| Gerardus Beekman Docharty - 1867 - 283 sider
...supposition. The side AB, then, being neither equal to AC nor less than it, must necessarily be greater. Q- **ED THEOREM x. The sum of any two sides of a triangle...side. Let ABC be a triangle : then will the sum of** two of its sides, as AB+BC, be greater than the third side AC. For the straight line AC is the shortest... | |
| Benjamin Greenleaf - 1868 - 320 sider
...an isosceles triangle are produced, the two exterior angles formed with the base will be equal. 3. **The sum of any two sides of a triangle is greater than the third side.** 4. If from any point within a triangle two straight lines are drawn to the extremities of either side,... | |
| Bernhard Marks - 1869 - 157 sider
...«ind see if yon can go through it without a second reading : — DEMONSTRATION. We wish to prove that **The sum of any two sides of a triangle is greater than the third side. Let** the figure abc be a triangle, then will the sum of any two sides, as ac, cb, be greater than the third... | |
| 1870 - 319 sider
...that the outward angle ABG,ot its equal CBD (Th. iii), is greater than the angle A. Of Triangles. _^__ **THEOREM X. The sum of any two sides of a triangle...third side. Let ABC be a triangle : then will the** scm of two of its sides, as AC, CB, be greater than the third side AB. For the straight line AB is... | |
| Adrien Marie Legendre - 1871 - 187 sider
...therefore equal in all their parts (I., D. 14 ); which was to be proved. PROPOSITION VII. THEOREM. **The sum of any two sides of a triangle is greater...Let ABC be a triangle : then will the sum of any two** sides, as AB, BC, be greater than the third side AC. For, the distance from A to C, measured on any... | |
| Edward Olney - 1872
...than Ai/FB, and AdcdB shorter than McgB. Therefore, AbedB is shorter than ACDEFB. QED 274. COR. 1. — **The sum of any two sides of a triangle is greater than the third side.** This is the same as the axiom that the shortest distance between two points is a straight line. 2 To.... | |
| Edward Olney - 1872 - 201 sider
...AJ/FB, and AicrfB shorter than McgB. Therefore, AbcdB is shorter than ACDEF'BQED 274. COR. 1.—The **sum of any two sides of a triangle is greater than the third side.** This is the same as the axiom that the shortest distance between two points is a straight Hue. 273.... | |
| 1874 - 455 sider
...are therefore equal in all their parts (I., D. 14) ; which was to be proved. PROPOSITION VH. THEOREM. **The sum of any two sides of a triangle is greater than the third side.** I Let AS C be a triangle : then will the sum of any two sides, as AS, SC, be greater than the third... | |
| Charles Davies - 1874
...was to be proved. PROPOSITION VH. THEOREM. Tf1e sum of any two sides of a triangle is greater than **third side. Let ABC be a triangle : then will the sum of any two** sides, as AB, BC, be greater than the third side AC. For, the distance from A to C, measured on any... | |
| William Guy Peck - 1876 - 366 sider
...obtuse•angled ; if all the angles are acute, the triangle is acute•angled. EFH . K PROPOSITION VI. THEOREM. **The sum of any two sides of a triangle is greater than the third side. Let** ACD be any triangle. The distance from A to D, measured on the broken line ACD, is greater than the... | |
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