52 LIMITS AND FLUXIONS 



Curvature formed by them ; and thence the Tangents, 

 Perpendiculars, Points of Inflexion and Retrogres- 

 sion, reflected and refracted Rays, etc. , of Curves. 



'*Polygons circumscribed about or inscribed in 

 Curves, whose Number of Sides infinitely augmented 

 till at last they coincide with the Curves, bave 

 always been taken for Curves themselves. . . . It 

 was the Discovery of the Ànalysis of Infinites that 

 first pointed out the vast Extent and Fecundity of 

 this Principle. . . . Yet this itself is not so simple 

 as Dr. Barrow afterwards made it, from a dose 

 Consideration of the Nature of Pohgons, which 

 naturally represent to the Mind a Httle Triangle 

 consisting of a Particle of a Curve (contained 

 between two infinitely near Ordinates), the Differ- 

 ence of the correspondent Absciss's ; and this 

 Triangle is similar to that formed by the Ordinate, 

 Tangent, and Subtangent. . . . Dr. Barrow . . . also 

 invented a kind of Calculus suitable to the Method 

 {Lect. Geoin., p. 80), tho' deficient. . . . The 

 Defect of this Method was supplied by that of 

 Mr. Leibnitz'z,^ [or rather the great Sir Isaac 

 Newton].'^ He began where Dr. Barrow and others 

 left off: His Calculus has carried him into Countries 

 hitherto unknown. ... I must bere in justice own 

 (as Mr Leibnitz himself has done, in Journal dcs 

 S^avans for August 1694) that the learned Sir Isaac 

 Newton likewise discover'd something like the 

 Calculus Differentialis, as appears by his excellent 



A Ada Eruàit. Lips., ann. 1684, p. 467. 

 2 See Commcrcùim Epistoluuni. 



