XV111 PREFACE. 



"In the beginning of the year 1665 I found the method of 

 approximating Series and the Rule for reducing any dignity of any 

 Binomial into such a series. The same year in May I found the 

 method of tangents of Gregory and Slusius, and in November had 

 the direct method of Fluxions, and the next year in January had 

 the Theory of Colours, and in May following I had entrance into the 

 inverse method of Fluxions. And the same year I began to think of 

 gravity extending to the orb of the Moon, and having found out 

 how to estimate the force with which [a] globe revolving within a 

 sphere presses the surface of the sphere, from Kepler's Rule of the 

 periodical times of the Planets being in a sesquialterate proportion 

 of their distances from the centers of their orbs I deduced that the 

 forces which keep the Planets in their Orbs must [be] reciprocally 

 as the squares of their distances from the centers about which they 

 revolve : and thereby compared the force requisite to keep the Moon 

 in her orb with the force of gravity at the surface of the earth, and 

 found them answer pretty nearly. All this was in the two plague 

 years of 1665 and 1666 ^ for in those days I was in the prime of my 

 age for invention, and minded Mathematicks and Philosophy more 

 than at any time since. What Mr Hugens has published since 

 about centrifugal forces I suppose he had before me. At length in 

 the winter between the years 1676 and 1677 2 1 found the Proposition 

 that by a centrifugal force reciprocally as the square of the distance 

 a Planet must revolve in an Ellipsis about the center of the force 

 placed in the lower umbilicus of the Ellipsis and with a radius 

 drawn to that center describe areas proportional to the times. And 

 in the winter between the years 1683 and 1684 3 this Proposition 

 with the Demonstration was entered in the Register book of the R. 

 Society. And this is the first instance upon record of any Proposi- 

 tion in the higher Geometry found out by the method in dispute. In 

 the year 1689 Mr Leibnitz, endeavouring to rival me, published a 

 Demonstration of the same Proposition upon another supposition, 

 but his Demonstration proved erroneous for want of skill in the 

 method." 



The above extract has been given here on account of its 

 intrinsic interest, although in writing it so many years after 



1 In 1666 Newton was in the 24th year of his age. 



2 Probably this should be changed to 1679 and 1680. 



3 Probably this should be changed to 1684 and 1685. 



