| Daniel Cresswell - Geometry - 1816 - 352 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 - 574 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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.... | |
| 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... | |
| John Playfair - Geometry - 1836 - 148 pages
...was to be proved. COR. Hence, every equiangular triangle is also equilateral. PROP. VII. THEOR. If **two triangles have the three sides of the one equal to the three sides of the other,** each to each ; the angles opposite the equal sides are also equal. Let the two triangles ABC, DEF,... | |
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