| Benjamin Greenleaf - Geometry - 1861 - 628 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 - 320 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 - 424 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 - 330 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 гл 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 - 472 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... | |
| 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... | |
| Edward Brooks - Geometry - 1868 - 294 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,... | |
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