358 PHILOSOPHICAL TRANSACTIONS. [aJJNO 1 687 • 



from this consideration to have entered with the greater zeal on the publication 

 of his own method. It has been followed by Sloane in his Natural History of 

 Jamaica, by Petiver in his Herbal, by Dillenius in his Synopsis of British 

 Plants, and by Mr. Martyn (father of the present Professor Martyn) in his Ca- 

 talogue of the Plants that grow in the neighbourhood of Cambridge. 



It should be observed that the system announced in the present article differs 

 considerably from the more finished one afterwards published. 



II. Philosophise Naturalis Principia Mathematica, Autore I. Newton, Trin. 

 Coll. Cantab. Soc. Matheseos Professore Lucasiano, et Soc. Reg. Sod. 4to. 

 Londini. 



This* incomparable author having at length been prevailed on to appear in 

 public, has in this treatise given a most notable instance of the extent of the 

 powers of the mind ; and has at once shown* what are the principles of natural 

 philosophy, and so far derived from them their consequences, that he seems to 

 have exhausted his argument, and left little to be done by those that shall suc- 

 ceed him. His great skill in the old and new geometry, assisted by his own 

 improvements of the latter, (I mean his method of infinite series) has enabled 

 him to master those problems, which for their difiiculty would have still lain un- 

 resolved, had one less qualified than himself attempted them. 



This treatise is divided into three books, whereof the first two are intitled 

 de Motu Corporum, the third de Systemate Mundi. The first begins with de- 

 finitions of the terms made use of, and distinguishes time, space, place, and 

 motion, into absolute and relative, real and apparent, mathematical and vulgar : 

 showing the necessity of such distinction. To these definitions are subjoined 

 the laws of motion, with several corollaries from them ; as concerning the com- 

 position and resolution of any direct force out of, or into any oblique forces, by 

 which the powers of all sorts of mechanical engines are demonstrated ; the laws 

 of the reflection of bodies in motion after their collision ; and the like. 



These necessary praecognita being delivered, our author proceeds to consider 

 curves generated by the composition of a direct impressed motion with a gravi- 

 tation or tendency towards a centre : and having demonstrated that in all cases 

 the areas at the centre, described by a revolving body, are proportional to the 

 times ; he shows how, from the curve described, to find the law or rule of the 

 decrease or increase of the tendency or centripetal forces as he calls it, in 

 different distances from the centre. Of this there are several examples : as, if 



* This account of Newton's Principia has much the appearance of having been drawn up by the 

 masterly talents of Dr. Halley, who about that time it seems was the person who published the 

 Transactions, and who bad been chiefly instrumental in procuring the publication of the above great 

 work of New ton. 



