^4 , PHILOSOPHICAL TRANSACTIONS. [aNNO I67I. 



The second treats of the usefulness of mathematics to natural philosophy; 

 showing that the empire of man may be considerably promoted by the na- 

 turalist's skill in those sciences, as well pure as mixed. — The third proves the 

 usefulness of mechanical principles to natural philosophy, showing that the 

 power of man may be much increased by the naturalist's skill in mechanics ; 

 forasmuch as nature plays the mechanician, not only in plants and animals and 

 their parts, but in many other curiously contrived bodies. — ^I'he fourth mani- 

 fests, that the good of mankind may be increased by the naturalist's insight 

 into trades : for the proof of which, the author endeavours to show that an in- 

 sight into trades may improve the naturalist's knowledge ; and that the natural 

 philosopher, as well by the skill thus obtained, as by the other parts of his 

 knowledge, may be enabled to improve trades, by suggesting improvements in 

 them. — ^The fifth shows, that that may be done by physical knowledge, which 

 is wont to require manual skill. — The sixth and last represents man's great ig- 

 norance of the uses of natural things ; or, that there is scarcely any one thing 

 in nature, whereof the uses to human life are yet thoroughly understood. 



II. Enchiridion Metaphysicum, sive de Rebus Incorporeis Dissertatio, per 

 H. M. Cantabrigiensem. Londini, 1671, in 4to. 



This book is intended to show the existence and agency of incorporeal be- 

 ings or substances, and to explain their nature. According to this author, 

 many of the more curious and occult phaenomena of nature, which philosophers 

 consider as effects of mechanical causes, are to be ascribed to the immediate 

 agency of immaterial beings or spirits. 



After all, he gives his definition of a spirit in general, with its explication ; 

 where he undertakes both to make it out, why an extended spirit is more cap- 

 able of perception, than extended matter: And to show how a spirit, so 

 subtle and penetrative, that it seems not capable of adhering to matter, may 

 yet be conceived able to move and impel matter : And that the cohesion of a 

 spirit with matter is as intelligible, as the union of one part of matter with 

 another. 



III. Diophanti* Alexandrini Arithmeticorum Libri sex, et de Numeris 

 Multangulis Liber unus ; cum Commentariis C. G. Bacheti, et Observationi- 



• Diophantus was a celebrated mathematician of Alexandria} of what aera is not certainly known, 

 some think a centviry or two before Christ, and others as much after. He lived to a great age, be- 

 ing 84 years old at his death. He is reputed tlie father of algebra, at least among the Europeans; 

 and was so highly esteemed among the ancients, as to be ranked with Pythagoras and Euclid for ma- 

 thematical learning. He wrote 13 books on numeral algebra j but only six of them are now ex- 

 tant; of these, the above article is the 3d or last edition. The 2d edition, by Bachet, in Greek and 

 Latin, was in 1621; and the first, by Xylander, in Latin only, was in 1575. 



