 | 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
...point A 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...sides BC be produced to D ; the exterior angle ACD is equal to the two interior and opposite angles CAB, ABC, and the three interior angles of the triangle,... | |
 | John Playfair - Euclid's Elements - 1835 - 336 pages
...to it. 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...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 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...sides BC be produced to D ; the exterior angle ACD is equal to the two interior and opposite angles CAB, ABC ; and the three interior angles of the triangle,... | |
 | John Playfair - Geometry - 1836 - 148 pages
...therefore, also, the angles CBA, BAC, ACB, are equal to two right angles. Wherefore, if a side of a tqangle be produced, the exterior angle is equal to the two...angles of every triangle are equal to two right angles. Which was to be proved. COR. I. All the interior angles of any rectilineal figure, together with four... | |
 | 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
...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 angle...angles of every triangle are equal to two right angles. Steps of the Demonstration. 1. Prove that the altern. Z BAC = alternate Z ACE, And since AB, CD are... | |
 | John Playfair - Euclid's Elements - 1837 - 332 pages
...is drawn through the given point A parallel to the given straight line BC. PROP. XXXII. THEOR. / If a side of any triangle be produced, the exterior angle...interior angles of every triangle are equal to two rightfmgles. Let ABC be a triangle, and let one of its sides BC be produced to D ; the exteripr angle... | |
 | 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.... | |
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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. 
