( ?9 ) 
give place to thofe that are more fiddly Geometri- 
cal ) that they have negle&ed to cultivate Geometry 
after the mofl regular manner. The Writers on diele 
Subjects commonly rife at once, from confidering the 
•Lines of the Second Order, or Conic Sections, to thofe 
of the Infinite Order, overlooking all the intermedi- 
ate Ranks. And hence it was, that all the Orders 
of Geometric Curves lay unregarded, without the 
known Limits of Geometry, bef ides the firft two, and 
a few of the fuperior Curves that had been confide- 
red with fome particular Views, till that great Au- 
thor, by enumerating the Lines of the Third Order, 
enlarged the Bounds of Geometry, and enriched it 
with almoft Seventy new Curves. Their Properties 
which he has given, and the manner of defcribing 
thofe of them that have a Vunffum Duplex, have al- 
moft brought them on a Level with the Lines of the 
Second Order; which alone had long ufuiped the Place 
in Geometry. 
After this great Example, ’tis attempted in this Trea- 
tife, to give an univerfal Defcription of all Geome- 
tric Lines of the Third, or any Order whatsoever. But 
becaufe the higher Kinds cannot be defcribed but by 
means of the inferior Sorts, fome of thefe muft be 
poftulated to defcribe thofe .* And becaufe ftreighe 
Lines are the fimpleft and moft eafily defcribed, and 
are always the fame, that is, of one Sort, therefore it 
was thought proper to inveftigate of what ufe they 
alone might be, for defcribing Lines of all the higher 
Orders, in the Firft Part of this Treatife * an Abftracft 
of which has been publifhed in the Tranfadfions for 
January and February laft. I fliall only add, that befides 
the Method of defcribing the Curves, the Manner of 
determining their Afymptotes and Species is alfo demon- 
ftrated ; and the more fimple Curves of every Order, 
F 2, are 
