ABSTRACT
This chapter defines mathematical analysis and synthesis based on Nicomachean and Eudemian Ethics, where analysis takes that which is as if it were admitted and passes from it through its successive consequences to something which is admitted as the result of synthesis; But in synthesis, reversing the process, one takes as already done that which was last arrived at in the analysis and, by arranging in their natural order as consequences what before were antecedents, and successively connecting them one with another, will arrive finally at the construction of what was sought; Now analysis is of two kinds, the one directed to searching for the truth and called theoretical, the other directed to finding what we are told to find and called problematical. Immovable principles such as those of mathematics do not possess absolute authority, although they are admitted as having similar force; for, even in mathematics, if the principle were changed, almost all the propositions proved would be altered.
