| 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 added together,... | |
| Charles Hutton - Mathematics - 1811 - 406 pages
...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 - Mathematics - 1816 - 610 pages
...side AB, 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...Third Side. Let ABC be a triangle ; then will the** sun) of any two of its sides be greater than -D the third side, as for instances, AC + CB S greater... | |
| Charles Hutton - Mathematics - 1822 - 616 pages
...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 - 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 and opposite... | |
| Charles Hutton - Mathematics - 1831 - 660 pages
...equal to AC, nor less than it, must necessarily be greater, a. ED T1IEOBEH X. THE sum of any two sidtes **of a triangle is greater than the third side. Let ABC be a triangle ; then will the** тч sum of any two of its sides be greater , than the third side, as for instance, ft ^ AC + ев... | |
| 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, half the... | |
| 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 side AB. For, produce... | |
| 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 two sides ; and... | |
| 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 a point in a... | |
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