| Euclides - 1845
...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 - 1845 - 352 sider
...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 - 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. s. Join DC. Then... | |
| Euclides - 1846
...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 - 1846 - 330 sider
...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
...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 - 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 and one... | |
| 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 than... | |
| 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 to... | |
| Elias Loomis - 1849 - 226 sider
...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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