GalileoÆs mathematical-experimental method was used to test the relationship between velocity and time for a falling body:
V ? T (Cohen, 1985). Since V could not be measured, he used a combination of mathematics and experimentation to verify this relationship: if V ? T, then D ? T2 by deduction, and this is a relationship which can be tested experimentally. By confirming this relationship experimentally, he could be confident that V ? T is valid. Because D ? T2 is derived from V ? T by mathematics, and then tested experimentally, this method was named the mathematical-experimental method. This method has also been called the hypothetico-deductive method because it is used to test a hypothesis which canÆt be tested directly by experimentation. Essentially, the hypothetico-deductive method allows for the experimenter to test a theory by proxy. In other words, because Galileo was unable to test V.T (there was no way for him to by experiment make a direct correlation between times and velocities because velocity was unknown), he instead tested the hypothetical deduction that followed from V.T. Because Galileo knew that if V.T was true then it would follow that D.Tsquared, he resolved to test D.Tsquared in order to validate the V.T supposition. Because Distance and Time were known entities, this was possible to do. By working backward in this fashion, Galileo was employing the hypothetico-deductive method (Cohen, 1985, p. 207).
Borrowing the symbolic terms proffered by I. Bernard Cohen in The Birth of a New Physics, it is clear that rather than testing ôAö, Galileo deduced ôBö from ôAö and tested it, and then concluded that ôAö would hold. Cohen reminds us that because ôBö is derived from ôAö by mathematics and then tested by experiments, then the method is also mathematico-deductive (or mathematical-experimental) (1985, p. 207).
The mathematical-experimental method was useful to Galileo as he endeavor...