I am aware that perhaps the earliest source concerning problems of maximum and minimum values occurs in Euclid's Elements. After Euclid, Archimedes of Syracuse and Apollonius of Perga seem to consider such problems in their treatises, but not with an extensive study of them. But after them, it seems that no mathematician gets interested in the realm till in the 17th Century A.D., Pierre de Fermat writes a paper to describe a method for solving problems of maxima and minima.[ See this paper: http://science.larouchepac.com/fermat/fermat-maxmin.pdf ]
But this paper, written by Fermat, makes me believe that there is still some previous activity regarding the study of maxima and minima. The degree of sophistication and certitude of this new style of problems concerning maximum and minimum properties of quantities is undeniably built on some Giant's shoulders.
Therefore I am curious if there was any mathematician in the middle or mid-late Renaissance time who contributed to this field. Precisely, I should say I am searching for a timeline of the study of maxima and minima, especially in the middle ages and in the Renaissance but before Fermat. However, I will still appreciate any related information regarding it.