Proving Fermat's principle without calculus?

[Nikhil Kumawat]

According to me this topic must be raised and discussed how fermat did it without calculus.What problems he faced since calculus was developed afterwards by Newton leibniz.

http://aapt.scitation.org/doi/10.1119/1.1514235

Moderator's edit: File substituted by link due to potential copyright violation.

 

[Nikhil Kumawat]

I need help over this topic too...and a clarification over how the series of events went in history..

 

[jim mcnamara]

@Nikhil Kumawat thread is being moved to General Math - the New Member forum is for introductions not questions.

 

[fresh_42]

I moved it to Classical Physics as there might be better chances of an answer. Although it is about mathematical techniques, it is a physical law at its heart. The historical aspect of it is also about the history of Snell's law.

@Nikhil Kumawat please remind me to move it back to mathematics in case you won't get answers here. Both subforums are suited, so the question where it belongs to has no unique answer.

The fact, that there was none of our modern notations doesn't imply they haven't had methods to deal with. There have been several wordings around which actually describe the calculations, simply in other terms. I've recently read an original paper from Leonhard Euler about the gamma function and couldn't identify even the function from this. This doesn't affect the fact, that it nevertheless contained the statement which we nowadays write down in a completely different manner.