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Reading about the scientific method I found that the classical definition I got in school (observation - induction - hypoteshis - experimentation - demostration or refutation and tesis or scientific law) was made by Francis Bacon who lived between 22 January 1561 – 9 April 1626. Was this the first definition of the scientific method or is there any older definition?

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    $\begingroup$ Bacon's idea of a scientific method was rather naive, the formula you are citing ("hypothetico-deductive method") was not coined until the second half of 19-th century. As for the general ideas of scientific methodology, they can be traced as far back as antiquity. Wikipedia gives a detailed account in History of scientific method. $\endgroup$ – Conifold Jan 30 '18 at 18:57
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    $\begingroup$ The answer is trivial, well known and can be found in Wikipedia. $\endgroup$ – Alexandre Eremenko Jan 30 '18 at 19:39
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The history of scientific method and its study (on which wikipedia has many good points and references) shows a great variety of attempted conceptualizations. This variety in itself arguably indicates that a final definition, whether classical or otherwise, has not yet been written.

With that proviso, an at least partial attempt can be made to answer the question "is there any older definition?" of scientific method (other than the quoted one attributed to Bacon). As Conifold has pointed out in his comment, the substance of the quoted definition is rather a 19th-century development or refinement, often referred to as the 'hypothetico-deductive' definition, where Bacon's own ideas were less developed or more naive.

Bacon's discussion of method came out in 1620 in his book 'Novum Organum' (Latin) (an English translated text is here).

And yes, there is to some extent an older anticipation of Bacon, at least one from 20 years before. It is from William Gilbert (1544-1603) in 'De Magnete' (Latin) of 1600. (An English translation by P Fleury Mottelay (1893, New York (Wiley)) is found here.) There were earlier writers whose works have been pointed out as examples of experimental method, but I do not know whether Gilbert was the first to discuss method itself.

Gilbert did not expand as much as Bacon on the subject of methodology, his book was mainly a groundbreaking study of magnetism, which achieved wide reception and had considerable influence in Europe. But it did contain explicit discussion of method, identified a core of experimental philosophy that was put into practice by its application to magnetic phenomena and has been described as "one of the finest examples of inductive philosophy".

According to Gilbert, "stronger reasons are obtained from sure experiments and demonstrated arguments than from probable conjectures and the opinions of philosophical speculators of the common sort". Gilbert wrote that he was dealing "in hypotheses that are provable, the things that we have through a long experience discovered." He discussed and rejected as insufficient the reliance that he ascribed to the classical Greeks, a reliance on terminology and logical argumentation alone. One sees in germ in Gilbert's work the principle of confrontation between arguments/hypotheses/ideas and the reality of experiment and observation.

(But Gilbert was also careful about the use of words, and in a paragraph that arguably still deserves attention from those who create jargon in modern times, he distinguished two kinds of motives for introducing new terms: "we sometimes employ words new and unheard-of, not (as alchemists are wont to do) in order to veil things with a pedantic terminology and to make them dark and obscure, but in order that hidden things which have no name and that have never come into notice, may be plainly and fully published.")

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