| Royal Society of Edinburgh - Science - 1880 - 864 pages
...space : — That the greater side of every triangle has the greater angl* opposite, and conversely. **That any two sides of a triangle are together greater than the third side.** Also Euclid I. 21. Euclid I. 24 and 25. Euclid I. 26 (the second part). Also the usual propositions... | |
| Euclides - 1845 - 546 pages
...AB ; therefore AC is greater than AB. Wherefore the greater angle, &c. QED PROPOSITION XX. THEOREM. **Any two sides of a triangle are together greater than the third side.** Let ABC be a triangle. Then any two sides of it together shall be greater than the third side, viz.... | |
| Euclid - Geometry - 1845 - 218 pages
...; therefore AC is greater than AB. Wherefore the greater angle, &c. QED PROPOSITION 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 sides... | |
| Scottish school-book assoc - 1845 - 444 pages
...together less than AB, the circles would not intersect, and the construction, would be impossible ; hence **any two sides of a triangle are together greater than the third,** which is established in a different manner in (Prop. 13.) PROPOSITION V. — THEOREM. If two triangles,... | |
| Euclides, James Thomson - Geometry - 1845 - 382 pages
...not equal to AB : therefore AC is greater than AB. Wherefore, if two angles, &c. PROP. XX. THEOB. — **Any two sides of a triangle are together greater than the third** side.t * Let the learner compare thia proposition and the following with the 5th and G1h of this book.... | |
| Great Britain. Admiralty - Geometry - 1846 - 128 pages
...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. s. Join... | |
| Euclides - 1846 - 292 pages
...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, AC greater... | |
| Sir J. Butler Williams - Geodesy - 1846 - 368 pages
...than the true length : this follows from Euclid's 20th proposition of the first book, which proves **that any two sides of a triangle are together greater than the third.** Also, the frequent repetition of errors in the coincidence of the extremities of the chain with the... | |
| Euclid, John Playfair - Euclid's Elements - 1846 - 334 pages
...and it has been shewn that it is not equal to AB ; therefore AC is greater than AB. 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 sides... | |
| Great Britain. Committee on Education - Education - 1847 - 624 pages
...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 and one... | |
| |