By Grossi M.

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The nature of the things is perfectly indifferent, of all things it is true that two and two make four. Thus we write down as the leading characteristic of mathematics that it deals with properties and ideas which are applicable to things just because they are things, and apart from any particular feelings, or emotions, or sensations, in any way connected with them. This is what is meant by calling mathematics an abstract science. The result which we have reached deserves attention. It is natural to think that an abstract science cannot be of much importance in the affairs of human life, because it has omitted from its consideration everything of real interest.

Thus he looked for tangential forces, as in the accompanying figure (4). But according to the Newtonian law, apart from some force the planet would move for ever with its existing velocity in a straight line, and thus depart entirely from the sun. Newton, therefore, had to search for a force which would bend the motion round into its elliptical orbit. This he showed must be a force directed towards the sun, as in the next figure (5). In fact, the force is the gravitational attraction of the sun acting according to the law of the inverse square of the distance, which has been stated above.

ISBN 0-7607-6588-X eISBN : 978-1-411-43142-3 Š Printed and bound in the United States of America Š 3 5 7 9 10 8 6 4 2 INTRODUCTION ALFRED North Whitehead舗s Introduction to Mathematics is one of the most charming books ever written about the queen of the sciences. In it the great British mathematician and philosopher gives a delightful and intellectually stimulating exposition of mathematical concepts, the history of their development, and the application thereof. Expertly written with razor-sharp clarity by a brilliant man, Introduction to Mathematics is filled with precious insights and lively prose.

### A nondegeneracy result for a nonlinear elliptic equation by Grossi M.

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