 | sir Thomas Dyke Acland (11th bart.) - 1858 - 270 ページ
...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... | |
 | Elias Loomis - 1858 - 256 ページ
...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... | |
 | Thomas Sutton - 1858 - 344 ページ
...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... | |
 | Euclides - 1858 - 248 ページ
...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 - 448 ページ
...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 - 1859 - 390 ページ
...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... | |
 | 1859 - 414 ページ
...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 ページ
...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... | |
 | Royal college of surgeons of England - 1860 - 332 ページ
...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... | |
 | Euclides - 1860 - 288 ページ
...is not equal to AB ; therefore AC is greater than AB." .* ',", PROPOSITION XX. THEOREM. '•,'. ;r:! Any two sides of a triangle are together greater than the third side. Given a triangle ABC ; to prove that any two sides, of it together are greater than the third side;... | |
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Any two sides of a triangle are together greater than the third side. 
