 | Charles Hutton - Mathematics - 1843 - 570 pages
...Prove by means of the equations that connect the sides and angles of a spherical triangle, that (1.) Any two sides of a triangle are together greater than the third. (2.) The difference of two sides is less than the third. (3.) If three sides of a triangle be equal... | |
 | 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... | |
 | 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...third side. Let ABC be a triangle ; any two sides of it together are greater than the third side, viz. the sides BA, AC greater than the side BC ; and AB,... | |
 | 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... | |
 | 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.... | |
 | 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,... | |
 | 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...third side. Let ABC be a triangle ; any two sides of it together are greater than the third side, viz. the sides BA, AC greater than the side BC ; and AB,... | |
 | 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... | |
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Any two sides of a triangle are together greater than the third side. 
