3 ms·
Depends way you look at it. In some ways, analytic geometry generalises a set of algebraic tools to geometric problems. Eg from the text > For the analysts, th
by freehorse 9mo ago
Depends way you look at it. In some ways, analytic geometry generalises a set of algebraic tools to geometric problems. Eg from the text
> For the analysts, this was irrelevant: algebra captured the essential relations expressed by the terms of the problem, which then served to guide the mathematician toward the solution. For the synthetics, by contrast, a solution to the original geometrical problem could only be geometrical in nature; and so, what the analysts were offering were not solutions but meaningless numbers.
> While the analysts strove for maximum generality, the synthetics argued for the specificity and locality of all mathematical methods. […] [For the synthetics] even more misleading would be to believe that there is a single universal method that can be applied to all kinds of problems.