental, the triangles are equal. * lt follows from the first corollary... | |
| Benjamin Peirce - Geometry - 1847 - 150 pages
...AB would by § 61 and the preceding demonstration, be equal to or less than AC. 63. Theorem. If two **triangles have two sides of the one respectively equal to two sides of the other, and** if die included angle of the first triangle is greater than the included angle of the second triangle,... | |
| 1851
...and B. 6. Solve the following equations: — Sx+1 Sx-1 2г + 5 (1.) (2.) xl x -t-1 2xt-1 7. If two **triangles have two sides of the one respectively equal to two sides of the other, and the** contained angles equal, prove that the triangles will be equal in every respect. 8. The square constructed... | |
| Euclides - 1852
...(Prop. 19.) ; but DG is equal to A c, therefore DF is greater than A c. WWD PBOP. XXV. THEOE. If two **triangles have two sides of the one respectively equal to two sides of the other, and** if the base of one be greater than the base of the other ; the angle opposite to the greater base is... | |
| Euclid - Geometry - 1853 - 136 pages
...to be by the " reductio ad absurdum." PROPOSITION VIII. THEOREM. — If two triangles (ABC and DEF) **have two sides of the one respectively equal to two sides of the other** (AB and AC to DE and DF), and have aho their bases equal (BC to EF), then the angles (A and D) formed... | |
| Euclides - Geometry - 1853 - 334 pages
...been cut off equal to c the less. Which was to be done. PEOP. IV. THEOEEM. ' If two triangles have (1) **two sides of the one respectively equal to two sides of the other** ; (2) the angle included by the two sides of the one equal to the angle included by the two sides of... | |
| Popular educator - 1854 - 1274 pages
...angle BA c is greater than the angle BDF. Wherefore, if two triangles, &c. QED Corollary. — If two **triangles have two sides of the one respectively equal to two sides of the other,** the base of the one is greater than, equal to, or less than the base of the other, according as the... | |
| Euclides - 1855
...the angle BAС is greater than the angle EDF. Wherefore, if two triangles, &o. QED Corollary. If two **triangles have two sides of the one respectively equal to two sides of the other,** the base of the one is greater than, equal to, or leas than the base of the ether, according as the... | |
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