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" The difference between any two sides of a triangle is less than the third side. "
The Elements of Euclid: With Many Additional Propositions, & Explanatory ... - Page 13
by Euclid - 1853 - 136 pages
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A Course of Mathematics: In Two Volumes : for the Use of Academies ..., Volume 1

Charles Hutton - Mathematics - 1816 - 610 pages
...points, is a single right line drawn from the one point to the other. THEOREM XI. THE Difference of any Two Sides of a Triangle, is LesS than the Third Side. Let ABC be a triangle ; then will the difference of any two sides, as AB — AC, be less than the third...
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Elements of Geometry, and Plane Trigonometry: With an Appendix, and Very ...

Sir John Leslie - Geometry, Modern - 1820 - 488 pages
...and BC, the two sides AB and BC are together greater than the third side Ac. PROP. XV. THEOR. ;. : The difference between any two sides of a triangle is less than the third side. Let the side AC be greater than AB, and from it cut off a part AE equal to AB; the remainder EC is...
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A Course of Mathematics: For the Use of Academies, as Well as Private ...

Charles Hutton - Mathematics - 1822 - 616 pages
...points, is a single right line drawn from the one point to the other. THEOREM XI. THK Difference of any Two Sides of a Triangle, is Less than the Third Side. Let ABC be a triangle ; then will the difference of any two sides, as AB — AC, be less than the third...
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Dictionary of the Mathematical and Physical Sciences, According to the ...

James Mitchell - Mathematics - 1823 - 666 pages
...known geometrical problem, though it is not found in Muclid's " Elements;" viz. "The difference of any two sides of a triangle is less than the third side." PROS. 4. Giving the hypothenuse of aright-angled triangle, and the side of its inscribed square, to...
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Elements of Geometry, Containing the First Six Books of Euclid

Euclid - 1826 - 234 pages
...вс, CA, greater than AB. Therefore two sides of every triangle, &c. Deductions. 1 . The difference of any two sides of a triangle is less than the third side. 2. Two sides of a triangle are together greater thaa twice the line from the vertex bisecting the base....
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Euclid's Elements of geometry, transl. To which are added, algebraic ...

Euclides - 1826 - 226 pages
...вс, CA, greater than AB. Therefore two sides of every triangle, &c. Deductions. 1. The difference of any two sides of a triangle is less than the third side. 2. Two sides of a triangle are together greater than twice the line from the vertex bisecting the base....
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Elements of Arithmetic, Algebra, and Geometry

George Lees - 1826 - 276 pages
...more remote ; there can be two equal lines, but there cannot be more than two. 5. The difference of any two sides of a triangle is less than the third side. 6. If, from the vertex of a triangle, two straight lines be drawn, one of which is perpendicular to...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1837 - 410 pages
...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...For, since BA and AC are together greater than BC, from each of these take AC; then (I. ax. 5.) BA is greater than the excess of BC above AC. PROP. XXI....
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Lessons on Form: Or, An Introduction to Geometry, as Given in a Pestalozzian ...

Charles Reiner - Geometry - 1837 - 246 pages
...by the greater side. 14. Any two sides of a triangle are together greater than the third side. 15. The difference between any two sides of a triangle is less than the third side. 16. The three sides of every triangle are together greater than double the length of any one side....
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Euclid's Elements of plane geometry [book 1-6] with explanatory appendix ...

Euclides - 1840 - 192 pages
...19). But BD = BA + AC (const.), which are therefore greater than the third side BC. COR. — Hence the difference between any two sides of a triangle is less than the third side. For the greater of those two sides is equal to the less side and the difference between them ; but, by...
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