VOL. XIX.] PHILOSOPHICAL TRANSACTIONS. 41 



nerating into a right line, the quadrature of the triangle I p u will be in effect 

 the same with the quadrature of Hippocrates's lunes. 



Carol. 2. If the semidiameter of the base be supposed infinite, the epicycloid 

 then being the common cycloid, the area of the said triangle will be equal to 

 the square of the radius of the generant, and so it falls in with that theorem 

 which Lalovera found, and calls Mirabile. 



Though I donotthink the aforesaid quadrature can easily be deduced from 

 what has been yet published of the epicycloid, I have not added the demonstra- 

 tion ; but think, it enough to name a general proposition from whence I deduced 

 it, viz. The segments of the generating circle are to the correspondent seg- 

 ments of the epicycloid, as c b to 2 c e -f- c b. For example, suppose f m g the 

 position of part of the generant when the point f of the exterior epicycloid was 

 designed, then the segment f m g n is to the segment d f n o :: as c b to 2 c e -|- 

 c B. And consequently the whole epicycloid to the, whole generant in the same 

 proportion, which is the only case demonstrated by M. De la Hire. It follows 

 also that in the common cycloid, its segments are triple of the correspondent 

 sectors of the generant, which was first shown by Dr. Wallis. 



An Account of Boohs. — 1. An Essay towards a Natural History of the Earth, 

 and Terrestrial Bodies, especially Minerals ; as aha of the Sea, Rivers, and 

 Springs. With an Account of the Universal Deluge, and of the Effects that it 

 had upon the Earth. By John Woodward,* M. D. Professor of Physic in 

 Gresham College, and F. R. S. 1695, 8vo. N° 21 7, p. 1 ] 5. 



The author begins this essay (which is only a prelude to a larger work which 

 he promises) with an account of his observations on the grosser and more massy 

 parts of the terrestrial globe, all which lie stratum super stratum in the earth ; 



* This medical philosopher, who acquired so much celebrity by the work above noticed, (with its 

 progressive enlargements,) was a native of Derbyshire, and was born in l665. After he had been 

 some years at a grammar school in the country, he was sent to London, where (we are told) he was 

 articled to a linen draper ; a situation ill adapted to a person of his studious turn. Accordingly he 

 soon quitted it for the pursuit of philosophy and physic ; in both which he made very great progress 

 in the course of a few years. In 1692, through the recommendation of his friend and patron. Dr. 

 Barwick, he was appointed to the vacant professorship at Gresham college ; and in 1695 the degree of 

 doctor of physic was conferred upon him by a patent from Archbishop Tenison. He was afterwards 

 admitted to the same degree at Cambridge. Besides his Natural History of the Earth, his Method 

 of Fossils, and several papers inserted in the Philosophical Transactions, he wrote a tract, entitled. 

 The State of Physic and Diseases, with an inquiry into the late increase of them, &c. printed in 1718. 

 He died in ]728, bequeathing to the University of Cambridge his collection of fossils (of which a 

 catalogue was published in 17'28), wijji an endowment for a lecturer on his favourite subject of in- 

 quiry, the natural histo ry of the earth. 



VOL. IT. G 



