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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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A Treatise on Special, Or Elementary Geometry

Edward Olney - Geometry - 1872 - 472 pages
...the shortest distance between two points is a straight liue. 275. COR. 2. — The difference between any two sides of a triangle is less than the third side. DEM.— Let a, b, and e be the sides. By Corollary 1st, a + b.> e. Therefore, transposing, a > с —...
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A Treatise on Special Or Elementary Geometry, Volumes 1-2

Edward Olney - Geometry - 1872 - 566 pages
...shortest distance between two points is a straight line. 2 To. COR. 2. — TJie difference bet 'ween any two sides of a triangle is less than the third side. DEM. — Let a, b, and e be the sides. By Corollary 1st, a + b > e. Therefore, transposing, a > e —...
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Pure mathematics, Volume 1

Edward Atkins - 1874 - 424 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 line...
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Elements of Euclid [selections from book 1-6] adapted to modern methods in ...

Euclides - 1874 - 234 pages
...opposite side. 2. By letting fall a perpendicular from any angle on the opposite side. Cor. — Hence the difference of any two sides of a triangle is less than the third side. For since AB and BC are greater than AC, if BC be taken from both, we shall have (ax. 5.) AB greater...
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Euclidian Geometry

Francis Cuthbertson - Euclid's Elements - 1874 - 396 pages
...the opposite sides are together greater than the semi-perimeter of the A . 19. The difference between any two sides of a triangle is less than the third side. 20. Find the shortest path from a given point in one of two straight lines to the other, and then back...
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Elements of Geometry and Trigonometry: From the Works of A.M. Legendre

Adrien Marie Legendre - Geometry - 1874 - 512 pages
...AS, SC, as SC, for example, there will remain (A. 5), AC - SC < AS; that is, the difference between any two sides of a triangle is less than the third side. Scholium. In order that any three given lines may represent the sides of a triangle, the sum of any...
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Manual of Geometry and Conic Sections: With Applications to Trigonometry and ...

William Guy Peck - Conic sections - 1876 - 376 pages
...the distance measured on the straight line AD; hence, AC + CD > DA; (1) which was to be proved. Cor. The difference of any two sides of a triangle is less than the third side. For, if from both members of (1), we subtract either AC, or CD, say AC, we have CD > DA - AC, or DA...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - Geometry - 1876 - 446 pages
...however near the point A may be to the line BC. It may be easily shewn from this proposition, that the difference of any two sides of a triangle is less than the third side. Prop. xxn. When tlie sum of two of the lines is equal to, and when it is less than, the third line;...
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Syllabus of Plane Geometry: (corresponding to Euclid, Books I-VI) ...

Association for the improvement of geometrical teaching - Geometry, Modern - 1876 - 66 pages
...opposite to it. PHEOR. 12. 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. 13. If from the ends of the side of a triangle two straight lines are drawn to a point within...
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Elements of geometry, based on Euclid, books i-iii

Edward Atkins - 1876 - 130 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 lino...
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