"We may regard the present state of the universe as the effect of its past and the cause of its future. An intellect which at a certain moment would know all forces that set nature in motion, and all positions of all items of which nature is composed, if this intellect were also vast enough to submit these data to analysis, it would embrace in a single formula the movements of the greatest bodies of the universe and those of the tiniest atom; for such an intellect nothing would be uncertain and the future just like the past would be present before its eyes."
—Pierre Simon Laplace, A Philosophical Essay on Probabilities, 1814
...term, equal to zero, will give then the limit of the sub- secants, a limit which is evidently the subtangent. This singularly happy method of obtaining the sub- tangent is due to Fermat, who has extended it to 46 A PHILOSOPHICAL ESSAY ON PROBABILITIES. transcendent curves. This great geometrician ex- presses by the character E the increment of the abscissa; and considering only the first power of this increment, he determines exactly as we do by differen- tial calculus the subtangents of the curves, their points of inflection, the maxima and minima of their ordinates, and in general those of rational functions. We see likewise by his beautiful solution of the problem of the refraction of light inserted in the Collection of the Letters of Descartes that he knows how to extend his methods to irrational functions in freeing them from irrationalities by the elevation of the roots to powers. Fermat should be regarded, then, as the true discoverer of Differential Calculus. Newton has since...
A Philosophical Essay On Probabilities - .xyz
Students of mathematics will find A Philosophical Essay on Probabilities an essential read for understanding this complex field of study and applying its truths to their lives.