| James Atkinson - Navigation - 1765 - 504 pages
...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... | |
| Charles Hutton - Mathematics - 1816 - 612 pages
...then, being neither equal to AC, nor less than it, must necessarily be greater, q. ED • THEOREM X. **THE Sum of any Two Sides of a Triangle is Greater than** the Third Side. Let ABC be a triangle ; then will the sun) of any two of its sides be greater than... | |
| Charles Hutton - Mathematics - 1822 - 616 pages
...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 is Greater than** the Third Side. Let ABC be a triangle ; then will the . lum of .ny two of its side* be greater than... | |
| John Playfair - Geometry - 1829 - 210 pages
...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... | |
| Adrien Marie Legendre - Geometry - 1836 - 382 pages
...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 than** the third side. Let ABC be a triangle : then will the sum of two of its sides, as AC, CB, be greater... | |
| William Scott - Measurement - 1845 - 288 pages
...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,... | |
| George Roberts Perkins - Geometry - 1847 - 326 pages
...is neither equal to AC, nor less than it, it must of necessity be greater. PROPOSITION XVI. THEOREM. **The sum of any two sides of a triangle is greater than** the third side. D In the triangle ABC, the sum of the two sides AC and BC is greater than the third... | |
| Samuel Moshaim Schmucker - Apologetics - 1848 - 494 pages
...harmonize. Thus for instance, a whole college of savans might examine for an age the proposition that **the sum of any two sides of a triangle is greater than** the third side ; or the theorem, the square of the hypothenuse is equal to the squares of the other... | |
| Perry Fairfax Nursey - Industrial arts - 1849 - 650 pages
...introducing this subject to the notice of the reader, the author remarks, that " Euclid has demonstrated that **the sum of any two sides of a triangle is greater than** the third side ; and from this proposition Mr. Simpson has solved the very useful problem of finding... | |
| Charles Davies - Trigonometry - 1849 - 372 pages
...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 than** the third side. For the straight line AB is the shortest distance between the points A and B (Def.... | |
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