 | Benjamin Greenleaf - Geometry - 1862 - 532 pages
...spheres, are mutually equilateral, they are equivalent. £et ABC, DEF be two triangles, having the three sides of the one equal to the three sides of the other, each to each, namely, А В to DE, AC to DF, and С В to EF; then their triangles will be equivalent. Let 0 be the... | |
 | Benjamin Greenleaf - Geometry - 1863 - 504 pages
...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.... | |
 | Charles Davies - Mathematics - 1867 - 186 pages
...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... | |
 | Education - 1868 - 516 pages
..." — 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 - Geometry - 1868 - 132 pages
...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... | |
 | Benjamin Greenleaf - Geometry - 1868 - 340 pages
...ABC. PROPOSITION XVII. — THEOREM. ELEMENTS OP GEOMETRY. Let ABC, DBF be two triangles, having the three sides of the one equal to the three sides of the other, eaeh to each, namely, AB to DE, AC toDF, andCB toEF; then their triangles will be equivalent. Let 0... | |
 | Horatio Nelson Robinson - 1869 - 276 pages
...CF, (Ax. 3); but BE = AC, and AF= BD, (Th. 24); hence we have two A's, CAF and EBD, which have the three sides of the one equal to the three sides of the other, each to each; therefore, the two A's are equal, (Th. 21). If, from the whole figure ABDC, we take away the A CAF,... | |
 | Euclides - 1871 - 136 pages
...be.equal, the sides wMch tubtend them are also equal. (Eucl. i. 6.) SE 2 If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles must be equal in all respects. -25 q _ Let the three sides of the A s ABO, DEF be equal,... | |
 | Elias Loomis - Geometry - 1871 - 302 pages
...to each, and the triangles themselves will be • •qua', Let ABC, DEF be two triangles having the three sides of the one equal to the three sides of the other, viz. : AB equal to DE. BC to EF, and AC to DF ; then' will the three angles also be equal, viz. : the... | |
 | Euclid, Charles Peter Mason - Geometry - 1872 - 216 pages
...equilateral A- (Prop. I.) To prove that the construction is correct we must know that — If two AS have the three sides of the one equal to the three sides of the other, each to each, then the /_s of the AS are equal. (Prop. VIII.) Let AB be the given right line, and C the given »... | |
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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. 
