“Francis Bacon, who died in the seventeenth century, argued strongly that philosophy and theology should be kept separate, and that we should concentrate our studies on the local problems and the interconnections between material and efficient causes. Final-cause analysis was just a distraction: ‘Inquiry into final causes is sterile, and, like a virgin consecrated to God, produces nothing.”

Book VII, 3
The Advancement of Learning (1605)

p.5.

Upon The Mother Of The Gods (c. 362-363)

Isaac Newton: Principia Mathematica (1687); Rules of Reasoning in Philosophy, Rule IV.
Misattributed

Book VII, 7
The Advancement of Learning (1605)

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" https://www.dropbox.com/s/o09w82abgtftpfr/1933-oldfather.pdf, Oldfather et al 1933
Context: 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. 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. 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. 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. 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. 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. 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.

Source: Guide for the Perplexed (c. 1190), Part III, Ch.13

XVII, 11
The Kitáb-I-Asmá
Context: Should a person lay claim to a cause and produce his proofs, then those who seek to repudiate him are required to produce proofs like unto his. If they succeed in doing so, his words will prove vain and they will prevail; otherwise neither his words will cease nor the proofs he hath set forth will become void. I admonish you, O ye who are invested with the Bayán, if ye would fain assert your ascendancy, confront not any soul unless ye give proofs similar to that which he hath adduced; for Truth shall be firmly established, while aught else besides it is sure to perish.

Book VII, 7
The Advancement of Learning (1605)