Title: History of scientific method
Content:  is too difficult a task for any one man or even for any one age. 'Tis much better to do a little with certainty, and leave the rest for others that come after you, than to explain all things. Newton's work became a model that other sciences sought to emulate, and his inductive approach formed the basis for much of natural philosophy through the 18th and early 19th centuries. Some methods of reasoning were later systematized by Mill's Methods (or Mill's canon), which are five explicit statements of what can be discarded and what can be kept while building a hypothesis. George Boole and William Stanley Jevons also wrote on the principles of reasoning.
Title: History of scientific method
Content:  by Immanuel Kant's Critique of Pure Reason in the late 18th century. Hume's arguments continue to hold a strong lingering influence and certainly on the consciousness of the educated classes for the better part of the 19th century when the argument at the time became the focus on whether or not the inductive method was valid. Hans Christian Ørsted, (Ørsted is the Danish spelling; Oersted in other languages) (1777–1851) was heavily influenced by Kant, in particular, Kant's Metaphysische Anfangsgründe der Naturwissenschaft (Metaphysical Foundations of Natural Science). The following sections on Ørsted encapsulate our current, common view of scientific method. His work appeared in 
Title: History of scientific method
Content:  In the late 19th century, Charles Sanders Peirce proposed a schema that would turn out to have considerable influence in the further development of scientific method generally. Peirce's work quickly accelerated the progress on several fronts. Firstly, speaking in broader context in "How to Make Our Ideas Clear" (1878), Peirce outlined an objectively verifiable method to test the truth of putative knowledge on a way that goes beyond mere foundational alternatives, focusing upon both Deduction and Induction. He thus placed induction and deduction in a complementary rather than competitive context (the latter of which had been the primary trend at least since David Hume a century before). Secondly, 
Title: Outline of scientific method
Content: Inductive reasoning appears to lie at the core of the scientific method, yet also appears to be invalid. ; David Hume was the person who first pointed out the problem of induction. ; Karl Popper offered one solution, Falsifiability The problem of induction questions the logical basis of scientific statements.
Title: John Stuart Mill
Content:  Mill joined the debate over scientific method which followed on from John Herschel's 1830 publication of A Preliminary Discourse on the study of Natural Philosophy, which incorporated inductive reasoning from the known to the unknown, discovering general laws in specific facts and verifying these laws empirically. William Whewell expanded on this in his 1837 History of the Inductive Sciences, from the Earliest to the Present Time, followed in 1840 by The Philosophy of the Inductive Sciences, Founded Upon their History, presenting induction as the mind superimposing concepts on facts. Laws were self-evident truths, which could be known without need for empirical verification. Mill countered this in 1843 in 
Title: Inductivism
Content:  Inductivism is the traditional and still commonplace, but an erroneous and implausible, philosophy of scientific method to develop scientific theories. Inductivism aims to neutrally observe a domain, infer laws from examined cases—hence, inductive reasoning—and thus objectively discover the sole naturally true theory of the observed. Inductivism's basis is, in sum, "the idea that theories can be derived from, or established on the basis of, facts". Evolving in phases, inductivism's conceptual reign spanned four centuries since Francis Bacon's 1620 proposal of such against Western Europe's prevailing model, scholasticism, which reasoned deductively from preconceived beliefs. In the 19th and 20th centuries, inductivism succumbed to hypotheticodeductivism—sometimes worded deductivism—as scientific method's realistic idealization. Yet scientific theories as such are now widely attributed to occasions of inference to the best explanation, IBE, which, like scientists' actual methods, are diverse and not formally prescribable.
Title: History of scientific method
Content:  the university. Bacon attempted to describe a rational procedure for establishing causation between phenomena based on induction. Bacon's induction was, however, radically different than that employed by the Aristotelians. As Bacon put it, "[A]nother form of induction must be devised than has hitherto been employed, and it must be used for proving and discovering not first principles (as they are called) only, but also the lesser axioms, and the middle, and indeed all. For the induction which proceeds by simple enumeration is childish. —Novum Organum section CV" Bacon's method relied on experimental histories to eliminate alternative theories. Bacon explains how his method is applied in his Novum Organum (published 1620). 
Title: History of scientific method
Content:  experimentation (tajriba). Avicenna criticized Aristotelian induction, arguing that "it does not lead to the absolute, universal, and certain premises that it purports to provide." In its place, he advocated "a method of experimentation as a means for scientific inquiry." Earlier, in The Canon of Medicine (1025), Avicenna was also the first to describe what is essentially methods of agreement, difference and concomitant variation which are critical to inductive logic and the scientific method. However, unlike his contemporary al-Biruni's scientific method, in which "universals came out of practical, experimental work" and "theories are formulated after discoveries", Avicenna developed a scientific procedure in which "general and universal questions came first and led to experimental work." Due to the differences between their methods, al-Biruni referred to himself as a mathematical scientist and to Avicenna as a philosopher, during a debate between the two scholars.
Title: History of scientific method
Content:  scientific writers of his time, Bernard wrote about his own experiments and thoughts, and used the first person. William Stanley Jevons' The Principles of Science: a treatise on logic and scientific method (1873, 1877) Chapter XII "The Inductive or Inverse Method", Summary of the Theory of Inductive Inference, states "Thus there are but three steps in the process of induction :-Jevons then frames those steps in terms of probability, which he then applied to economic laws. Ernest Nagel notes that Jevons and Whewell were not the first writers to argue for the centrality of the hypothetico-deductive method in the logic of science.
Title: History of scientific method
Content:  reading Whewell's History of the Inductive Sciences. Mill may be regarded as the final exponent of the empirical school of philosophy begun by John Locke, whose fundamental characteristic is the duty incumbent upon all thinkers to investigate for themselves rather than to accept the authority of others. Knowledge must be based on experience. In the mid-19th century Claude Bernard was also influential, especially in bringing the scientific method to medicine. In his discourse on scientific method, An Introduction to the Study of Experimental Medicine (1865), he described what makes a scientific theory good and what makes a scientist a true discoverer. Unlike 

Question: who was an early advocate for using scientific methods based on inductive reasoning?
Answer: Aristotle.
René Descartes.