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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

Minutes of the Committee of Council on Education, Volume 1

...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...

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...

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...

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...

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...

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...

The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

...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,...

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...