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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 ... - Σελίδα 44
των Euclides - 1884
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Epitome of the Art of Navigation; Or, a Short, Easy, and Methodical Way to ...

James Atkinson - 1765 - 504 σελίδες
...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...

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

Charles Hutton - 1816 - 610 σελίδες
...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...

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

Charles Hutton - 1822 - 616 σελίδες
...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...

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

John Playfair - 1829 - 210 σελίδες
...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...

Elements of Geometry and Trigonometry

Adrien Marie Legendre - 1836 - 394 σελίδες
...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...

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

William Scott - 1845 - 288 σελίδες
...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,...

Elements of Geometry: With Practical Applications ...

George Roberts Perkins - 1847 - 326 σελίδες
...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...

The Errors of Modern Infidelity: Illustrated and Refuted

Samuel Moshaim Schmucker - 1848 - 494 σελίδες
...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...

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

Perry Fairfax Nursey - 1849 - 650 σελίδες
...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...

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

Charles Davies - 1849 - 372 σελίδες
...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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