Pappus of Alexandria

"Analysis... takes that which is sought as if it were admitted and passes from it through its successive consequences to something which is admitted as the result of synthesis: for in analysis we assum…"

"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. In the theoretical ki…"

"He spent a very long time with the pupils of Euclid at Alexandria, and it was thus that he acquired such a scientific habit of thought."

"But in synthesis, reversing the process, we take as already done that which was last arrived at in the analysis and, by arranging in their natural order as consequences what were before antecedents, a…"

"The so called άναλυόμϵνος is... a special body of doctrine provided for the use of those who, after finishing the ordinary Elements, are desirous of acquiring the power of solving problems which may b…"

"Walter William Rouse Ball, A Short Account of the History of Mathematics"