This essay focuses on the central themes that will be examine Your analysis must be thorough, well organize, write in paragraph format (no bullet points), and support by arguments.

the central themes that will be examine

Instructions: Your analysis must be thorough, well organize,  in paragraph format (no bullet points), and support by arguments., and incorporating your perspective. PARAPHRASE, PARAPHRASE, PARAPHRASE. When defining concepts or theories, you are require to use your own words. Provide a solid conclusion: wrapping up all the central themes you just discuss in the analysis. Include references at the end of your post.

PLEASE USE THE ATTACH CASE STUDY TO COMPLETE THIS ASSIGNMENT AS WELL AS ADDRESS THE DISCUSSION QUESTIONS BELOW:

The terms synthesis and analysis are used in mathematics in a more special sense than in logic. In ancient mathematics they had a different meaning from what they now have. The oldest definition of mathematical analysis as opposed to synthesis is that given in [appended to] Euclid, XIII. 5, which in all probability was framed by Eudoxus: “Analysis is the obtaining of the thing sought by assuming it and so reasoning up to an admitted truth; synthesis is the obtaining of the thing sought by reasoning up to the inference and proof of it.”

The analytic method is not conclusive, unless all operations involve in it are  to be reversible. To remove all doubt, the Greeks, as a rule, added to the analytic process a synthetic one, consisting of a reversion of all operations occurring in the analysis. Thus the aim of analysis was to aid in the discovery of synthetic proofs or solutions.

James Gow uses a similar argument as Cajori,

with the following clarification, in his A Short History of Greek Mathematics (1884):

The synthetic proof proceeds by shewing that the propose new truth involves certain admitted truths. An analytic proof begins by an assumption, upon which a synthetic reasoning is . The Greeks distinguish theoretic from problematic analysis. A theoretic analysis is of the following kind. To prove that A is B, assume first that A is B. If so, then, since B is C and C is D and D is E, therefore A is E. If this be  a falsity, A is not B. But if this be a known truth and all the intermediate propositions be convertible, then the reverse process, A is E, E is D, D is C, C is B, therefore A is B, constitutes a synthetic proof of the original theorem.