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" AB>AC-BC: that is, the difference of any two sides of a triangle is less than the third side. "
A Course of Mathematics: In Two Volumes. For the Use of Academies, as Well ... - Page 257
by Charles Hutton - 1818
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Elements of geometry, based on Euclid, book i

Edward Atkins - 1877 - 68 pages
...a given point within, then the line bisecting the third angle will pass through the same point. 22. The difference of any two sides of a triangle is less than the third side. 23. If the angles at the base of a right-angled isosceles triangle be bisected, the bisecting lins...
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Elementary geometry

James Maurice Wilson - 1878 - 448 pages
...But AD is equal to AB and BC together, therefore AB and BC are together greater than AC\. QED COR. The difference of any two sides of a triangle is less than the third side. THEOREM 13. If from the ends of the side of a triangle two straight lines be drawn to a point within...
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Mathews' Euclid examination papers ... on Euc. i.-iv

Edward Harri Mathews - 1879 - 90 pages
...sides of a triangle are together greater than the third side. Hence prove that the difference between any two sides of a triangle is less than the third side. Section II. 1. If a side of any triangle be produced, the exterior angle is equal to the two interior...
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The Oxford examiner, ed. by M.W.I. Shilleto, Issues 1-5

Mary W I. Shilleto - 1882 - 414 pages
...angles to the given line. 2. Any two sides of a triangle are together greater than the third side. The difference of any two sides of a triangle is less than the third side. 3. If a straight line be divided into two equal parts, and also into two unequal parts, the rectangle...
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Geometrical Exercises for Beginners

Samuel Constable - Geometry - 1882 - 218 pages
...I. 21.] 3. Prove, by showing that the angle BDC is greater than the angle BCD in fig. Prop. 13, that the difference of any two sides of a triangle is less than the third. 4. Prove that the angle included between any two straight lines is equal to the angle included between...
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Class lessons on Euclid

Marianne Nops - 1882 - 274 pages
...as a fraction of a right angle the interior angle of a regular octagon. 13. The difference between any two sides of a triangle is less than the third side. 14. Describe an equilateral triangle having its side equal to a given finite straight line, and having...
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Syllabus of plane geometry, books 1-3, corresponding to Euclid, books 1-4 ...

Mathematical association - 1883 - 86 pages
...opposite to it. THEOR. 13. Any two sides of a triangle are together greater than the third side. COR. The difference of any two sides of a triangle is less than the third side. THEOR. 14. If from the ends of a side of a triangle two straight lines are drawn to a point within...
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The Elements of Euclid, books i. to vi., with deductions, appendices and ...

Euclides - 1884 - 434 pages
...any two sides ; .-. the sum of any two sides of a triangle is greater than the third side. COR. — The difference of any two sides of a triangle is less than the third side. For BA + AC is greater than BC. I. 20 Taking AC from each of these unequals, there remains BA greater...
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The elements of plane geometry, Volume 1

Mathematical association - 1884 - 146 pages
...Similarly it may be shown that AC and CB are together greater than AB, and CB and BA than AC. QED COR. The difference of any two sides of a triangle is less than the third side. D 2 *Ex. 1 8. The straight line drawn from the vertex of a triangle to the middle point of the base...
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Knowledge: An Illustrated Magazine of Science, Volume 5

Science - 1884 - 534 pages
...PQ. Let QD cut А В in E, and join EP : with this construction the proof is obvious. PROP. 20. 54. The difference of any two sides of a triangle is less than the third side. 55. A point P is taken within the triangle А В С ; show that the cum of the distances PA, PB, and...
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