## AN INTRODUCTION TO MATHEMATICS |

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A. N. Whitehead abstract algebraic form angle applied arc AP argument astronomer axis bers called chapter circle conic sections consider continuous function convergent coordinate geometry correlation corresponding cosine curve defined definite number diagram Differential Calculus direction easy ellipse equal equation example exponential function fact force fractions func function x2 fundamental geometric series graph Greek Hence hyperbola imaginary important incommensurable infinite series integers interpretation interval Leibniz length limit magnitude mathe mathematical ideas mathematicians matical meaning measure method multiplication namely nature negative numbers Newton notation number of terms ordered couple origin pair of numbers parabola parallelogram law particular period periodic function phenomena plane properties quantity rate of increase real numbers relation represents result satisfied sensations sense sine standard of approximation straight line sum to infinity symbols theory things thought tion triangle trigonometry uniformly convergent variable numbers vector velocity vibration whole

### Popular passages

Page 43 - Every body continues in its state of rest or of uniform motion in a straight line, except in so far as it may be compelled by impressed forces to change that state.

Page 59 - By relieving the brain of all unnecessary work, a good notation sets it free to concentrate on more advanced problems, and in effect increases the mental power of the race.

Page 217 - Hark! the rushing snow! The sun-awakened avalanche! whose mass, Thrice sifted by the storm, had gathered there Flake after flake, in heaven-defying minds As thought by thought is piled, till some great truth Is loosened, and the nations echo round, Shaken to their roots, as do the mountains now.

Page 61 - ... speeches, that we should cultivate the habit of thinking of what we are doing. The precise opposite is the case. Civilization advances by extending the number of important operations which we can perform without thinking about them. Operations of thought are like cavalry charges in a battle — they are strictly limited in number, they require fresh horses, and must only be made at decisive moments.

Page 27 - There is no more common error than to assume that, because prolonged and accurate mathematical calculations have been made, the application of the result to some fact of nature is absolutely certain'.

Page 15 - MATHEMATICS as a science commenced when first someone, probably a Greek, proved propositions about any things or about some things, without specification of definite particular things.

Page 59 - Before the introduction of the Arabic notation, multiplication was difficult, and the division even of integers called into play the highest mathematical faculties. Probably nothing in the modern world would have more astonished a Greek mathematician than to learn that, under the influence of compulsory education...

Page 61 - It is a profoundly erroneous truism, repeated by all copy-books and by eminent people when they are making speeches, that we should cultivate the habit of thinking ^ what we are doing. The precise opposite is the case. Civilization advances by extending the number of important operations which we can perform without thinking about them.

Page 223 - It is a well-founded historical generalization that the last thing to be discovered in any science is what the science is really about. Men go on groping for centuries, guided merely by a dim instinct and a puzzled curiosity, till at last 'Some great truth is loosened.

Page 28 - Newton's law of gravitation states that any two bodies attract each other with a force proportional to the product of their masses and inversely proportional to the square of the distance between them...