la , PHILOSOPHICAL TRANSACTIONS. [aNNO 1/03. 



Physica Coelestis of Kepler, the Vortices of Cartesius, and those of the ingenious 

 Mons. Leibnitz, whose several theories he sufficiently confutes ; and then he 

 gives an account of the other three celebrated systems of the universe, the 

 Ptolemaic, Tychonic, and Semi-Tychonic, and the different forces that are ne- 

 cessary to make the planets move in the order, which those systems require. 



In the 2d book are explained all those things that depend on the motion of 

 the primum mobile, the doctrine of the sphere, the genesis of the circles, the 

 use of the globes, spheres, and other instruments, that are contrived to repre- 

 sent the diurnal motions of the stars, together with the method of determining, 

 by observations, the positions of the circles in respect of each other, and the 

 places of the stars, their longitudes, latitudes, &c. the method of making ca- 

 talogues of the fixed stars, with an historical account of all those catalogues 

 that have been hitherto made. Here also he shows the way of solving all the 

 common problems of the sphere by trigonometry, as also the foundation and 

 method of making all sorts of dials by the same calculus: and lastly, the various 

 ways of determining the parallax and refractions of the stars, with their de- 

 monstrations. 



In the 3d book he descends more particularly to the theory of t1ie primary 

 planets. And, because each planet so moves in an ellipse round the sun, that 

 it describes areas always proportional to the times, he gives the methods of di- 

 viding the area of an ellipse by a line drawn from its focus in a given proportion ; 

 which may be done either by the indirect method of Kepler, or directly by a 

 series of his own, which he demonstrates ; and then he shows Dr. Ward's 

 Theory (wherein the planets are supposed to describe about the other focus 

 angles always proportional to the times) to be only an approximation to the 

 true one, wherein they describe areas at the other focus that are proportional 

 to the times, and as such it is expressly mentioned by Kepler in his Epitome 

 Astronomiae Copernicanae ; but if the distance between the foci be great, this 

 method will not give the exact place of the planet, and therefore it wants the 

 approximation of Bulliald, which is only a nearer approach to truth. Here 

 also he considers the oval figure, in which Mons. Cassini supposes the planets 

 to move; and he proves, that if a planet moved in that curve according to 

 M. Cassini's Theory, it would describe round the sun equal areas in equal 

 times; and by consequence a centripetal force of a determined kind acting on 

 the planet, might make it describe this curve; whereas Dr. Ward's Theory is 

 physically impossible, there being no centripetal force towards the sun, that can 

 make them move in an ellipse according to this law ; but then he shows, that 

 the Theory of Cassini does not answer observations, nor will give the true 

 anomaly of the planet, and its distance from the sun. After this he comes 



