Scientia Media

In his preface to Newton's Principia, Cotes igives a syllogistic argument for the attraction of all planetary bodies towards the sun that could be construed as a syllogism in “scientia media” form (the major term is more mathematical, Prop.2 of Principia; and the minor term seems more physical, Kepler’s second law). (From Cohen’s edition, p.387-88, with my [additions]/italics):

“Now, it is reasonable to accept something that can be found by mathematics and proved with the greatest certainty: namely, that:
[M:] all bodies moving in some curved line described in a plane, which by a radius drawn to a point (either at rest or moving in any way) describe areas about that point proportional to the times, are urged by forces that tend toward that same point.
Therefore, since it is agreed among astronomers that
[m:] the primary planets describe areas around the sun proportional to the times, as to the secondary planets around their own primary planets,
[C:] it follows that [etc.] ...  This force can, appropriately, be called centripetal ... From whatever cause it may in the end be imagined to arise."

I understand the last phrase to be Cotes’ recognition that mathematical physics as a scientia media abstracts from considering physical causes as such.


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