Problemata Geometrica ‘tiaria*

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emonstrat. For whcrefoemer the plain ab (perpendiculario tbc common axis e g f)fball cut the fphere y and the jpheroidesifeSlions fball becircles. And becaufe this is jo in everyfitch lif^e fetiion, as also becaufe thofe circles are evcryrvberehtwecn themfelves in the fame proportion , that foewes that*hey ha<ve that proportion : As in an Ellipfis$ which isclothed^ont with a circnmference , becaufe the lines ordinately applyedar e fiill in the fame proportiontherefore it is y that a circle y isto an ellipsi /, as the diameter of the circle<> to the leffer diameter°fthe ellipsis.

Ul. Confequently thefe things are true.

1 Caroll. As l ofthe sphericiis to the bafeof the cylinder,So is the fphere to the cy linder.

2 Coroll. As the circle of the fphere y is to the circle of thefpberoides: So is the fphere , to the fpheroides.

Iherefore , as\ of the sphericiis to ' ofthe spherici\ : Socylinder , to a fpheroides mithin it. That zx,

F ig. 2-

As 14 , to

5 as 6 is to 4: or, as 2 is to 3 ; Sö'is a cylinder , to a fphere

lric htded in it.

Of the Varakk .

The Parabola is * of the circumfcribedlparallelogram.

I J^OrAC. AS::CD.Sa (RP> ^AC.AR ::

R pj by 20.1. of Apollon.l her esore A C.A SA R *-—• OrN O.N d-N P :: .Then FTo -N Qi*- :N O.N P , that is, as a

y inder isto a cone : : So is the parallelogram AD,f0 the trvl * Zll *n APD M. Therefore, ifM C bc a cylinder, and AMD^° n e(J)oth of them uponthe bafe TsADßhc circle ofthe cylinder0 ßsall be to the circle of the cone N Q_? as N O to N P. Butj r a jf? is the nght line N Ö ofthe parallelogram CM; to the^fht h m N P of the trihneum APjDM A ,and this ßjall al-(( fy Qs happen ivherefoe<ver the line NO/x drawn » T heres ore,Ax! Je ^° ne A D M,/x * of the cylinder C M; So the trihneumW ' ofthe parallelogram C M- And half the Para~

a A. C D P A> is * of the parallelogram C M, as it ought to be.

PRO

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