Books Books
The surface of a sphere is equal to the product of its diameter by the circumference of a great circle.
Elements of Geometry and Trigonometry - Page 215
by Adrien Marie Legendre - 1852 - 432 pages

## Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1837 - 376 pages
...described by ED + DC, is equal to (HI + IP) x circ. ON, or equal to IIP x circ. ON. PROPOSITION X. THEOREM. The surface of a sphere is equal to the product of...its diameter by the circumference of a great circle. D E O A Let ABCDE be a semicircle. Inscribe in it any regular semi-polygon, and from the centre O draw...

## An Elementary Treatise on Plane and Solid Geometry

Benjamin Peirce - Geometry - 1837 - 216 pages
...surface generated by the circular segment ABCD is a zone. Hence the area of the surface of a sphere is the product of its diameter by the circumference of a great circle. And, the area of a zone is the product of its altitude by the circumference of a great circle. 473....

## A Course of Mathematics: Containing the Principles of Plane ..., Volumes 1-3

Jeremiah Day - Geometry - 1838 - 416 pages
...surface of a hemisphere is equal to the product of its radius into the circumference of its base ; and the surface of a sphere is equal to the product of its diameter into its circumference. Cor. 1. From this demonstration it follows, that the surface of any segment...

## First Lessons in Geometry: With Practical Applications in Mensuration, and ...

Charles Davies - Geometrical drawing - 1840 - 262 pages
...circle. If it does not pass through the centre, the circle of section is called a small circle. 24. The surface of a sphere is equal to the product of...its diameter by the circumference of a great circle. Thus, the surface of the sphere whose centre is C, is equal to circumference ABDEy. AD. Q.UEsT. —...

## Elements of Geometry

Adrien Marie Legendre - Geometry - 1841 - 288 pages
...circle. This axis FG will be at the same time the diameter of the circumscribed circle. THEOREM. 535. The surface of a sphere is equal to the product of...its diameter by the circumference of a great circle. Demonstration. 1. We say that the diameter of a sphere multiplied by the circumference of a great circle...

## Pantology: Or, A Systematic Survey of Human Knowledge; Proposing a ...

Roswell Park - Best books - 1841 - 722 pages
...by its slant height, or distance from the vertex to any point of the circumference just named: and the surface of a sphere, is equal to the product of...its diameter by the circumference of a great circle, that is, of the sphere itself. The measure of the solidity of a cylinder, is the product of its base...

## Elements of Geometry: On the Basis of Dr. Brewster's Legendre : to which is ...

James Bates Thomson - Geometry - 1844 - 268 pages
...ease, the centres and the point of contact lie in the same straight line. PROPOSITION IX. THEOREM. The surface of a sphere is equal to the product of its diameter into its circumference. GE OMETRY. polygon inscribed in a semicircle FBE, whose axis is EF : the semicircle...

## Elements of plane (solid) geometry (Higher geometry) and trigonometry (and ...

Nathan Scholfield - 1845 - 894 pages
...circle, it evidently follows that every section of a sphere is a circle. PROPOSITION XXII. THEOREM. The surface of a sphere is equal to the product of its circumference multiplied by its diameter. / For it has been shown (Prop. XVIII.) that the surface of...