| John Playfair - Geometry - 1836 - 148 pages
...drawn through the given point A, parallel to the given point BC. Which was to be done. PROP. V. THEOR. **If a side of any triangle be produced, the exterior...and the three interior angles of every triangle are** equal to two right angles. Let ABC be a triangle, and let any of its sides BC be produced to D ; the... | |
| Mathematics - 1836 - 488 pages
...XXX. Straight lines which are parallel to the same straight line are parallel to one another. XXXII. **If a side of any triangle be produced, the exterior angle is equal to the two interior and** op. posite angles ; and the three interior angles of every triangle are equal to two right angles.... | |
| John Playfair - Euclid's Elements - 1836 - 488 pages
...be done. x'i PROP. XXXII. THEOR. If a side of any trin iglc be produced, the exterior angle is e^ual **to the two 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... | |
| Euclides - Euclid's Elements - 1837 - 112 pages
...line / through a given point parallel to a g - f, given straight line. 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. Steps of the Demonstration. 1. Prove that the altern. Z BAC = alternate... | |
| Euclid, James Thomson - Geometry - 1837 - 410 pages
...line equal to that which is described by either extremity of the base.* BOOK I. PROP. XXXII. THEOR. **IF a side of any triangle be produced, the exterior angle is equal to the two interior and** remote angles ; and the three interior angles of every triangle are together equal to two right angles.... | |
| John Playfair - Euclid's Elements - 1837 - 332 pages
...angles ACD, ACB are equal (13. 1.) to two right angles; therefore also the angles CBA, BAC, ACB are **equal to two right angles. COR. 1. All the interior angles of any rectilineal figure** are equal to twice as many right angles as the figure has sides, wanting four right angles. For any... | |
| Charles Reiner - Geometry - 1837 - 246 pages
...the exterior angle is greater than either of the interior and opposite angles. 7. If one side of a **triangle be produced, the exterior angle is equal to the two interior and opposite angles.** 8. If each of the sides of a triangle be produced, the three exterior angles are, together, equal to... | |
| Andrew Bell - Euclid's Elements - 1837 - 290 pages
...A parallel to the given straight line BC. PROPOSITION XXXII. THEOREM. If a side of any triangle he **produced, the exterior angle is equal to the two interior and opposite angles ; and** vie three interior angles of every triangle are equal to two right angles. Let ABC he a triangle, and... | |
| Euclides - 1838 - 264 pages
...the given point A, parallel to the given straight line BC. Which was to be done. PROP. XXXII. THEOR. **If a side of any triangle be produced, the exterior...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... | |
| Euclid - Geometry - 1838 - 470 pages
...given point A parallel to the given straight line BC. Which was to be done. PROP. XXXII. THEOR. Ir **a side of any triangle be produced, the exterior angle...and the three interior angles of every triangle are** equal to two right angles. ROOK I. triangle, viz. ABC, BCA, CAB, are together equal to two right angles.... | |
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