| Elias Loomis - Conic sections - 1858 - 234 pages
...PROPOSITION XXVII. THEOREM. If one side of a triangle is produced, the exterior angle tn equal to the sum of **the two interior and opposite angles ; and the three interior angles of every triangle are** equal to two right angles. ^et ABC be any plane triangle, and let the side BC be produced uo D ; then... | |
| Sandhurst roy. military coll - 1859 - 1869 pages
...of -0031843449. EUCLID. 1. If a side of a triangle be produced the exterior angle is equal to both **the two interior and opposite angles, and the three...every triangle are together equal to two right angles.** Hence show that all the exterior angles of any rectilineal figure made by producing the sides successively... | |
| Education - 1859
...than the third side. Madras ^e difference of any two sides is always less than the third side. " 4. **The three interior angles of every triangle are together equal to two right angles.** How many degrees are there in an angle of a regular octagon? 5. In any right angled triangle, tire... | |
| Anthony Nesbit - Measurement - 1859 - 450 pages
...produced to D; the exterior angle ACD is equal to the two interior and opposite angles CAB, ABC ; also **the three interior angles of every triangle are together equal to two right angles.** (Euc. I. 32. Simp. I. 9 & 10. Em. H. 1 & 2.) THEOREM V. Parallelograms standing on the same base, and... | |
| Joseph Charles Parkinson - 1860
...shall be less than the other two sides of the triangle, but shall contain a greater angle. 3. PROP. **XXXII. — If a side of any triangle be produced,...prove the corollaries of the last proposition. 5.** PBOP. XLIV. — To a given straight line to apply a parallelogram, which shall be equal to a given... | |
| Civil service
...these shall be less than the other two sides of the triangle, but shall contain a greater angle. PROP. **XXXII. — If a side of any triangle be produced,...every triangle are together equal to two right angles.** Enunciate and prove the corollaries of the last proposition. PROP. XLIV. — To a given straight line... | |
| John Paxton Hall - 1860
...these shall be less than the other two sides of the triangle, but shall contain a greater angle. PROF. **XXXII. — If a side of any triangle be produced,...every triangle are together equal to two right angles.** Enunciate and prove the corollaries of the last proposition. PROP. XLIV. — To a given straight line... | |
| Robert Potts - Geometry, Plane - 1860 - 361 pages
...been drawn a straight line EAF parallel to the given straight line BC. QEF PROPOSITION XXXII. THEOREM. **If a side of any triangle be produced, the exterior...every triangle are together equal to two right angles.** Let ABCbe a triangle, and let one of its sides UCbe produced to D. Then the exterior angle A CD shall... | |
| 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... | |
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