An Unabridged Printing With Text And All Figures Digitally Enlarged. Originally Titled: Sir Isaac Newton's Enumeration Of Lines Of The Third Order, Generation Of Curves By Shadows, Organic Description Of Curves, And Construction Of Equations By Curves. Translated From The Latin With Notes And Examples: The Orders Of Lines - The Properties Of Conic Sections Are Analogous To Those Of Curves Of Higher Orders - The Reduction Of All Curves Of The Second Genus To Four Cases Of Equations - The Enumeration Of Curves - The Generation Of Curves By Shadows - Of The Organic Description Of Curves - The Construction Of Equations By The Description Of Curves - NOTES TO SECTIONS: Orders Of Lines - Diameters - Ratio Of The Products Of Ordinates And Abscissas - Hyperbolic And Parabolic Branches - Asymptotes - Infinite Branches - Hyperbola With Six Branches - Diameters Of Redundant Hyperbola - Absolute Diameters - Redundant Hyperbola Without A Diameter - Hyperbolas With A Diameter - Hyperbolas With Three Diameters - Hyperbolas With Converging Asymptotes - Defective Hyperbolas - Cissoid - Parabolic Hyperbolas - Hyperbolisms Of The Conic Sections - Witch - Trident - Semi-Cubic Parabolas - Cubic Parabola - Examples- Loci Of The Third Order - Problems Having Reference To Lines Of The Third Order