 | Daniel Cresswell - Geometry - 1816 - 352 pages
...semicircumference. PROP. III. (86.) Theorem. If two spherical triangles * on the same sphere, or on equal spheres, have the three sides of the one equal to the three sides of the other, each to each, the angles also of the one shall be equal to the angles of the other, each to each, to... | |
 | Adrien Marie Legendre - Geometry - 1819 - 574 pages
...straight 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... | |
 | Adrien Marie Legendre, John Farrar - Geometry - 1825 - 294 pages
...straight line AD from the veriest 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... | |
 | Adrien Marie Legendre, John Farrar - Geometry - 1825 - 280 pages
...arc AMD will be equal to the arc ENG. For, if the radii CD, OG, be drawn, the two triangles ACD, EOG, will. have the three sides of the one equal to the three sides of the other, each to each, namely, AC = EO, CD = OG and AD=. EG ; therefore these triangles are equal (43) ; hence... | |
 | Adrien Marie Legendre - Geometry - 1825 - 276 pages
...AMD will be equal to the arc EJVG. For, if the radii CD, OG, be drawn, the two triangles ACD, EOG, will have the three sides of the one equal to the three sides of the other,~each to each, namely, AC= EO, CD = OG and AD — EG ; therefore these triangles are equal (43)... | |
 | George Lees - 1826 - 276 pages
...base at right angles. OF GEOMETRY. Book I. s Sup. PROP. IV. THEOREM. If two triangles, ABC and DEF, have the three sides of the one equal to the three sides of the other, each to each, viif. AB to DE, AC to DF, and BC to EF, the triangles are equal in every respect. Let... | |
 | James Hayward - Geometry - 1829 - 218 pages
...their parts ; they are not different, therefore, but equal; and we say, universally, When two triangles have the three' sides of the one equal to the three sides of the other respectively, the angles will also be equal, respectively, and the two triangles will be equal in all their parts.... | |
 | Alexander Ingram - Mathematics - 1830 - 458 pages
...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.... | |
 | 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 - 684 pages
...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... | |
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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. 
