| 1856
...restriction is plain, when we consider that he had previously proved in his Prop. XX., Book I. that **any two sides of a triangle are together greater than the third.** This, however, is manifest without demonstration, if we adopt Archimedes's definición of a straight... | |
| Middle-class education - 1857
...line. What figure would be formed by placing two equilateral triangles base to base ? 81. Prove that **any two sides of a triangle are together greater than the third side.** Is the same proposition true of the angles of a triangle ? Give reasons for your answer. 32. Prove... | |
| JOHN GRAY - 1857
...each ? 5. If a : b : : c : d show that a + b : J : : c + d : d and that am : b" : : C" : d" EUCLID. 1. **Any two sides of a triangle are together greater than the third side.** the squares of the sides containing it by twice the rectangle contained by the side upon which, when... | |
| Elias Loomis - 1858 - 234 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... | |
| sir Thomas Dyke Acland (11th bart.) - 1858
...line. What figure would be formed by placing two equilateral triangles base to base ? 31. Prove that **any two sides of a triangle are together greater than the third side.** Is the same proposition true of the angles of a triangle? Give reasons for your answer. 32. Prove geometrically... | |
| 1858
...plane rectilineal angle, and show how to bisect one, that is, to divide it into two equal angles. 2. **Any two sides of a triangle are together greater than the third side.** Is the same proposition true of the angles of a triangle? 3. What is a parallelogram? Prove that the... | |
| Euclides - 1858
...given difference A D. The figure ABC therefore is the triangle required. PROP. 20.— THEOR. side. **Any two sides of a triangle are together greater than the third** CONSTRUCTION. — Pst. 2. A st. line may be lengthened out in a st. line. P. 3. From the greater line... | |
| Thomas Sutton - 1858 - 423 sider
...Petzval's arrangement ; for it appears that CO is greater than Cm. The proof of this is easy enough. **Any two sides of a triangle are, together, greater than the third,** therefore OC and CA are together greater than AO, and therefore than Km. Take away the common part... | |
| Thomas Sutton - 1858
...Petzval's arrangement ; for it appears that С 1 is greater than С m. The proof of this is easy enough. **Any two sides of a triangle are, together, greater than the third,** therefore 1 С and С A are together greater than A 1, and therefore than A m. Take away the common... | |
| 1859
...the sides also which subtend, or are opposite to the equal angles, shall be equal to one another. 4. **Any two sides of a triangle are together greater than the third side.** The difference of any two sides of a triangle is always less than the third side. 5. The three interior... | |
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