 | Alexander Ingram - 1830 - 458 σελίδες
...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 - 1830 - 584 σελίδες
...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... | |
 | 1835 - 684 σελίδες
...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 - 1836 - 394 σελίδες
...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 - 1836 - 148 σελίδες
...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... | |
 | Thomas Keith - 1839 - 498 σελίδες
...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 - 192 σελίδες
...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 - 1840 - 386 σελίδες
...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 - 1841 - 288 σελίδες
...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... | |
 | Nicholas Tillinghast - 1844 - 108 σελίδες
...are equal (Def. 4), therefore AD=DB (BI Prop. 19, Cor. 2); hence the two triangles ACD, BCD, having the three sides of the one equal to the three sides of the other, are equal, (B. I. Prop. 22), and the angles ACD, BCD, are equal ; and therefore the arcs AE, EB,are... | |
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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. 
