...all the others are referred. C, the centre of the primitive, will be the projection of the point A, the pole of the primitive. Any circle of the sphere,...which OEF is a section through the axis. Moreover, the section SAT, made by the plane of projection, is the projection of the circle EyF. It is proposed to...

...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...

...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,...which OEF is 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...

...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,...

...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...

...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...

...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....

...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...

...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...

...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...