| 1858 - 380 pages
...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... | |
| Elias Loomis - Conic sections - 1858 - 256 pages
...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... | |
| Euclides - 1858 - 248 pages
...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 - 344 pages
...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... | |
| Thomas Sutton - Photography - 1858 - 448 pages
...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 Lund - Geometry - 1859 - 390 pages
...angles. COB. Hence no triangle can have more than one right angle, or one obtuse angle. 38. PROP. XVI. **Any two sides of a triangle are together greater than the third side.** Qlf this be not evident from the fact that the straight line joining any two points is less than any... | |
| Education - 1859 - 414 pages
...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... | |
| Sandhurst roy. military coll - 1859 - 672 pages
...hour-and-a-half after the rider. What is the distance between the two places ? EUCLID, B. 1, 2, 3. 1. **Any two sides of a triangle are together greater than the third.** 2. The straight lines which join the extremities of equal and parallel straight lines toward the same... | |
| Robert Potts - Geometry, Plane - 1860 - 380 pages
...AB ; therefore AC is greater than AB. Wherefore the greater angle, &c. QED PROPOSITION XX. THEOREM. **Any two sides of a triangle are together greater than the third side.** Let ABChe a triangle. Hen any two sides of it together shall be greater than the third side, -viz.... | |
| Royal college of surgeons of England - 1860 - 332 pages
...Kidsummer, 1863. WEDNESDAY, July 15th,— Morning, 12 to 2. GEOMETRY. Examiner — THE REV. G. FEOST, MA 1. **Any two sides of a triangle are together greater than the third side.** 2. If two triangles have two sides of the one equal to two sides of the other, each to each, but the... | |
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