| Benjamin Donne - 1796 - 120 pages
...the line DF will coincide with AC, and EF with BC. THEOREM 16. If two triangles have three sides of one equal to the three sides of the other, each to each, thefe triangles are equal in every rcfpeft. — 8 E. 1, or 17 D. 1. Ciť For if the triangle DEF be... | |
| Daniel Cresswell - Geometry - 1816 - 338 pages
...triangles, which are equal to them, are equal to one another. (2l6.) COR. 2. Hence, if two spherical triangles have the three sides of the one equal to the three sides of the other, or two sides and the included angle in the one, equal to two sides and the included angle, in the other,... | |
| Adrien Marie Legendre - Geometry - 1819 - 576 pages
...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); hence the angle ACD... | |
| Adrien Marie Legendre, John Farrar - Geometry - 1825 - 280 pages
...the figure will be a parallelogram. Demonstration. Draw the diagonal BD ; the two triangles ABD, BDC, have the three sides of the one equal to the three sides of the other, each to each, they are therefore equal, and the angle ADB opposite to the side AB is equal to the angle DBC opposite... | |
| Adrien Marie Legendre, John Farrar - Geometry - 1825 - 294 pages
...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 the angle... | |
| Adrien Marie Legendre - Geometry - 1825 - 276 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 qther, each to each, namely, AD common to both, AB — AC, by hypothesis, and BD = DC, by construction... | |
| 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 AB be that side... | |
| James Hayward - Geometry - 1829 - 228 pages
...coincide in all their parts ; they are not different, therefore, but equal; and \ve 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... | |
| Alexander Ingram - Mathematics - 1830 - 458 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... | |
| Pierce Morton - Geometry - 1830 - 586 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... | |
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