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" America, but know that we are alive, that two and two make four, and that the sum of any two sides of a triangle is greater than the third side. "
The Elements of Euclid, books i. to vi., with deductions, appendices and ... - Page 44
by Euclides - 1884
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Epitome of the Art of Navigation; Or, a Short, Easy, and Methodical Way to ...

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...
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A Course of Mathematics: In Two Volumes : for the Use of Academies ..., Volume 1

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...
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A Course of Mathematics: For the Use of Academies, as Well as Private ...

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...
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Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry

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...
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Elements of Geometry and Trigonometry

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...
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Plane Trigonometry and Mensuration for the Use of the Royal Military College

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,...
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Elements of Geometry: With Practical Applications ...

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...
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The Errors of Modern Infidelity: Illustrated and Refuted

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...
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Iron: An Illustrated Weekly Journal for Iron and Steel ..., Volume 51

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...
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Elements of Geometry and Trigonometry Translated from the French of A.M ...

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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