 | Charles Hutton - Mathematics - 1831 - 632 pages
...and ев, taken together (by constr.) ; therefore AC + ев ¡3 also greater than AB. QED Carol. The shortest distance between two points, is a single...THE difference of any two sides of a triangle, is lese than the third side. Let ABC be a triangle ; then will the difference of any two sides, as AB... | |
 | Charles Hutton - Mathematics - 1831 - 660 pages
...ев, taken together (by constr.) ; therefore AC -f- ев is also greater than AB. a. ED Carol. The shortest distance between two points, is a •single...right line drawn from the one point to the other. ТПЕОВЕ91 XI. THE difference of any two sides of a triangle, is less than the third side. Let... | |
 | Euclid, James Thomson - 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... | |
 | 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.... | |
 | 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... | |
 | Euclides - 1840 - 192 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,... | |
 | Euclid, James Thomson - Geometry - 1845 - 382 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... | |
 | Scottish school-book assoc - 1845 - 444 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... | |
 | Euclides - 1845 - 546 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... | |
 | 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 Difference of any Two Sides of a Triangle, is Less than the Third Side. 
