 | Charles Davies - Geometry - 1864 - 358 pages
...latter an indirect demonstrationTHEOREM VIIIIf two triangles have the three sides of the one cqva* to the, three sides of the other, each to each, the three angles wil! al *1 £« equal, each to eachLet the two triangles ABC, ABD, have the side AB equal to the side... | |
 | Charles Davies, William Guy Peck - Mathematics - 1865 - 592 pages
...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...equal, each to each and the triangles themselves will bo eqoa.." Prop. V. " When two triangles have two sides, and the included angle of the one equal to... | |
 | Horatio Nelson Robinson - Conic sections - 1865 - 474 pages
...remain ED = 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, e,ach to each; therefore, the two A's are equal, (Th. 21). If, from the whole figure ABDC, we take away the A CAF,... | |
 | Benjamin Greenleaf - Geometry - 1866 - 328 pages
...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 to... | |
 | Charles Davies - Mathematics - 1867 - 186 pages
...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...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... | |
 | Education - 1868 - 516 pages
...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...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... | |
 | Edward Brooks - Geometry - 1868 - 284 pages
...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 DE,... | |
 | James Maurice Wilson - Geometry - 1868 - 132 pages
...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... | |
 | James Maurice Wilson - Geometry - 1868 - 150 pages
...are therefore equal. And if the chord AB is given equal to the chord PQ, then the triangles AOB, POQ have the three sides of the one equal to the three sides of the other; and therefore the angle AOB=\he angle POQ; and therefore also the arc AB = the arc PQ. COR. 1. If the... | |
 | Benjamin Greenleaf - Geometry - 1868 - 340 pages
...than 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... | |
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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. 
