 | Thomas Perronet Thompson - Euclid's Elements - 1833 - 168 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 - 336 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 - 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 - 148 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 - 488 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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IF a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles ; and the three interior angles of every triangle are equal to two right angles. 
