| Royal college of surgeons of England - 1860
...the same : and thence show that two straight lines cannot have a common segment. 4. If the side of a **triangle be produced, the exterior angle is equal...every triangle are together equal to two right angles.** 5. Describe a square on a given straight line. 6. Define " a gnomon" and " a rectangle." 7. The parallelograms... | |
| Euclides - 1860
...drawn through the given point A parallel to the given straight line BC. PROPOSITION XXXII. THEOREM. **If a side of any triangle be produced, the exterior...and the three interior angles of every triangle are** equal to two right angles. Given a triangle ABC, having one of its sides BC produced to D ; to prove... | |
| EDUCATION SOCIETY'S PRESS, CULLA - 1860
...\ , <z, O\ '4' 3v A ' 4\ K ' 2 ^ 3 6. If a side of any triangle be produced, the exterior nngle ia **equal to the two interior and opposite angles; and the three interior angles of every triangle are** equal to two right angles. Show how the corners of a triangular piece of paper may be turned down,... | |
| Young Men's Christian Associations (London, England) - Christianity - 1860
...a triangle be produced, the exterior angle is equal to the sum of the two angles which subtend it ; **and the three interior angles of every triangle are together equal to two right angles."** One day, when he was busied with the demonstration of this theorem, his father caught him in the act... | |
| John Playfair - Geometry - 1860 - 317 pages
...PROP. XXXII. TIIEOR. If a side of any triangle lie produced, the exterior angle is equal to the tiro **interior and opposite angles ; and the three interior angles of every triangle are** equal to two right angles. Let ABC be a triangle, and let one of its sides BC be produced to D ; the... | |
| John Fellows - Mysteries, Religious - 1860 - 366 pages
...four. Of the geometrical theorems ascribed to Pythagoras, the following are the principal ; that the **interior angles of every triangle are together equal to two right angles;** that the only polygons which fill up the whole space about a given point, are the equilateral triangle,... | |
| Woolwich roy. military acad - 1861
...I0«(s-s1)=*2-s. 9. Find the value of - — --- Q'^— by means of 10o the logarithmic tables. 10. **If a side of any triangle be produced, the exterior...and the three interior angles of every triangle are** equal to two right angles. The angle between the lines bisecting two adjacent exterior angles of any... | |
| Mary W I. Shilleto - 1882
...In Euclid's figure for this proposition, if BG, CF meet in H, show that AH bisects the angle BAG. 2. **If a side of any triangle be produced, the exterior...and the three interior angles of every triangle are** equal to two right angles. Enunciate and prove the corollaries to this proposition. Trisect a right... | |
| Herbert Spencer - Psychology - 1882
...case. therefore also the angles CBA, BAC, ACB, are together equal to two right angles. " Therefore **if a side of any triangle be produced, the exterior...and the three interior angles of every triangle are** equal to two right angles. QED" Thus in each step by which the special conclusion is reached, as well... | |
| College of preceptors - 1882
...any triangle ABO is bisected by Bit, which cuts the base in D ; prove that BO is greater than GD. 4. **The three interior angles of every triangle are together equal to two right angles.** Enunciate the two corollaries of this Proposition, but give the proof of the second corollary only.... | |
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