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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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Collection of Examples and Problems in Pure and Mixed Mathematics: With ...

Alfred Wrigley - Mathematics - 1862 - 330 pages
...which it shall be the diagonal. 9. To trisect a given finite straight line. 10. The difference between any two sides of a triangle is less than the third side. 11. If any two sides of a triangle be bisected, and from the middle points, perpendiculars be drawn...
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Conic Sections and Analytical Geometry: Theoretically and Practically ...

Horatio Nelson Robinson - Conic sections - 1863 - 350 pages
...EG. Because EF is equal to EG we have EF'—EF=EF'—EG. But EF' — EG, is less than F'G, because the difference of any two sides of a triangle is less than the third side. That is, EF' — EF is less than A' A; consequently the point E is without the curve (Prop. 2), and...
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Euclid's plane geometry, practically applied; book i, with explanatory notes ...

Euclides - 1863 - 72 pages
...than CE : And BA -f- AC > BE + CE, which are equal to BC. Therefore any two sides, &c. QED CoR. — The difference of any two sides of a triangle is less than the rem. side. D. 1 by P. 20. The sides AC and BC are > AB ; 2 Sub. take AC both from (AC + BC,) and also...
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The school edition. Euclid's Elements of geometry, the first six books, by R ...

Euclides - 1864 - 448 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 the sum of two of the lines is equal to, and when it is less than, the third line ;...
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Report of the Secretary for Public Instruction ...

Queensland. Department of Public Instruction - Education - 1866 - 332 pages
...any two sides of a triangle are together greater than the third side. Show from this proposition that the difference of any two sides of a triangle is less than the third side. 4. Prove that in any right-angled triangle, the square which is described upon the side subtending...
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The College Euclid: Comprising the First Six and the Parts of the Eleventh ...

Euclides - 1865 - 402 pages
...be drawn from the given point to the given straight line, one on each side of the perpendicular. 19. The difference of any two sides of a triangle is less than the third. 20. The three sides of a triangle taken together are greater than the double of any one side, but less...
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Elements of Plane and Solid Geometry: And of Plane and Spherical ...

Gerardus Beekman Docharty - Geometry - 1867 - 474 pages
...Corol. If from both members of the inequality we subtract the side BC, we shall have AB>AC-BC: that is, the difference of any two sides of a triangle is less than the third side. THEOREM XI. If from a point within a triangle two lines be drawn to the extremities of either side,...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1868 - 434 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 the sum of two of the lines is equal to, and when it is less than, the third line ;...
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Gradations in Euclid : books i. and ii., with an explanatory preface [&c ...

Euclides - 1870 - 270 pages
...and AC > BE and CE, which arc' equal to BC. Recap. Therefore, any two sides, &c. QED COR. — Tlie difference of any two sides of a triangle is less than the remaining side. DEM. 1 by P. 20. Sub. Ax. 5. The sides AC and BC are >AB ; take away AC both from (AC...
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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - Geometry - 1871 - 302 pages
...Book V. has been studied GEOMETRICAL EXERCISES ON BOOK I. THEOREMS. Prop. 1 . The difference between any two sides of a triangle is less than the third side. Prop. 2. The sum of the diagonals of a quadrilateral is less than the sum of any four lines that can...
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