ptolejiy verms copeknicus.

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Au Ellipse is the curve described by a point p, which movesso that the sum of its distances from two other given points,s and h, remains constant. It may in practice he most easilydrawn by fastening a thread, or string, at s and h ; the pointof a pencil which is carefully moved so as to keep the stringstretched will then describe the curve.

s and h are called the Foci of the Ellipse , c half-way betweenthem is its centre. The ovalness of the curve depends uponthe proportion which the distance sh hears to the longestdiameter ashz, which always equals in length the sum of thetwo lines sp and HP. This diameter is generally termedthe Major Axis ; another at right angles to it through o being-called the Minor Axis. If s and h are brought together to c

mmm

Fig . XXXIV.—Two Ellipses of different degrees of ovalness.

the ellip.se then becomes a circle. The ovalness is not veryapparent to the eye, unless the Foci are considerably removedfrom c towards a and z. It is found, for instance, thatunless sc be greater than Ith of ca, the semi-minor axiscb will not differ from the semi-major axis ac by more than■roth part of the latter; the approximate rule for obtaining thedifference in any particular case being, to square the number oftimes that ca contains cs, multiply by two, and take the resultas the denominator of a fraction with a numerator unity, whichwill indicate to what extent bc will fall short of ac. Forexample, if cs equals -^th of ca, then twice the square of<30 being 7200, bc will only fall short of ac by a T ^ n thpart. The above rule depends upon the properties of an ellipsewhich are proved in treatises upon Conic Sections.

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