| William Chauvenet - Geometry - 1871 - 380 pages
...by the arc CD. This zone is called the base of the spherical sector. PROBOSITION IX.— LEMMA. 36. The area of the surface generated by a straight line...revolving about an axis in its plane, is equal to the projection of the line on the axis multiplied by the circumference of the circle whose radius is the... | |
| William Chauvenet - Mathematics - 1872 - 382 pages
...by the arc CD. This zone is called the base of the spherical sector. PROPOSITION IX.— LEMMA. 36. The area of the surface generated by a straight line...revolving about an axis in its plane, is equal to the projection of the line on the axis multiplied by the circumference of the circle whose radius is the... | |
| David Munn - 1873 - 160 pages
...circular cone is equal to the circumference of the base multiplied by half the slant height 64 VII. Lemma. The surface generated by a straight line revolving about an axis in its plane, is equal to the projection of the line on the axis, multiplied by the circumference of the circle, whose radius is... | |
| Harvard University - 1876 - 554 pages
...is measured by the excess of the sum of its three angles over two right angles. Prove. 7. Given that the area of the surface, generated by a straight line revolving about another in the same plane with it as an axis, is the product of the length of the revolving line by... | |
| George Albert Wentworth - Geometry - 1877 - 416 pages
...generated by the revolution of a straight line about another line in the same plane with it as an axis, is equal to the product of the projection of the line on the axis by the circumference whose radius is perpendicular to the revolving line erected at its middle point and terminated by the axis. Let the... | |
| George Albert Wentworth - Geometry - 1877 - 416 pages
...generated by the revolution of a straight line about another line in the same plane with it as an axis, is equal to the product of the projection of the line on the aj-is by the circumference whose radius is perpendicular to the revolring line erected at its middle... | |
| George Albert Wentworth - Geometry - 1877 - 426 pages
...straight line about another line in the same plane with it as an axis, is equal to the product of 1 'he projection of the line on the axis by the circumference whose radius is perpendicular to the revolving line erected at its middle point and terminated 6// the axis. Let the... | |
| George Albert Wentworth - Geometry - 1877 - 416 pages
...about another line in the same plane with it as an axis, is equal to the product of the proj ection of the line on the axis by the circumference whose radius is perpendicular to the revolving line erected at its middle point and terminated by the axiť. Let the... | |
| J. G - 1878 - 408 pages
...surface of a sphere. This is found usually in a more general way, and rests upon the principle that the surface generated by a straight line revolving about an axis in its plane is equal to the projection of the line on the axis multiplied by the circumference of the circle whose radius is the... | |
| William Chauvenet, William Elwood Byerly - Geometry - 1887 - 331 pages
...spherical sector is bounded by a plane, a conical surface, and a zone. PROPOSITION VIII.—LEMMA. 34. The area of the surface generated by a straight line...revolving about an axis in its plane, is equal to the projection of the line on the axis multiplied by the circumference of the circle whose radius is the... | |
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