OfOXFO%p^SHI%E. i%j 
ing the Titles of Dukes of Northumberland and Earls of Warwick 
2nd Lekesler ^ which Titles others fay, and perhaps more right- 
ly too, were conferred on them by the Pope^ in whofe Quarrel 
they were pretended atleaft to have been loft^. 
195. Of later years the highly ingenious Sir Chriflofher Wren^ 
in the year 1 668* firft found out a flraight 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, 
Chancellor to Her Majefty, and Prefident of the Royal Society ; a^d 
the Reverend and Learned T>x:.John Walli5 \ The fame Right Wor- 
fbipful and very learned Perfon Sir Chri§lopher Wren, found out 
alfo feveral new Geometrical Bodies^thzt arife by the application of 
two Cylinders 2nd one Lenticular Body, fit for grinding one ano- 
ther ; by whofe mutual attrition will neceifarily be produced a Co- 
noides HyperboHcum, and two Cylindroidea Hyperbolica : The En- 
gine whereby this may be done being reprefented m Sculpture in 
our Philofopkical Tranfa^ions, and defigned for grinding Hyperbo- 
licalglafes ^. He alfo firft obferved that a plain Jiraight edged Chi^ 
fel, fet any way obliquely to a Cylinder of wood, did neceffarily 
torn it into a Cylindroides Hjperbolicum Convexo-concavum, the fe- 
veral feSiions whereof are accuratly demonftrated by the Reverend 
and Learned Dr. John Wallis our Englifli Archimedes \ 
196. The idimeDr, yohnWallh, Savilian Vicofe^for of Geome- 
try in this Vniverfity, intheyear 1656. publiOied 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 Kis 38 Propofition) fliewd the way of 
comparing Hraight and crookedYines, which gave occafion to Mr. 
William Neil (in purfuance thereof) in the year 1657. to find out 
(the firft of any Man) a Jiraight line equal to a Curve, of which 
we have an account in the Philofophical Tranfa^ions of Novemb.ij, 
1673-. 
197. The fame Reverend and Learned Dr. JohnWallis, a- 
mongft his other numerous and new Performances in Arithnetick 
and Geometry, firft demonftrated the impoffibility of fquaringthe 
Circle, Arithmetically, according to any way of notation yet ge- 
* Ex Itinerariojoh. Ba.rgra.veS-T.P. ^PrAend. Ecclefi^Chrifti Cant.M^ penes felpfiim. iPhilofopb. 
Tranfadl. Numh- 98. ^ ibid. Numb. 5^ . ' Walhfii Mechanka,five de Motu,part. 2 de Calculo Centri gra ■ 
nitatis, cap. j.Prop. 32. •» Philofoph. Tranfadt- Num. 98. 
nerally 
