...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 ;...

...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...

...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...

...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...

...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...

...+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...

...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...

...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,...

...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,...

...sides of a triangle be unequal, the greater side has the greater angle opposite. 8. Prove Euc. 1. '.iO. Any two sides of a triangle are together greater than the third tide. 9. Prove Kuc. I. 48. If the square described upon one side of a triangle be equal to the squares...