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" Every section of a circular cone made by a plane parallel to the base is a circle. "
An Elementary Treatise on the Application of Trigonometry to Orthographic ... - Page 6
by John Farrar - 1822 - 153 pages
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An Elementary Treatise on the Application of Trigonometry: To Orthographic ...

John Farrar - Logarithms - 1822 - 270 pages
...cone formed by rays proceeding from the circumference of this circle to the eye ; and when the ciicle is parallel to the primitive, its representation upon...the cone formed by the visual rays is also oblique. Tini circle, for example, which has for its diameter the chord EF, will be the base of a cone of which...
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An Elementary Treatise on the Application of Trigonomentry to Orthographic ...

John Farrar - Trigonometry - 1833 - 276 pages
...all the others are referred. C, the centre of the primitive, will be the projection of the point ^, the pole of the primitive. Any circle of the sphere,...a section through the axis. Moreover, the section SNT, made by the plane of projection, is the projection of the circle EyF. It is proposed to determine...
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An Elementary Treatise on the Application of Trigonomentry to Orthographic ...

John Farrar - Trigonometry - 1833 - 274 pages
...all the others are referred. C, the centre of the primitive, will be the projection of the point *3, the pole of the primitive. Any circle of the sphere,...which OEF is a section through the axis. Moreover, the sec\ tion SNT, made by the plane of projection, is the projection of the I circle EyF. It is proposed...
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An Elementary Treatise on Plane and Solid Geometry

Benjamin Peirce - Geometry - 1837 - 216 pages
...NOP — BCD, &c. The polygons are therefore similar, by art. 169. 378. Corollary. The section of a cone made by a plane parallel to the base is a circle. 379. Corollary. If the perpendicular ST is let fall from S upon the base, meeting the section at R,...
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A collection of examples in pure and mixed mathematics, with hints and ...

Alfred Wrigley - 1845 - 222 pages
...from the extremities of the major axis upon the axis of the cone. 125. Find the latus rectum of the section of a right cone made by a plane parallel to the slant side ; and when the plane passing through the directrix of the section, and the vertex of the...
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An Elementary Treatise on Plane and Solid Geometry

Benjamin Peirce - Geometry - 1847 - 204 pages
...C, JVOP = B CD, &c. The polygons are therefore similar, by i5 170. 378. Corollary. The section of a cone made by a plane parallel to the base is a circle. Equivalent Pyramids and Cones. 379. Corollary. If the perpendicular ST is let fall from S upon the...
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Orr's Circle of the Sciences: Organic nature, vols. 1-3 (1854-1856)

William Somerville Orr - Science - 1854 - 534 pages
...added together, the required volume is one third of the Fig. 47. 13. To find the Volume of the Frustum, of a right Cone made by a Plane parallel to the Base. Let ABCD be the frustum of the cone PCD. Join POOj where 001 are the centres of the ends of the frustums....
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Collection of Examples and Problems in Pure and Mixed Mathematics: With ...

Alfred Wrigley - Mathematics - 1862 - 330 pages
...dropped from the extremities of the major axis upon the axis of the cone. 7. Find the latus rectum of the section of a right cone made by a plane parallel to the slant side ; and when the plane passing through the directrix of the section, and the vertex of the...
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The elements of mechanism

Thomas Minchin Goodeve - 1870 - 294 pages
...greater leverage, and with more effect. 147. The theoretical form of the fusee is an hyperbola, being the section of a right cone made by a plane parallel to the axis of the cone. To prove this statement we must first recognise the law according to which an elastic...
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An Elementary Geometry

William Frothingham Bradbury - Geometry - 1872 - 124 pages
...we should find Therefore the polygons GI and BD are similar (II. 19). 40. Corollary. A section of a cone made by a plane parallel to the base is a circle. THEOREM VIII. 41 1 The convex surface of a right pyramid is equal to the perimeter of its base multiplied...
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