( ? 3 ‘ ) 
in our Curve, the great eft Breadth is when the Point F divides 
the Line A B in ext re am and mean Proportion: whereas in the 
Foliate it is when A B is triple in porter to B F. And the great e(l 
E F or Ordinate in the Foliate is to that of cur Curve nearly 
as 3 to 4, or hcaBly as s/ \ V* \ — -j to v' 5 \/j _ 5- -j. 
But ft ill theft Differences are not enough to make them two 
diftincl Species, they being both defined by a like Equation , if 
the Aiymptote S G P he taken for the Diameter . And they 
are both comprehended under the fortieth Kind of the Curves 
of the third Order, as they (land enumerated by Sir Ifaac 
Newton, in his incomparable Treatife on that Subject. 
IV. An eafy Mechanical Way to divide the Nautical 
Meridian Line in Mercator’* Tro]eBion 3 tvith an 
Account of the {[(elation of the fame Meridian Line 
to the Curva Catenaria. % J. Perks, M. A. 
T H E mod ufeful Proje&ion of the Spheric Surface 
of Earth and Sea for Navigation, is that common- 
ly call’d Mercator S; tho’ its true Nature and Conftrudicn 
is faid to be firft demonftrated by our Countryman 
Mr. Wright , in his Correction of the Errors in Navigation. 
In this Projection the Meridians are all parallel Lines, not 
divided equally , as in the common plain Chart (which is 
therefore erroneous,) but the Minutes and Degrees (or 
ftridly, the Fluxions of the Meridian,) at every feverai 
Latitude are proportional to their .efpedive Secants . Or 
a Degree in the proje&ed Meri ian at any Latitude, is 
to a Degree of Longitude in the Equator, as the Secant 
of the fame Latitude is to Radius . 
The- 
