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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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Minutes of the Committee of Council on Education, Volume 1

Great Britain. Committee on Education - School buildings - 1850
...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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Elementary Geometry: With Applications in Mensuration

Charles Davies - Geometry - 1850 - 218 pages
...greater than the angle C, Of Triangles. 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 sum of two of its sides, as AC, CB, be greater than the third side AB. For, the straight line AB is...
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An Epitome of Navigation and Nautical Astronomy, with Improved Lunar Tables ...

Janet Taylor - Nautical astronomy - 1851 - 702 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
...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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The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

Royal Military Academy, Woolwich - Mathematics - 1853
...the angles at the vertex made by producing the equal sides of the triangle. 3. The difference between any two sides of a triangle is less than the third side. 4. If two straight lines which meet one another be parallel to two other lines which meet one another,...
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Elements of Geometry, Plane and Spherical Trigonometry and Conic Sections

Horatio Nelson Robinson - Conic sections - 1854 - 350 pages
...scholium), therefore, AC is common to the two A's ABC, ADC; and the A's are identical. QED THEOREM 18. The difference of any two sides of a triangle is less than the third tide. Let ABC be the A, and let AC be greater than AB; then we are to prove that AC — AB is less...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - Geometry - 1854 - 436 pages
...coincide. 26 GEOMETRY. PROPOSITION vl1. 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 AB, BC, be greater than the third side AC For the straight line AC is the...
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Elements of Geometry and Trigonometry: From the Works of A.M. Legendre

Adrien Marie Legendre - Geometry - 1857 - 444 pages
...take away either of the sides, as BC, we shall have (JL.5) AC-BC<AB: that is, the difference between any two sides of a triangle is less than the third side. PROPOSITION VIII. TIIEOREM. If from any point within a triangle, two straight lines be drawn to the...
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