 | Benjamin Greenleaf - Geometry - 1862 - 532 pages
...equal 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 - 1862 - 518 pages
...mutually equilateral, they are equivalent. ELEMENTS OF GEOMETRY. Let ABC, DEF be two triangles, having the three sides of the one equal to the three sides of the other, each to each, namely, AB to DE, AC to DF, andCBtoEF; then their triangles will be equivalent. Let 0 he the pole of... | |
 | Benjamin Greenleaf - Geometry - 1861 - 638 pages
...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 - Geometry - 1863 - 504 pages
...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.... | |
 | Charles Davies - 1863 - 436 pages
...latter an indirect demonstrationTHEOREM VIllIf two triangles have the three sides of the one eqvai to the, three sides of the other, each to each, the three angles will equal, each to eachLet the two triangles ABC, ABD, have the side AB equal to the side AB, the side... | |
 | 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... | |
 | 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
...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 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... | |
 | C. Davies - 1867 - 342 pages
...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 a line... | |
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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. 
