 | 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... | |
 | 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... | |
 | Bengal (India) - 1848 - 520 pages
...+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 than... | |
 | Euclides - 1848 - 52 pages
...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 to... | |
 | Elias Loomis - Conic sections - 1849 - 252 pages
...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 sum... | |
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Any two sides of a triangle are together greater than the third side. 
