 | Benjamin Greenleaf - 1861 - 638 sider
...arcs AD, EG will be equal. For, if the radii CD, 0 G are drawn, the triangles ACD, E 0 G, having tlffe three sides of the one equal to the three sides of the other, each to each, are themselves equal (Prop. XVIII. Bk. I.) ; therefore the angle ACD is equal to the angle E 0 G (Prop.... | |
 | Benjamin Greenleaf - 1863 - 504 sider
...the arcs AD, EG will be equal. For, if the radii CD, 0 G are drawn, the triangles ACD, E 0 G, having the three sides of the one equal to the three sides of the other, each to each, are themselves equal (Prop. XVIII. Bk. I.) ; therefore the angle ACD is equal to the angle E 0 G (Prop.... | |
 | Horatio Nelson Robinson - 1865 - 474 sider
...(Ax. 5). Hence the theorem ; the difference between any two sides of a triangle, etc. THEOREM XXI. jf two triangles have the three sides of the one equal to the three sides of the .other, each to each, the two triangles are equil, and the equal angles are opposite the equal sides. la two triangles, as... | |
 | Charles Davies, William Guy Peck - 1865 - 592 sider
...need the following, which have been before proved, viz : Prop X. (of Legendre). " When two triansles have the three sides of the one equal to the three sides of the other, each to each, the three angles will also be equal, each to each and the triangles themselves will bo eqoa.." Prop.... | |
 | Benjamin Greenleaf - 1866 - 328 sider
...equal to it ; hence the angle A must be greater 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... | |
 | Charles Davies - 1867 - 186 sider
...proposition, we need the following, which have 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... | |
 | C. Davies - 1867 - 342 sider
...EAD will be equal to the angle KFor, draw the chord DE- Then the two triangles IKL and EAD, having the three sides of the one equal to the three sides of the other, each to each, the angle EAD will be equal -o the angle K (Bk- I- Th- viii)PROBLEM IXThrough a g1ven point to draw... | |
 | Edward Brooks - 1868 - 284 sider
...AB. If it falls upon AB, the theorem is true by A. 7. Therefore, if two triangles, etc. THEOREM IX. 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. Let ABC and DEF be two triangles, having AB equal to... | |
 | 1868 - 516 sider
...similarity to those of the other. " — Campbells Rhet. 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... | |
 | James Maurice Wilson - 1868 - 132 sider
...one triangle can be constructed so as to have its sides equal to three given lines, it is clear that if two triangles have the three sides of the one equal to the three sides of the other, these triangles must be identical, or be equal in all respects. And a similar remark may be made on... | |
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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. 
