Of X FO^'S HI%E. 187 



ing the Titles of Dukzs of Northumberland and Earls of Warwick. 

 and Leiceiler ; which Titles others fay, and perhaps more right- 

 ly too, were conferred on them by the Pope, in whofe Quarrel 

 they were pretended at leaft to have been loft \ 



195. Of later years the highly ingenious Sir Chriftopher Wren i 

 in the year 1 66S. firft found out a Straight line equal to a Cycloid 

 and the parts thereof, as is clearly made appear in his behalf by 

 the Right Honorable and Learned, the Lord Vifcount Brouncker i 

 Chancellor to Her Majefty, and Prefident of the Royal Society ; a,nd 

 the Reverend and Learned Dr .John Wallk '. The fame Right Wor- 

 fhipful and very learned Perfon Sir Chrislopher Wren, found out 

 alfo feveral new Geometrical Bodies,thzt arife by the application of 

 two Cylinders and one Lenticular Body, fit for grinding one ano- 

 ther ; by whofe mutual attrition will neceffarily be produced a Co* 

 noides Hyperbolicum, and two Cylindroidea Hyperbolica : The - 

 gine whereby this may be done being reprefented in Sculpture in 

 our Pbilofophical Tranfafiions, and defigned for grinding Hyperbo- 

 lical glajfes k . He alfo firft obferved that zplainjiraight edged ChU 

 fel, fet any way obliquely to a Cylinder of wood, did necevTarily 

 torn it into a Cylindroides Hyperbolicum Convexo-concavum, the fe- 

 verzl feSiions whereof are accuratly demonftrated by the Reverend 

 and Learned Dr. JohnWalli* our Englifh Archimedes \ 



196. The fame Dr. John Wallis, Savilian ProferTor of Geome^ 

 try in this Vniverfity, intheyear 1656. publiftied his new method 

 called his Arithmetick of Infinites, for the more expedite and ef- 

 fectual enquiry into the Quadrature of Curvilinear figures, or o- 

 ther difficult Problems in Geometry ; and therein, amongft other 

 things (at the Scholium of his 3 8 Propofition) fhewd the way of 

 comparing slraight and crooked lines, which gave occafion to Mr. 

 William Neil (in purfuance thereof) intheyear 1657. to find out 

 (the firft of any Man) a flraight line equal to a Curve, of which 

 we have an account in the Pbilofophical Tranfafiions of Novemb.\j. 

 i73 ffl . 



197. The fame Reverend and Learned Dr. JohnWallit, a- 

 mongft his other numerous and new Performances in Arithmetick. 

 and Geometry, firft demonftrated the impoffibility of fquaringthe 

 Circle, Arithmetically, according to any way of notation yet ge- 



fc Exltinerario]oh. Bargravc,?. T. p. l$?r abend. Ecckfi<eChrifti Cant. Mi penes feipfum. ' Philofoph 

 Tranfaft. Numb- 98- k ibid. Numb. 53. ^Walltfii Mechanica,five de Moturfart.T. de CakukCentri gra- 

 vitate, cap. 5. Ptop. 32. m Philofoph. Tranfadt. Ni. 98. 



nerally 



