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It seems to me that very few if any scientists/philosophers stated that science could be used for predictions before the early 1900s. In the scientific context I have only encountered the use of the word prediction only in relation to astronomy. I suppose this may be due to the few predictive theories outside astronomy back then

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    $\begingroup$ Are you asking when they actually spelled out the word "prediction"? Because Euclid predicted what reflections in a circular mirror would look like, Archimedes predicted when submerged bodies would float, Galileo predicted that projectiles would have the longest range when launched at 45°, etc. $\endgroup$ – Conifold Sep 7 at 11:16
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    $\begingroup$ This is too vague and smeared over centuries as a result. They were deciding what "theory" predicts and then staging experiments to see if that is so since they were staging experiments, even earlier in astronomy since no staging was required. Newton "describes" it for special cases in Principia, and he was not the first. But if you want it at the level of abstraction of the modern terminology in your post then it is likely mid-19th century when Whewell and others started writing treatises on "scientific method". $\endgroup$ – Conifold Sep 7 at 12:00
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    $\begingroup$ Hooke writes "Now as the theory is very short, so the way of trying it is very easie...", Newton writes "Hitherto I have laid down such principles as have been received by mathematicians, and are confirmed by abundance of experiments... But to prevent an objection that may perhaps be alledged against the rule, for the proof of which this experiment was made...". Does it count? $\endgroup$ – Conifold Sep 7 at 13:35
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    $\begingroup$ This is one of those questions that at its heart is ahistorical, since continued minor tweaking what "scientific context" means will lead you back further and further. Surely the prediction of eclipses by the Greeks qualifies. What about even earlier predictions of planetary motion, the rise and fall of the Nile river a couple of thousand years before this, the prediction of sunrise/sunset times probably even earlier, etc.? $\endgroup$ – Dave L Renfro Sep 7 at 15:29
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    $\begingroup$ "It is a test of true theories not only to account for, but to predict phenomena", Whewell, The philosophy of the inductive sciences (1840). Plato called it "saving the phenomena" two millennia earlier. Although, characteristically, it was not his "theory" which "predicted" celestial bodies moving in perfect circles, but the phenomena, that required saving. Duhem took it to be what Ptolemy was doing in Almagest. $\endgroup$ – Conifold Sep 7 at 21:00

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