Plane and solid geometry . Given CD a section of cone V-AB made by a plane II base prove section CD a O. Outline of Proof 1. Let It and S be any two points on the boundary of sectionCD; pass planes through OV and points R and S, 2. Prove A VOM ~ A VPR and A VON ~ A VPS. OM ON o rr\. OM VO .ON VO o. Ihen — = — and —? = — ; PR VP PS VP PR PS 4. But OM = ON, .-. PS — PR, P is equidistant from anytwo points on the boundary of section CD, 5. .-. section CD is a O. 849. Cor. Any section of a cone parallel to its base isto the base as the square of its distance from the vertexi
Plane and solid geometry . Given CD a section of cone V-AB made by a plane II base prove section CD a O. Outline of Proof 1. Let It and S be any two points on the boundary of sectionCD; pass planes through OV and points R and S, 2. Prove A VOM ~ A VPR and A VON ~ A VPS. OM ON o rr\. OM VO .ON VO o. Ihen — = — and —? = — ; PR VP PS VP PR PS 4. But OM = ON, .-. PS — PR, P is equidistant from anytwo points on the boundary of section CD, 5. .-. section CD is a O. 849. Cor. Any section of a cone parallel to its base isto the base as the square of its distance from the vertexis to the square of the altitude of the cone. Outline of Proof By § 563, section CD PRbase AB OM^ Prove PR VP VEOM VO VF Then section CD VE^ base AB yp^For applications of §§ 848 and 849, see Exs. 392 SOLID GEOMETRY MENSURATION OF THE CYLINDER AND CONE Areas 850- Def. A plane is tangent to a cylinder if it containsan element, bnt no other point, of the cylinder. 851. JDef. A prism is- inscribed in a cylinder if its lateraledges are elements of the cylinder, and the bases of the twofigures lie in the same plane. 852. Def. A prism is circumscribed about a cylinder if its lateral faces are all tangent to the cylinder, and the bases ofthe two figures lie in the same plane. Ex. 1378. How many planes can be tangent to a cylinder? If twoof these planes intersect, the line of intersection is parallel to an are the bases of the cylinders in §§ 850-852 restricted ? (See § 834.) 853. Before proceeding further it might be well for thestudent to review the more important steps in the develop-ment of the area of a circle. In that development it wassho^vn that: (1) The area of a regular polygon circumscribed about acircle is greater, and che area of a regular polygon inscribed
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Keywords: ., bookcentury1900, bookdecade1910, booksubjectgeometr, bookyear1912
