 | 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. Ci» For if the triangle DEF be... | |
 | Daniel Cresswell - Geometry - 1816 - 352 pages
...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 - 574 pages
...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)... | |
 | Adrien Marie Legendre, John Farrar - Geometry - 1825 - 294 pages
...will lie 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 to the... | |
 | Adrien Marie Legendre, John Farrar - Geometry - 1825 - 280 pages
...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 A... | |
 | Adrien Marie Legendre - Geometry - 1825 - 276 pages
...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
...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... | |
 | John Playfair - Geometry - 1829 - 210 pages
...without demonstration. PROPOSITION VIII. THEOREM If two triangles have the three sides of one triangle equal to the three sides of the other, each to each, they are equal in all respects. Let ABC, DEF be two triangles having the side AB equal to DE, and AC to DF, and BC to EF;... | |
 | James Hayward - Geometry - 1829 - 218 pages
...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... | |
 | Alexander Ingram - Mathematics - 1830 - 458 pages
...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... | |
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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. 
