| Euclides - 1846
...equal to it ; therefore AC is greater than AB. Wherefore, The greater angle %c. QED PROP. XX. THEOR. **Any two sides of a triangle are together greater than the third** side. Let ABC be a triangle : any two sides of it are together greater than the third side, viz. BA,... | |
| Great Britain. Admiralty - 1846
...It has been shown that AC ^ AB, AC > AB. Therefore the greater Z., &c. PROP. XIX. THEOR. 20. 1 Eu. **Any two sides of a triangle are together greater than the third** side. Let ABC be a <^, then AB + AC> BC, AB+ BOAC, BC + AC> AB. Produce BA to D. Make AD = AC. Prop.... | |
| Great Britain. Committee on Education - 1847
...equal to two right angles, these two straight lines shall be in one and the same straight line. 2. **Any two sides of a triangle are together greater than the third** side. Section II. 1. To divide a straight line into two such parts that the rectangle of the whole... | |
| Euclides - 1847
...is > AC — BC, and AC > BC — AB. Wherefore any side Sec.— QED PROP. XX. THEOR. GEN. ENUN. — **Any two sides of a triangle are together greater than the third** side. PART. ENUN. — Let ABC be any A. Then the sum of any two of its sides is > the third side, viz.,... | |
| Euclides - 1848
...triangle is subtended by the greater side, or has the greater side opposite to it. PROP. XX. THEOREM. **Any two sides of a triangle are together greater than the third** side. PROP. XXI. THEOREM. If from the ends of a side of a triangle, there be drawn two straight lines... | |
| Bengal (India) - 1848
...+P xa~l+P xn-z+ ........ +J» = 0 J * n and in the quadratic equation »* — px + </=0 Geometry. 6. **Any two sides of a triangle are together greater than the third** side. 7. In a circle, the angle in a semicircle is a right angle, but the angle in a segment greater... | |
| Euclides, Thomas Tate - 1849 - 108 páginas
...is not equal to AB; therefore AC is greater than AB. Wherefore the angle, &c. QED PROP. XX. THEOR. **Any two sides of a triangle are together greater than the third** side, Let ABC be a triangle; any two sides of it together are greater than the third side, viz. the... | |
| 1884
...appellation to Euclid, i. 5, is a modern error, and that the original asses' bridge was the proposition, " **Any two sides of a triangle are together greater than the third** side," the demonstration being that an ass at A will walk along the third side AB to his provender... | |
| Elias Loomis - 1849 - 226 páginas
...difference. Let two circumferences cut each other in the point A. Draw the radii CA, DA ; then, because **any two sides of a triangle are together greater than the third** side (Prop. VIII., B. I.), CD must be less than the sum of AD and AC. Also, DA must be less than the... | |
| 1884
...appellation to Euclid, i. 6, is a modern error, and that the original asses' bridge was the proposition, " **Any two sides of a triangle are together greater than the third** side," the demonstration being that an ass at A will walk along the third side AB to his provender... | |
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