| John Muller - Mathematics - 1773 - 204 pages
...to r ; then unity is to r as the radius PM (y) is to ry its femi-circumference, by Art. 40 ; and as **the area of a circle is equal to the product of the** radius by half its circumference, by Art. 41 ; ihall have yXry or ryy, for the circle defcribed, defcribed... | |
| Adrien Marie Legendre - Geometry - 1819 - 208 pages
...entire circles are as the squares of the.' therefore sect. ACB : sect. DOE : : AC: DO\ THEOREM. 289. **The area of a circle is equal to the product of its circumference by half** of the radius. Demonstration. Denoting by surf. CA the surface or area of a circle whosc radius is... | |
| Adrien Marie Legendre - Geometry - 1822 - 367 pages
...the squares of their radii; therefore sect. ACB : sect. DOE : ACa : DO2. 96 PROPOSITION XII. THEOREM. **The area of a circle is equal to the product of its circumference by half the radius** Let us designate the surface of the circle whose radius is CA by surf. CA ; we shall have surf. CA=JCA... | |
| Etienne Bézout - Calculus - 1824 - 195 pages
...made. Let us apply this theory of indeterminates to some examples. Let it be proposed to prove that **the area of a circle is equal to the product of its circumference by half the radius;** that is, that calling this radius R, the ratio of the circumference to radius sr, and consequently... | |
| Adrien Marie Legendre, John Farrar - Geometry - 1825 - 280 pages
...°ntire circles ; but the entire circles are as the squares of their radii ; therefore THEOREM. 289. **The area of a circle is equal to the product of its circumference by half** of the radius. Demonstration. Denoting by surf. CA the surface or area of a circle whose radius is... | |
| Adrien Marie Legendre - Geometry - 1825 - 224 pages
..."ntire circles ; but the entire circles are as the squares of their radii ; therefore I THEOREM. / 289. **The area of a circle is equal to the product of its circumference by half** of the radius. Demonstration. Denoting by surf. CA the surface or area of a circle whose radius is... | |
| Adrien Marie Legendre - Geometry - 1828 - 316 pages
...again are as the squares of their radii ; therefore sect. ACB : sect. DOE : AC2 DOJ THEOREM. ' 289. **The area of a circle is equal to the product of its circumference by half the** radiusl Let us designate the surface of the circle whose radius is CA by surf. CA ; we shall have surf.... | |
| Timothy Walker - Geometry - 1829 - 129 pages
...area of the polygon its perimeter multiplied by half the radius of the inscribed . circle. 105. — **The area of a circle is equal to the product of its circumference by half the radius** — . This follows directly from the preceding. For the circumference of the circle is the perimeter... | |
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