THE ELEMENTS OF

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perimeter A V C B, then the area A V C B willbe greater than EFG by (T. XVI. B. IV.)and COR. II. of the preceding problem; andin like manner A BI will be greater thanEGHL; therefore I A V C B must necessarilybe greater than EFGHL,

THEOREM XVIII.

Suppose B D KI E C any conic sectionconcave to its principal axis IP, andsuppose L O K any other axis, and DOEits conjugate bisected in O, and drawB L C parallel to DOE. Also, supposethe curve by its revolution round itsprincipal axis IP, to describe the solidB D K E C g; produce O K, which (byconies) will meet tangents to the curvedrawn from D and E in the fame pointV; and through D E and B C drawplanes perpendicular to the plane DVE,and consequently forming similar curvesD e E, BgC.

Compleat the cone TDVEGQ^, anddraw D a and E r parallel to K L; also