278 A SHORT HISTORY OF SCIENCE 



system of coordinates are of similar antiquity. The great step 

 made by Descartes was his recognition of the equivalence of an 

 equation and the geometrical locus of a point whose coordinates 

 satisfy that equation. On this foundation facts known or ascer- 

 tainable about geometry may be translated into algebra and con- 

 versely. The advantage is comparable with that conferred by the 

 possession of two arms or eyes, or even two senses, under a common 

 will. The intricate but powerful machinery of algebra becomes 

 available for solving geometrical problems, while, on the other 

 hand, the geometrical illustration makes the algebra visible and 

 concrete. 



Later works dealt with philosophy and physical science, in par- 

 ticular with a theory of vortices. Descartes enunciates ten 

 natural laws, the first two corresponding with the first two of 

 Newton's. He argues that all matter is in motion and that this 

 must result in the formation of vortices. The sun is the centre of 

 one great vortex, each planet of its own, thus approximating 

 vaguely the future nebular hypothesis. Newton thought it worth 

 while to refute this theory, which was chiefly notable as a bold 

 attempt to interpret the phenomena of the universe by means of 

 a single mechanical principle. 



Lord Kelvin has expressed, with all his force, that the sole satis- 

 factory explanation of the phenomena of nature is that which leads 

 them back in the last analysis to motion in a continuous incompres- 

 sible fluid. This however was the guiding thought with Descartes. 



Timerding. 



Descartes's achievements in mathematics leave no doubt of his 

 exceptional intellectual power. He had neither the data nor the 

 scientific method for accomplishing similar results in other branches 

 of science, and in mathematics he would doubtless have accom- 

 plished much more had he not expended his energies so widely 

 in over-confident reliance on his logical method. He died at 

 Stockholm in 1650. 



INDIVISIBLES. CAVALIERI. While Descartes was thus as it 

 were incidentally laying the foundations of modern geometrical 



