150 PHILOSOPHICAL TRANSACTIONS. [aNNO 1704. 



used in every art and science, but likewise the arts and sciences themselves. 

 The author has been very full and particular in all the parts of the mathematics. 

 In Geometry, under the name of each figure, he demonstrates its essential 

 properties, and shows its construction and use. Under such words as Parabola, 

 Ellipsis, Hyperbola, the author is very large, and not only defines those figures, 

 but demonstrates their most remarkable and primary properties; as likewise those 

 of the Conchoid, Cycloid, Logarithmic Line, Cissoid, Quadratrix, and Spiral 

 Lines; and is very full in the useful arts of trigonometry, both plane and sphe- 

 rical, with their uses and applications; in spherical geometry, or the art of 

 projecting the sphere in piano, in surveying, dialling, &c. in all which he has 

 not so strictly confined himself to other authors, but that the reader may meet 

 with something that is new. 



Under Algebra and the terms belonging it, such as equation, construction, 

 &c. he has given a clear and distinct account of the nature of that science ; 

 giving all the rules, with their reasons and denionstrations, the resolution of 

 affected equations, the constructions of cubics and biquadratics, with the in- 

 vestigation of Mr. Baker*s central rule, &c. 



Under the word Asymptote, he has several considerations concerning 

 asymptotical curves; where he shows that curves which admit of no rectilineal 

 asymptote, may yet be asymptomatical to one another, with several other 

 considerations of the like nature. Nor has he been less full in what we call 

 the new methods; under the word Fluxions, he has given the first principles of 

 that science, viz. the nature and algorithm of them ; and their use and appli- 

 cation he has every where given under prop)er heads, and by these is shown a 

 universal method of drawing tangents to all curves; of determining the points 

 of inflexion and retrogression; of resolving questions de maximis et minimis ; 

 of finding the centres of gravity, oscillation, &c. 



All the parts of Arithmetic are here explained, with its application to ana- 

 tocism, compound interest, and Annuities, together with the doctrine of surds, 

 the method of extracting roots by converging series, logarithms, and fi-actions, 

 both vulgar, decimal, and sexagesimal. 



He has likewise given the description and use of both the celestial and te- 

 restrial globe ; the different hypotheses of astronomers, with an explication of 

 the terms belonging to each ; the parallaxes, magnitudes, motion, and distances 

 of the planets; with several curious observations relating to the heavenly 

 bodies; Mr. Newton's Theory of the Moon, with a large account of comets, 

 from the same author; the nature and use of optics, catoptrics, dioptrics, 

 with several methods for finding the foci of spherical glasses, the doctrine 

 of the acceleration of heavy bodies; the composition of motion, geography, 

 music, &c. 



