The ancients considered mechanics in a twofold respect: as rational, which proceeds accurately by demonstration, and practical. To practical mechanics all the manual arts belong, from which mechanics took its name.
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The description of right lines and circles, upon which geometry is founded, belongs to mechanics. Geometry does not teach us to draw these lines, but requires them to be drawn.
Mechanics is the paradise of the mathematical sciences, because by means of it one comes to the fruits of mathematics.
The merit of painting lies in the exactness of reproduction. Painting is a science and all sciences are based on mathematics. No human enquiry can be a science unless it pursues its path through mathematical exposition and demonstration.
In the beginning of the year 1665, I found the method of approximating series and the rule for reducing any dignity of any binomial into such a series.
The latest authors, like the most ancient, strove to subordinate the phenomena of nature to the laws of mathematics.
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