 | Francis Joseph Grund - Geometry, Plane - 1830 - 274 pages
...triangles coincide with each other throughout ; that is, their angles are also equal, each to each. 6. In every triangle the greater side is opposite to the greater angle, and the greatest side to the greatest angle ; and the reverse is also true, namely : the greater angle... | |
 | Francis Joseph Grund - Geometry, Plane - 1834 - 204 pages
...triangles coincide with each other throughout ; that is, their angles are also equal, each to each. 6. In every triangle, the greater side is opposite to the greater angle, and the greatest side to the greatest angle. 7. In a right-angled triangle, the greatest side is opposite... | |
 | Adrien Marie Legendre - Geometry - 1836 - 394 pages
...therefore, the triangle BAG is isosceles. PROPOSITION XIII. THEOREM. The greater side of every triangle is opposite to the greater angle ; and- conversely,...the greater angle is opposite to the greater side. First, Let the angle C be greater than the angle B ; then will the side AB, opposite C, be greater... | |
 | Charles Reiner - Geometry - 1837 - 246 pages
...that is, the triangle is isosceles. 11. If a triangle be equiangular, it is likewise equilateral. 12. In every triangle the greater side is opposite to the greater angle. 13. In every triangle the greater angle is subtended by the greater side. 14. Any two sides of a triangle... | |
 | John Charles Snowball - 1837 - 322 pages
...27.) Let ¿ NAC be less than 45°. Then, since ¿ NAC + ¿NCA = 90°, ¿NCA is greater than 45°. And in every triangle the greater side is opposite to the greater angle, (Eucl. i. 19-) ; .-. AN>NC; AN NC " лс ' > Tc ' or cos A > sin A. Similarly, for angles between 45°... | |
 | Roswell Park - Best books - 1841 - 624 pages
...§ 2. Of Plane Rectilinear Figures, we have only room to give some of the more important measures. In every triangle, the greater side is opposite to the greater angle : and either side is always less than the sum of the other two. In every triangle, the sum of the three angles... | |
 | Joseph Gwilt - Architects - 1842 - 1114 pages
...angle LAB is made equal to the angle G ; the angle D is therefore equal to the angle G. 921. PROP. XLV. In every triangle the greater side is opposite to the greater angle, and the greater annlr tn the greater side. In the triangle ABC (ßg. 277.), if the side AB be greater than... | |
 | Anna Cabot Lowell - Geometry - 1846 - 216 pages
...EDF; and the triangle ABC = DEF, (126.) In each case equal angles are opposite to equal sides. 139. In every triangle the greater side is opposite to the greater angle, (fig. 90.) If AC > AB, then is angle B > angle C. Dem. In the side AC take AD= AB and draw BD. Angle... | |
 | Roswell Park - Best books - 1847 - 626 pages
...§ 2. Of Plane Rectilinear Figures, we have only room to give some of the more important measures. In every triangle, the greater side is opposite to the greater angle : and either side is always less than the sum of the other two. In every triangle, the sum of the three angles... | |
 | Education - 1849 - 682 pages
...diameter* Geometry. Demonstrate the following propositions: — 1. The greater side of every triangle is opposite to the greater angle ; and conversely,...the greater angle is opposite to the greater side. 2. In every triangle the sum of the three angles is equal to two right angles. 3. Two equal chords... | |
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Theorem. In every Triangle the greater side is opposite to the greater angle, and conversely, the greater angle is opposite to the greater side. 
