1, Mathematics and Plausible Reasoning (1954) 459 Spcimen de usu observationum in mathesi pura, as quoted by George Pólya, Induction and Analogy in Mathematics Vol. But one ought to make a special effort to see that both ways of approach to the solution of the problem be laid open for thus not only is one solution greatly strengthened by the other, but, more than that, from the agreement between the two solutions we secure the very highest satisfaction. Of course, when the effective causes are too obscure, but the final causes are more readily ascertained, the problem is commonly solved by the indirect method on the contrary, however, the direct method is employed whenever it is possible to determine the effect from the effective causes. Since, therefore, two methods of studying effects in Nature lie open to us, one by means of effective causes, which is commonly called the direct method, the other by means of final causes, the mathematician uses each with equal success. Now there exist on every hand such notable instances of this fact, that, in order to prove its truth, we have no need at all of a number of examples nay rather one's task should be this, namely, in any field of Natural Science whatsoever to study that quantity which takes on a maximum or a minimum value, an occupation that seems to belong to philosophy rather than to mathematics. Wherefore there is absolutely no doubt that every effect in the universe can be explained as satisfactorily from final causes, by the aid of the method of maxima and minima, as it can from the effective causes themselves. For since the fabric of the universe is most perfect, and is the work of a most wise Creator, nothing whatsoever takes place in the universe in which some relation of maximum and minimum does not appear. Kontext: All the greatest mathematicians have long since recognized that the method presented in this book is not only extremely useful in analysis, but that it also contributes greatly to the solution of physical problems. Introduction to De Curvis Elasticis, Additamentum I to his Methodus Inveniendi Lineas Curvas Maximi Minimive Proprietate Gaudentes 1744 translated on pg10-11, "Leonhard Euler's Elastic Curves", Oldfather et al 1933
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