 | Horatio Nelson Robinson - Geometry - 1860 - 470 pages
...manner, we show that ED is equal and parallel to PO, and BD to MO; hence the triangles are equal, hs ring the three sides of the one, respectively, equal to the three sides of the other. That their planes are parallel, follows from Cor., TL?o rem 16. THEOREM XVIII. Any one of the three... | |
 | Euclides - 1861 - 464 pages
...Cos. 17, Ш. 1, Ш. Pst. 1. DEM. 18, Ш. 36, Ш. Ax. 1. Def. 15, 1. Cor. 16, Ш. 8, 1. If two Дз have the three sides of the one respectively equal to the three sides of the other ; then these triangles shall be cqnal in every respect. EI 2 3 CI 2 3 Hyp. 1. „ 2. Cone. 17, 1II.... | |
 | Euclides - 1862 - 140 pages
...equal to the angle contained by the two sides, equal to them, of the other. Or, If two triangles have three sides of the one respectively equal to the three sides of the other, they are equal in every respect. ^References — Prop. I. 7; ax. 8.) Hypothesis. — Let ABC, DEF,... | |
 | Benjamin Greenleaf - Geometry - 1862 - 532 pages
...than the angle D. PROPOSITION XVIII. — THEOREM. 80. If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles themselves will be equal. Let the triangles ABC, DEF have the side AB equal to DE, А С... | |
 | Euclides - 1865 - 80 pages
...respectively equal to the three given straight lines CD, DE, EC ; and because the triangles CDE and AFG have the three sides of the one respectively equal to the three sides of the other, they are equal in every respect, and therefore the angle FAG is equal to the angle DCE. PROPOSITION... | |
 | Benjamin Greenleaf - Geometry - 1866 - 328 pages
...than the angle D. PROPOSITION XVIII. — THEOREM. 80. If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles themselves will be equal. Let the triangles ABC, DEF have the side AB equal to DE, AC to... | |
 | Charles Davies - Mathematics - 1867 - 186 pages
...been before proved ; viz. : Prop. X. (of Legendre). "If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles will be equal in all their parts." Prop. V. " If two triangles have two sides and the included... | |
 | James Maurice Wilson - Geometry - 1868 - 132 pages
...shall be perpendicular to BC. Proof. For if AD, AE be joined, it is clear that the triangles AFD, AFE have the three sides of the one respectively equal to the three sides of the other; therefore the angle AFD = the corresponding angle AFE, and therefore AF is perpendicular to BC. A large... | |
 | Horatio Nelson Robinson - Geometry - 1868 - 276 pages
...manner, we show that ED is equal and parallel to PO, and BD to MO; hence the triangles are equal, ha ring the three sides of the one, respectively, equal to the three sides of the other. That their planes are parallel, follows from Cor., Thpo rem 16 THEOREM XVIII. Any one of the three... | |
 | Education - 1868 - 516 pages
...This structure is very often neglected. Examples : "If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles will be equal in all their parts." The article before one here is improper, because the reference... | |
| |
If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent. 
