| Thomas Perronet Thompson - Euclid's Elements - 1833 - 150 pages
...any triangle be prolonged, the exterior angle is equal to the sum of the two interior and opposite **angles. Let ABC be a triangle, and let one of its sides,** as BC, be produced to D. The exterior angle ACD shall be equal to the two interior and opposite angles... | |
| Euclides - 1834 - 518 pages
...from the vertex to the point of section, divides the outward angle of the triangle into tlvo equal **angles. Let ABC be a triangle, and let one of its sides** BA be produced to E ; and let the outward angle CAE be divided into two equal angles by the straight... | |
| Euclid - 1835 - 540 pages
...parallel to the given ^-Y"**' straight line BC. Which was to be done. PROP. XXXII. THEOR. If a side **of any triangle be produced, the exterior angle is...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 Playfair - Euclid's Elements - 1835 - 316 pages
...In that case, CAI and EDF would be together equal to two right angles. PROP. XXV. THEOR. If a side **of any triangle be produced, the exterior angle is...equal to the two interior and opposite angles ; and** (he three interior angles of every triangle are equal to two right angles. Let ABC be a triangle, and... | |
| Mathematics - 1835 - 684 pages
...(o) The three angles of a triaugle are together equal to two right angles; and if one of the sides **be produced, the exterior angle is equal to the two interior and opposite angles** . 14 (/>) In a right angled triaugle — 1. One of the angles, viz. the right angle, is equal to the... | |
| John Fellows - Druids and druidism - 1835 - 432 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,... | |
| John Playfair - Geometry - 1836 - 114 pages
...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 angle is...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... | |
| 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... | |
| Mathematics - 1836 - 472 pages
...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.... | |
| Euclides - Euclid's Elements - 1837 - 112 pages
...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 angle is...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... | |
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