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" 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 perpendicular erected at the middle of the... "
Mensuration of lines, surfaces, and volumes - Page 1
by David Munn - 1873
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1871 - 380 pages
...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...the middle of the line and terminated by the axis. Let AB be the straight line revolving about the axis XY; ab its projection on the axis ; OI the perpendicular...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Mathematics - 1872 - 382 pages
...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...the middle of the line and terminated by the axis. Let AB be the straight line revolving about the axis XY; ab its projection on the axis ; O1 the perpendicular...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1877 - 396 pages
...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...by the circumference of the circle whose radius is ike perpendicular erected at the middle of the line and terminated by the axis. Let AB be the straight...
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First B.A. Examination, University of London: A Hand-book to the Study of ...

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...the middle of the line, and terminated by the axis. We may then easily show that the surface of a spherical zone is equal to the product of its altitude...
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The Elements of Geometry

Webster Wells - Geometry - 1886 - 392 pages
...altitude 9. 357 PROPOSITION IX. THEOREM. 723. The area generated by the revolution of a straight line about an axis in its plane is equal to the projection...line on the axis, multiplied by the circumference of a circle whose radius is the length of the perpendicular erected at the middle point of the line and...
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Chauvenet's Treatise on Elementary Geometry

William Chauvenet, William Elwood Byerly - Geometry - 1887 - 331 pages
...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...the middle of the line and terminated by the axis. Let AB be the straight line revolving about the axis J^Y; ab its projection on the axis; 01 the perpendicular...
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Chauvenet's Treatise on Elementary Geometry

William Chauvenet - Geometry - 1887 - 342 pages
...formulated, V= I* IPX. PROPOSITION VIII. The area of the surface generated by a straight line revoking about an axis in its plane is equal to the projection...by the circumference of the circle whose radius is tin? perpendicular erected at the middle of the lino and terminated by the axis. PROPOSITION IX. The...
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Chauvenet's Treatise on Elementary Geometry

William Chauvenet - Geometry - 1888 - 826 pages
...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...by the circumference of the circle whose radius is ike perpendicular erected at the middle of the line and terminated by the axis, Let AB be the straight...
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The Elements of Plane and Solid Geometry: With Numerous Exercises

Edward Albert Bowser - Geometry - 1890 - 420 pages
...is bounded by a plane surface, a conical surface, and a zone. Proposition 9. Theorem. 788. The area generated by a straight line revolving about an axis in its plane, is equal to the product of the projection of the line on the axis by the circumference whose radius is the perpendicular...
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Elementary Geometry

William Chauvenet - 1893 - 340 pages
...sector is bounded by a plane, a conical surface, and a zone. PROPOSITION Vm.—LEMMA. 34. The area of the surface generated by a straight line revolving...the middle of the line and terminated by the axis. Let AB be the straight line revolving about the axis JTY; ab its projection on the axis; OI the perpendicular...
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