| Alexander Ingram - Mathematics - 1830 - 462 pages
...plane of one and the same great circle, meet in the poles of that circle. PROP. V. If two spherical **triangles have the three sides of the one equal to the three sides of the other, each to each, the** angles which are opposite to the equal sides are likewise equal ; and conversely. PROP. VI. If two... | |
| Pierce Morton - Geometry - 1830 - 584 pages
...the three angles of the one equal to the three angles of the other, each to each, they shall likewise **have the three sides of the one equal to the three sides of the** othrr, each to each, viz. those which are opposite to the equal angles.* Let the spherical triangles... | |
| Mathematics - 1835
...and С с ; draw P О perpendicular to Ce; and join OQ. Then, because the triangles С P с, С Q с **have the three sides of the one equal to the three sides** scribe two circles, and kt them cut one another in P; and from P draw PM perpendicular to А В : then... | |
| Adrien Marie Legendre - Geometry - 1836 - 359 pages
...these results contradicts the hypothesis: therefore, BAC is greater than EDF. PROPOSITION X. THEOREM. **If two triangles have the three sides of the one equal...the other, each to each, the three angles will also** b« equal, each to each, and the triangles themselves will be equal. Let the side ED=BA, the side EF-BC,... | |
| John Playfair - Geometry - 1836 - 114 pages
...Which was to be proved. COR. Hence, every equiangular triangle is also equilateral. PROP. VII. THEOR. **If two triangles have the three sides of the one equal...to the three sides of the other, each to each ; the** angles opposite the equal sides are also equal. Let the two triangles ABC, DEF, have the three sides... | |
| Adrien Marie Legendre - Geometry - 1838 - 386 pages
...results contradicts the hypothesis: therefore, BAC is greater• than EDF. PROPOSITION X. THEOREM. **If two triangles have the three sides of the one equal...each, and the triangles themselves will be equal.** 20 GEOMETRY. Let the side ED=BA, the side EF=BC, and the side DF=AC ; then will the angle D=A, the... | |
| Thomas Keith - 1839 - 498 pages
...through two given points on the surface of the sphere. Hence, the three sides of the one triangle being **equal to the three sides of the other, each to each, the** triangles are equal. (Prop. VH.) Secondly, let the triangles be situated on contrary sides of the centre... | |
| Euclides - 1840 - 194 pages
...agree in having two sides, and the angle contained by those sides, equal (as in Prop. 4); or, in having **the three sides of the one equal to the three sides of the other** (as in Prop. 8) ; or, finally, in having two angles and a side, similarly placed with respect to the... | |
| Dionysius Lardner - Curves, Plane - 1840 - 386 pages
...different forms. This proposition is usually enounced thus : — If two triangles have the three sides of **one equal to the three sides of the other each to each,** then the three angles will le equal each to each, and their areas will be equal. (63.) When two sides... | |
| Adrien Marie Legendre - Geometry - 1841 - 235 pages
...line AD from the vertex A to the point D, the middle of the base BC ; the two triangles ABD, ADC, will **have the three sides of the one equal to the three sides of the other, each to each,** namely, AD common to both, AB = AC, by hypothesis, and BD = DC, by construction; therefore (43) the... | |
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