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In a famous memoir, Clerk Maxwell showed nearly a hundred years ago that Saturn's rings would be unstable if they were solid, and that they must consist of a swarm of separate bodies. In a system of particles rotating about a centre of gravitational attraction the innermost particles will rotate more rapidly than the outermost, in order to counteract the stronger gravitational pull towards the centre. In studying the problem of Galactic rotation we are almost entirely dependent on the determination of velocities in the line of sight, which can be measured spectroscopically by the Doppler effect. ...On the theory of Galactic rotation stars which are further from the centre than the sun will tend, in general, to move more slowly, i.e. relative to the sun they will lag behind, whereas stars nearer to the centre will race ahead.
James Clerk Maxwell
As long as algebra and geometry travelled separate paths their advance was slow and their applications limited. But when these two sciences joined company, they drew from each other fresh vitality and thenceforward marched on at a rapid pace towards perfection. It is to Descartes that we owe the application of algebra to geometry,-an application which has furnished the key to the greatest discoveries in all branches of mathematics.
René Descartes
The core study of geography is the study of places, that is the analysis of the significant differences that distinguish the various areas of the world from each other. Among the differences that are significant to this areal differentiation, one of the more obvious are differences in landforms; one of the least obvious to the eye, but nonetheless important in molding the character of areas, are the differences in their political organization. In pursuing these and other separate topics, geographers "radiate out in diverse directions" "and for various distances, toward the cores of other disciplines." As long as they realise where they are in reference to the central core, they may hope to understand each other purposes.
Richard Hartshorne
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