| Benjamin Greenleaf - Geometry - 1863 - 502 pages
...Conversely, if the chord AD is equal to the chord EG, the arcs AD, EG will be equal. For, if the radii CD, OG **are drawn, the triangles ACD, E 0 G, having the three...semicircle ADB be applied to its equal EGF, with the radius** A0 on its equal E0, since the angles ACD, E 0 G are equal, the radius CD will fall on OG, and the point... | |
| C. Davies - 1867 - 342 pages
...the angle 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... | |
| Charles Davies - Mathematics - 1867 - 186 pages
...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... | |
| Benjamin Greenleaf - 1868 - 338 pages
...greater 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... | |
| James Maurice Wilson - Geometry - 1868 - 150 pages
...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... | |
| Bernhard Marks - Geometry - 1869 - 170 pages
...side A B. 'D It PROPOSITION XIX. THEOREM. DEMONSTRATION. We wish to prove, that, If two triangles have **the three sides of the one equal to the three sides of the other, each to each,** they are equal in all their parts. Let the two triangles ABC, ADC, have the side AB of the one equal... | |
| Horatio Nelson Robinson - 1869 - 276 pages
...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, each to each;** therefore, the two A's are equal, (Th. 21). If, from the whole figure ABDC, we take away the A CAF,... | |
| Charles Davies - Geometry - 1870 - 319 pages
...called a direct, and the latter an indirect demonstration. THEOREM via. If two triangles have tlie **three sides of the one equal to the three sides of the other, each to each,** the three angles will aho be equal, each to each. Let the two triangles ABC, ABD, have the side AB... | |
| Bernard Marks - Geometry - 1871 - 172 pages
...ILLUSTRATED. PROPOSITION XIX. THEOREM. DEMONSTRATION. We wish to prove that, If two triangles have **the three sides of the one equal to the three sides of the other, each to each,** they are equal in all their part's. Let the two triangles ABC, ADC, have the side AB of the one equal... | |
| Euclides - 1871
...triangle 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,... | |
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