 | Euclides - 1846 - 292 σελίδες
...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 - 368 σελίδες
...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... | |
 | Great Britain. Committee on Education - 1847 - 624 σελίδες
...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... | |
 | Euclides - 1847 - 128 σελίδες
...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... | |
 | Euclides - 1848 - 52 σελίδες
...angle of every 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... | |
 | Bengal (India) - 1848 - 520 σελίδες
...+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... | |
 | Euclid, Thomas Tate - 1849 - 120 σελίδες
...is not equal to AB; therefore AC is greater than AB. Wherefore the angle, &c. QED 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,... | |
 | Elias Loomis - 1849 - 252 σελίδες
...DF, each to each, and the angle A to the angle D. Therefore, if two triangles, &c. PROPOSITION VIII. THEOREM. Any two sides of a triangle are together greater than the third side. For the straight line AB is the shortest path between the points A and B (Def. 3); hence AB is less... | |
 | 1884 - 668 σελίδες
...appellation to Euclid, i. 5, is a modern error, and that the original asses' bridge was the proposition, " Any two sides of a triangle are together greater than the third side," the demonstration being that an ass at A will walk along the third side AB to his provender at в,... | |
 | 1884 - 672 σελίδες
...appellation to Euclid, i. 6, is a modern error, and that the original asses' bridge was the proposition, " Any two sides of a triangle are together greater than the third side," the demonstration being that an ass at A will walk along the third side AB to his provender at в,... | |
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Any two sides of a triangle are together greater than the third side. 
