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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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The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1845 - 380 pages
...sides AB, BC are greater than CA, and BC, CA greater than AB. Therefore, any two sides, &c. Cor. Hence the difference of any two sides of a triangle, is less than the third side. For, since BA and AC are together greater than BC, from each of these take AC ; then (I. ax. 5) BA...
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845 - 544 pages
...ED produced meet AB produced in F ; then 3 . AEF = 2 right angles + AFE. 6. The difference between any two sides of a triangle is less than the third side. 7. ABC is/ a triangle right-angled at B, and having the angle A double the angle C; shew that the side...
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Elements of plane (solid) geometry (Higher geometry) and trigonometry (and ...

Nathan Scholfield - 1845 - 896 pages
...ED=BA, and the side DF=AC. PROPOSITION X. THEOREM. The nan 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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A collection of examples in pure and mixed mathematics, with hints and ...

Alfred Wrigley - 1845 - 222 pages
...given finite straight line. (Euclid, i. 9, 28. Cape, prob. 5, and i. 20.) Ю. The difference between any two sides of a triangle is less than the third side. (Euclid, i. 16, 19. Cape, i. 10, 11.) 11. If any two sides of a triangle be bisected, and from the...
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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 - 130 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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Elementary Geometry: With Applications in Mensuration

Charles Davies - Geometry - 1850 - 236 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. D For, the straight line AD...
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The English Journal of Education, Volume 4

Education - 1850 - 484 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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