| Daniel Cresswell - Geometry - 1816 - 294 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 - 208 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 - Geometry - 1825 - 224 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 - 280 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 - 272 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 - 120 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
...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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