| Education - 1844 - 688 pages
...sides of the one shall be equal to the angle contained by the two sides equal to them of the other. 3. **Any two sides of a triangle are together greater than the third side.** 4. The straight lines which join the extremities of two equal and parallel straight lines towards the... | |
| John Playfair - Euclid's Elements - 1844 - 338 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** suie. Let ABC be a triangle ; any two sides of it together arc greater than the third side, viz. the... | |
| Royal Society of Edinburgh - Science - 1880 - 864 pages
...: — 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... | |
| 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 - 1845 - 546 pages
...pass through the point A, let it fall otherwise, if possible, as FGDH, and join AF, AG. Then, because **two sides of a triangle are together greater than the third side,** (i. 20.) therefore FG, GA are greater than FA : but FA is equal to FH ; (i. def. 15.) therefore FG,... | |
| Euclid, 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 DC. Then... | |
| Euclides - 1846 - 292 pages
...the triangle, but contain an angle BDC greater than the angle BAC. Produce BD to E : Then, because **any two sides of a triangle are together greater than the third side** (1. 20), the two sides, BA, AE, of the triangle ABE are greater than BE : To each of these add EC ;... | |
| Sir J. Butler Williams - Geodesy - 1846 - 368 pages
...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... | |
| Euclides - 1847 - 128 pages
...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., BA... | |
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