(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:)
