Slam Newton: a Paleography

(with apologies to the imcomparable Sir Isaac Newton, but he should've thought about that before he wrote his articles so difficult to parse)

CURVES.    The incomparable Sir Ifaac Newton 
gives this following Ennumeration of Geometri-
cal Lines of the Third or Cubick Order; in which 
you have an admirable account of many Species of 
Curves which exceed the Conick-Sections, 
for they go no higher than the Quadratick or Se-
Second Order.


The Orders of Geometrick Lines.
   
1: GEOMETRICK-LINES, are beft diftinguifh'd into 

  Claffes, Genders, or Orders, 
        according
        to the Number of the Dimenfions 
        of an Equation, 
  expreffing the relation 
  between Ordinates and the Abfiffae;

OR, which is much at one, 
     according to the Number of Points in which they may 
      be cut by a Right Line.


Wherefore,
a Line of the Firft Order will be only a Right Line:

Thefe of the Second or Quadratick Order, will be 
   the Circle and the Conick-Sections;

and thefe of the Third or Cubick Order, will be 
   the Cubical and Nelian Parabola's,
   the Ciffoid of the Antients, and 
   the reft as belew ennumerated.

But a Curve of the Firft Gender 
   (becaufe a Right Line can't be reckoned among the Curves)
   is the fame with a Line of the Second Order, 
and a Curve of the Second Gender; 
   the fame with a Line of the Third Order,
and a Line of an Infinitefimal Order, is 
   that which a Right Line may cut in infinite Points, 
   as the Spiral, 
                Cycloid, the 
            Quadratrix, 
        and every Line generated by the Infinite Revolutions 
         of a Radius or
                            Rota.

(this concludes part 1:)