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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 Mechanic's Calculator: Comprehending Principles, Rules, and Tables in ...

William Grier - Mechanical engineering - 1836 - 344 pages
...any two of its sides be greater than the third side; as, for instance, AC -(- CB greater than AB. 11. Let ABC be a triangle ; then will the difference of...two sides, as AB — AC, be less than the third side BC. 12. Let the line EF cut the two parallel lines AB, CD ; then will the angle AKF be equal to the...
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The Mechanic's Calculator: Comprehending Principles, Rules, and Tables in ...

William Grier - Mechanical engineering - 1836 - 380 pages
...any two of its sides be greater than the third side; as, for instance, AC + CB greater than AB. 1 1. Let ABC be a triangle ; then will the difference of...two sides, as AB — AC, be less than the third side BC. 12. Let the line EF cut the two parallel lines AB, CD; then will the angle AEF be equal to the...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1836 - 359 pages
...will mutually coincide. PROPOSITION VII. THEOREM. 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...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid - Geometry - 1837 - 410 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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Lessons on Form: Or, An Introduction to Geometry, as Given in a Pestalozzian ...

Charles Reiner - Geometry - 1837 - 246 pages
...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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The Mechanic's Calculator: Comprehending Principles, Rules, and Tables in ...

William Grier - Mechanical engineering - 1839 - 344 pages
...two of its sides be greater than the third side ; as, for instance, AC + CB greater than AB. 1 1 . Let ABC be a triangle ; then will the difference of any two sides, as AB — AC, be less thairthe third side Bp. 12. Let the line EF cut the two parallel lines AB, CD ; then will the angle...
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The figures of Euclid with the enunciations, as printed in Euclid's Elements ...

Euclides - 1840 - 82 pages
...sides of a triangle are together greater than the third side. COR..—Hence the difference between any two sides of a triangle is less than the third side. • '•'.> Sllj ' (•'>: ••••': -• : i •hnnjd.'i? ..!.• r 1 ' 1 PROP. XXI. THEOR. If...
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Euclid's Elements of plane geometry [book 1-6] with explanatory appendix ...

Euclides - 1840 - 194 pages
...(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,...
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The Mechanic's Calculator: Comprehending Principles, Rules, and Tables in ...

William Grier - Mechanical engineering - 1842 - 320 pages
...two of its sides be greater than the third side ; as, for instance, AC -f- CB greater than AB. 11. Let ABC be a triangle; then will the difference of any two sides, as AB—AC, be less than the third side BC. 12. Let the line EF cut the two parallel lines AB, CD; then...
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A system of practical mathematics; being no.xvi. of a new series of school-books

Scottish school-book assoc - 1845 - 434 pages
...lines cut one another, a straight line be drawn to the third angle, it will bisect the third angle. 4. The difference of any two sides of a triangle is less than the third side. 5. The sum of two sides of a triangle is greater than twice the straight line drawn from the vertex...
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