...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...

...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...side, viz. the sides BA, AC greater than the side BC ; and AB, BC greater than AC ; and BC, CA greater than AB. (i. 3.) AD equal to AC ; and join DC. ,..---'/...

...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...

...plane triangle, it will cut the other two sides proportionally, [Eu. vi. 2.] or Theorem D, page 26. Any two sides of a triangle are together greater than the third side [Eu. i. 20.] or Theorem IX. page 19. From this it follows also, that the difference of any two sides...

...another, the side opposite that angle is greater than the side opposite the other.] PROP. XX. THEOR. Any two sides of a triangle are together greater than...side, viz. the sides BA, AC greater than the side BC ; and AB, BC greater than AC ; and BC, CA greater than AB. Produce BA to the point D, and make a AD...

...the side is greater than, equal to, or less than the angle opposite to the other. PEOP. XX. ТНЕOB. Any two sides of a triangle are together greater than the third side. In the triangle ABC, the sides л в and в c „ are greater than AC, the sides вc and CA are greater,...

...an assertion relating to the mind is proved by an induction as wide as that on which we believe that any two sides of a triangle are together greater than the third, we have a right to suppose it true for us ; we feel it to be true by our intuition, our experience...