30 PHILOSOPHICAL TRANSACTIONS. [aNNO I695. 



intermixed, relating to the same. 3. A Treatise concerning Proportions ; with 

 a Preface concerning Cubic Equations. 4. A Treatise of Conic Sections, in a 

 new and easy method ; considered as plain figures, out of the cone. 5. His 

 Arithmetic of Infinites, being a new method of investigation, or inquiry into 

 the quadrature of the circle and other curve-lined figures ; and many other 

 mysteries in mathematics. 6. An Observation of a Solar Eclipse at Oxford, 

 Aug. 2, 1654. O. S. 7. A Treatise of the Cycloid, with the bodies and 

 surfaces thence derived. 8. A Treatise of the Cissoid ; and the Rectification 

 and Complanation of Curve Lines and Surfaces. 9. His Mechanica, or a large 

 Treatise of Motion : wherein are handled, not only the machines or engines, 

 commonly called the mathematical or mechanical powers, but the whole doctrine 

 of motion, derived and demonstrated from its genuine and first principles : the 

 doctrine of percussions, repercussions, springs, and reflexions ; the doctrine of 

 hydrostatics, from the counterpoise of the air ; and many other things newly 

 discovered. 



In the latter volume are contained, 1. A large Treatise of Algebra, Historical 

 and Practical : siiowing the origin and progress of that art, from time to time, 

 and the steps by which it has attained to its present height. 2. A Treatise of 

 Combinations, Alternations ; and Aliquot Parts and divers Problems relating 

 to the same. 3. A Treatise of Angular Sections, with other things appertain- 

 ing ; as the Canon of Sines, Tangents, and Secants, &c, 4. A Treatise of the 

 Angle of Contact, showing it to be of no magnitude, and not any part of a 

 right lined angle. 5. A Defence of that Treatise, against the Objections of 

 Leotaud and others; with several Discourses concerning Composition of Mag- 

 nitudes, Inceptives of Magnitudes, and Compositions of Motion. 6. A Dis- 

 course concerning Euclid's Fiith Postulate, and his Fifth Definition of his 

 Sixth Book. 7. A Treatise of the Cono-Cuneus, or a Body representing 

 partly a Cone, and partly a Wedge, with the sections thereof made by a Plane; 

 considered in like manner as what are called the Conic Sections. 8. A Geo- 

 metrical Disquisition of Gravity and Gravitation ; wherein the doctrini,e of the 

 counterpoise of the air is defended against that of the ancients' Fuga Vacui. 

 9. A New Hypothesis concerning Tides, or the Sea's Ebbing and Flowing ; 

 derived from the common centre of gravity of the earth and moon, considered 

 as conjunct bodies. 10. Commercium Epistolicum : being a collection of let- 

 ters whicli passed between Messrs. Fermat and Frenicle on the one part, and 

 Lord Brounker and Dr. Wallis on the other part, by the intervention of Sir 

 KenelmDigby; concerning divers mathematical questions. 11. A Treatise of 

 Trigonometry, plain and spherical, of Mr. John Caswell.* 



* A ihird, very large volume, was published afterwards, containing many iniscelLmeous plecej. 



