 | Andrew Bell - Euclid's Elements - 1837 - 290 pages
...corresponding zones, formed by planes perpendicular to the axis of the cylinder, are equal. He also proved that the area of a circle is equal to half the rectangle contained by its circumference and radius, and he showed how to approximate as near as may be required to the quadrature... | |
 | Euclides - 1845 - 546 pages
...remaining one is placed upon them. Find the distance of the upper ball from the ground. THEOREMS. 5. The area of a circle is equal to half the rectangle contained by two straight lines which are equal to its circumference and radius. 6. Compare the angle in a segment,... | |
 | Euclid, Robert Potts - Euclid's Elements - 1847 - 118 pages
...same way. 22. This is shewn from Euc. xn. 2 ; i. 47 ; v. 18. 23. Assuming that the area of a sector of a circle is equal to half the rectangle contained by the radius and the arc, the sector AOC is shewn to be equal to the triangle AOB. 24. By Euc. xii. 2, the area of the... | |
 | Homersham Cox - Calculus, Integral - 1852 - 156 pages
...of the Circle and Polygon inscribed in it are ultimately equal. He demonstrated that the area of the circle is equal to half the rectangle contained by the radius and circumference, and thus found out a problem of Integration. His method is known as the method of Exhaustions.... | |
 | Robert Potts - 1865 - 528 pages
...and AE, may be proved to be equal to the sector ACD or DCK. 25. Assuming that the area of a sector of a circle is equal to half the rectangle contained by the radius and the arc, the sector AOC is shewn to be equal to AOB. 26. Let POQ be any quadrant, O being the center... | |
 | James Maurice Wilson - Geometry - 1868 - 150 pages
...shall shew that a regular pentagon can be described, and by means of it the decagon, quindecagon, &c. THEOREM. The area of a circle is equal to half the rectangle contained by the radius and a straight line equal to the circumference. Let C be the centre of a circle DBF. And let AB be the side... | |
 | Robert Potts - 1868 - 434 pages
...and AE, may be proved to be equal to the sector ACD or DCE. 21. Assuming that the area of a sector of a circle is equal to half the rectangle contained by the radius and the arc, the sector AOC is shewn to be equal to AOB. 22. Let POQ be any quadrant, O being the center... | |
 | Ellis A. Davidson - Mechanical drawing - 1869 - 140 pages
...branches of science relating to the areas of curves and sections of curved surfaces. He proved that the area of a circle is equal to half the rectangle contained by its circumference and radius, and showed how to approximate, as near as may be required, to the quadrature... | |
 | James Maurice Wilson - 1869 - 260 pages
...that a regular pentagon can be described, and by means of it the decagon, quindecagon, &c. THEOREM 14. The area of a circle is equal to half the rectangle contained by the radius and a straight line equal to the circumference. Let C be the centre of a circle DEF. And let AB be the side... | |
 | Robert Potts - Geometry - 1876 - 446 pages
...and AE, may be proved to be equal to the sector ACD or DCE. 21. Assuming that the area of a sector of a circle is equal to half the rectangle contained by the radius and the arc, the sector AOC is shewn to be equal to AOB. 22. Let POQ be any quadrant, 0 being the center... | |
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Let the arc of a semicircle on the diameter AB be trisected in the points D, E ; C being the center ; join AD, AE, CD, CE ; then the difference of the segments on AD and AE, may be proved to be equal to the sector ACD or DCE. 