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" THE Difference of any Two Sides of a Triangle, is Less than the Third Side. "
A Course of Mathematics ...: Composed for the Use of the Royal Military ... - Page 275
by Charles Hutton - 1811
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The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846 - 292 pages
...within the triangle ABC but not from the extremities of the base) are together greater than AC, BC. 11. The difference of any two sides of a triangle is less than the third side. 12. Let AB bisect CD at right angles in B ; from any point E draw EC through the nearest extremity...
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The Elements of Geometry, Symbolically Arranged

Great Britain. Admiralty - Geometry - 1846 - 128 pages
...A perpendicular is the least distance of a given point from a given line. 8. The difference between any two sides of a triangle is less than the third side. 9. The difference between the sum of any two sides of a triangle and the third side, is less than twice...
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First Lessons in Geometry: Upon the Model of Colburn's First Lessons in ...

Alpheus Crosby - Geometry - 1847 - 190 pages
...$79. a.) AsBC<BA + AC, BC — ACswBA? 30.3-. And BC — BA «y AC ? COR. i. The difference between any two sides of a triangle is less than the third side. § 80. i.) Given, OB and OC, drawn from any point 0 within 2 ABC, to the extremities of one side BC....
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Iron: An Illustrated Weekly Journal for Iron and Steel ..., Volume 51

Perry Fairfax Nursey - Industrial arts - 1849 - 650 pages
...two given points, their sums shall be the least ; but I do not know that it has ever been shown that the difference of any two sides of a triangle is less than the third side, though this is equally true and useful. I shall therefore demonstrate it in the manner that Euclid...
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The English Journal of Education, Volume 4

Education - 1850 - 488 pages
...of section, divides the vertical angle into two equal angles. SECTION VI. 1. The difference between any two sides of a triangle is less than the third side. 2. The chord of 60° is equal to the radius of the circle. 3. The square of the excess of one straight...
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Minutes of the Committee of Council on Education, Volume 1

Great Britain. Committee on Education - School buildings - 1850 - 790 pages
...shall bisect it. 2. To describe a circle about a given triangle. Section 4. 1. The difference between any two sides of a triangle is less than the third side. 2. Divide a square into four equal portions by three straight lines drawn from any point in one of...
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An Epitome of Navigation and Nautical Astronomy, with Improved Lunar Tables ...

Janet Taylor - Nautical astronomy - 1851 - 674 pages
...together greater than the third side [Eu. i. 20.] or Theorem IX. page 19. From this it follows also, that the difference of any two sides of a triangle is less than the third side. PRACTICAL RULES For the solution of all the different cases of right-angled plane triangles with their...
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Annual Report of the Commissioners ...

1851 - 382 pages
...an equilateral triangle, to construct it, 2. Trisect a right angle, .... 3. The difference between any two sides of a triangle is less than the third side< . , . 4. Prove that (A+B) »-)- (AB) » = 2(A»+B«), 5. Describe a square which shall be equal to...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1852 - 436 pages
...take away either of the sides, as BC, we shall have (A. 5) AC-BC<AB\ that is, the difference between any two sides of a triangle is less than the third side. PROPOSITION VIII. THEOEEM. If from any point loithin a triangle, two straight lines be drawn to the...
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The Elements of Euclid: With Many Additional Propositions ..., Part 1

Euclid - Geometry - 1853 - 176 pages
...greater than the third side BC. COROLLARY. It follows from this proposition that the difference between any two sides of a triangle is less than the third side; for since BA and AC are together greater than BC, if AC be subtracted from each, BA will be greater...
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