| James Atkinson - 1765 - 447 sider
...Circles cutting each other, the Angles which are oppofite and contrary, are equal to one another. 4. **The Sum of any two Sides (of a Triangle) is greater than the third Side.** 5. The Sum of the three J jjJJ*^ lis lefs than a J more than i8od. _r6. Any two Sides added together,... | |
| Charles Hutton - 1811
...The side AB, then, being neither equal to AC, nor less than it, must necessarily be greater. QED i **THEOREM X. THE Sum of any Two Sides of a Triangle...Greater than the Third Side. Let ABC be a triangle** ; t'jien will the < I) sum of any two of its sides be greater than the third side, as for instance,... | |
| Charles Hutton - 1822
...supposition. The side AB, then, being neither equal to AC, nor less than it, must necessarily be greater, o.. **ED THEOREM X. THE Sum of any Two Sides of a Triangle...Third Side. Let ABC be a triangle ; then will the** . lum of .ny two of its side* be greater than the third side, as for instances, AC -J-cB greater than... | |
| John Playfair - 1829 - 186 sider
...the greater angle; and, conversely, the greater of any two angles is subtended by the greater side. **The sum of any two sides of a triangle is greater than the third side.** If one side of any triangle be produced, the external angle is equal to both the internal and opposite... | |
| William Grier - 1832
...opposite the greater side AB, be greater than the angle B, opposite the less side AC.— (Fig. 8.) 10. **Let ABC be a triangle ; then will the sum of any two...its sides be greater than the third side ; as, for** instance, AC + CB greater than AB.— (Fig. 9.) 58 GEOMETRY. two siiles, as AB — AC, be less than... | |
| Adrien Marie Legendre - 1836 - 359 sider
...may be applied to each other, and the equal parts will mutually coincide. PROPOSITION VII. THEOREM. **The sum of any two sides of a triangle, is greater...side. Let ABC be a triangle : then will the sum of** two of its sides, as AC, CB, be greater than the third side AB. For the straight line AB is the shortest... | |
| William Grier - 1836 - 344 sider
...angle ACS, opposite the greater side AB, be greater than the angle B, opposite the less side AC. 10. **Let ABC be a triangle; then will the sum of any two...its sides be greater than the third side; as, for** instance, AC + CB greater than AB. 1 1. Let ABC be a triangle ; then will the difference of any two... | |
| William Grier - 1842 - 308 sider
...angle ACB, opposite the greater side AB, be greater than the angle B, opposite the less side AC. 10. **Let ABC be a triangle; then will the sum of any two...its sides be greater than the third side ; as, for** instance, AC -f- CB greater than AB. 11. Let ABC be a triangle; then will the difference of any two... | |
| 1845
...respectively equal, namely, the angle D=A, the side ED=BA, and the side DF=AC. PROPOSITION X. THEOREM. The nan **of any two sides of a triangle is greater than the...side. Let ABC be a triangle : then will the sum of** two of its sides, as AC, CB, be greater than the third side AB. For the straight line AB is the shortest... | |
| 1845
...of ж2 =c2 — y1, or in that of the area of the triangle deduced from the expression — . ¿ Since **the sum of any two sides of a triangle is greater than the third side,** (Eue. i. 20.) half the sum of any two sides is greater than half the third side : therefore, half the... | |
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