 | Daniel Cresswell - 1816 - 352 σελίδες
...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 - 1819 - 574 σελίδες
...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... | |
 | Adrien Marie Legendre, John Farrar - 1825 - 294 σελίδες
...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, John Farrar - 1825 - 280 σελίδες
...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... | |
 | Adrien Marie Legendre - 1825 - 276 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 qther, each to each, namely, AD common to both, AB — AC, by hypothesis, and BD = DC, by construction... | |
 | George Lees - 1826 - 276 σελίδες
...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 - 1829 - 218 σελίδες
...coincide in all 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... | |
 | 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.... | |
 | 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... | |
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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. 
