PROP. V. THEOR. The area of any circle is equal to the rectangle contained by the semidiameter, and a straight line equal to half the circumference. Let ABC be a circle of which the centre is D, and the diameter AC ; if in AC produced there be taken AH... Alternate circles and their connection with the ellipse - Page 1by Edward Adolphus Seymour (11th duke of Somerset.) - 1851Full view - About this book
| John Playfair - Mathematics - 1806 - 320 pages
...A and B are not unequal, that is, they are equal to each other. / PROP. V. THEOR. ' THE area of any circle is equal to the rectangle contained by the semidiameter and a straight line equal to half the circumference. Let ABC be a circle, of which the centre is D, and the diameter AC... | |
| John Playfair - Euclid's Elements - 1833 - 346 pages
...Therefore, A and B are not unequal ; that is, they are equal to one another. PROP. V. THEOR. The area of any circle is equal to the rectangle contained by the semidiameter, and a straight line equal to half the circumference. Let ABC be a circle of which the centre is D, and the diameter AC... | |
| Mathematics - 1836 - 488 pages
...other inscribed in it, which shall differ from one another by a space less than any given space. V. The area of a circle is equal to the rectangle contained by the semi. diameter, and a straight line equal to half the circumference. Cor. 2. Hence a polygon may... | |
| John Playfair - Euclid's Elements - 1842 - 332 pages
...Therefore, A and B are not unequal ; that is, they are equal to one another. PROP. V. THEOR. The area of any circle is equal to the rectangle contained by the semi-diameter, and a straight line equal to half the circumference. Let ABC be a circle of which the centre is D, and the diameter AC... | |
| Euclid, John Playfair - Euclid's Elements - 1846 - 334 pages
...Therefore, A and B are not unequal ; that is, they are equal to one another. PROP. V. THEOR. The area of any circle is equal to the rectangle contained by the semi-diameter, and a straight line equal to half the circumference. Let ABC be a circle of which the centre is D, and the diameter AC... | |
| Samuel Hunter Christie - 1847 - 172 pages
...the circle are not unequal, that is, they are equal to one another. PROP. IX. THEOR. The area of any circle is equal to the rectangle contained by the semidiameter, and a straight line equal to half the circumference. Let ABC (fig. 8) be a circle, of which the centre is L, and diameter... | |
| Thomas Tate (mathematical master.) - 1848 - 284 pages
...greater than cir. circle OQ, it follows that, CA ; OQ : ! cir. circle CA ; cir. circle OQ. 75. THEOREM. The area of a circle is equal to the rectangle contained by its circumference and half the radius : that is, area circle CD = cir. circle CD x ^ CD. For if cir.... | |
| Education - 1850 - 488 pages
...a pyramid is equal to the third part of that of a prism of the same base and altitude. 2. Show that the area of a circle is equal to the rectangle contained by the circumference and half the radius. 4. Investigate a general expression for the solidity of a rectangular... | |
| Euclides - 1860 - 288 pages
...therefore A and B are not unequal j that is, they are equal to one another. PROPOSITION VII. THEOREM. Every circle is equal to the rectangle contained by the semidiameter, and a straight line equal to half the circumference. Let ABC be a circle of which the centre is D, and the diameter AC... | |
| 1860 - 462 pages
...CONSTRUCTION OF ТНК ARKA OF A CIRCLE.* By CHAUNCKY SMITH, of the Suffolk Bar, Boston. PROPOSITION. The area of a circle is equal to the rectangle contained by its semicircuniference and semidiameter. Children usually find this proposition in their arithmetics,... | |
| |