JMifcellanea Curiofal 1 3 



Now, any Area^ as COPS, being given, 'tis 

 fequir'd to find the Angle CSP, and the Di- 

 ftance CS, From the Nature of the Para- 

 bola RQ. is ever = \ the Parameter of xhtAxis^ 

 and corifequently if the Parameter be put = 2, 

 then RQL = t- Let CQ^z ^ then PCifhall = 

 * zz, and the Parabolick Segment COP=^^r 

 But the Triangle CSP will = is, and fo the 

 Mixtilineal Area COPS=f a V-J(-$ whence 

 &Hr3 £.-12**. Wherefore refolving this Cu- 

 bical Equation, z. or the Ordinate CQL will be 

 known. Now, let the Area OPS be propos'd 

 to be divided into 100 Parts ^ this Area isf 2 of 

 the Square of the Parameter, and confequent- 

 ly 1 2 a is = that Square == 4. If therefore the 

 Roots of thefe Equations ^-+-3 z. = o, 04 : 0,08 2 

 0,12: o, i& 7 : &c. be fucceffively extra&ed, 

 there will beobtain'dfo many z or Ordinate* 

 CQLrefpedively, and the Area SOP will be di- 

 vided into ioo Parts. And in like manner is 

 the Calculus to be continued beyond the Place 

 O. Now the Root of this Equation (fince RQ. 

 is = i) is the Tabular Tangent of the Angle 

 CRQ, or ; the Angle CSP, and fo the Angle 

 CSP is given. And RC, the Secant of the fame 

 Angle CRQj is a mean Proportional between 

 RQor Unity, and RT, which is the Double of 

 SC, as is plain from the Comcks. But if SP be put 

 = 1, and fo the Lam Rettum — 4 (as in our Ta- 

 ble) then RT will be the Diftance fought, viz. 

 the Double of SC in the former Parabola, Af- 

 ter this manner therefore, I composed the fore- 

 going Table, which ferves to reprefent the 

 Motions of all Comets : For hitherto there has 

 been none obferv'd, but comes within the Laws 

 of the Parabola, 



It 



