"Mathematical analysis of the infintesimal", peaked in the works of Euler, was just that: an attempt to mathematically analyze, among other things, the notion and applications of the infinitely small (and infinity in general); for some reason the words "mathematical" and "infinity" were subsequently dropped, and we are left just with a generic term "analysis" which now requires context to be understood properly.
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"Mathematical analysis of the infintesimal", peaked in the works of Euler, was just that: an attempt to mathematically analyze, among other things, the notion and applications of the infinitely small (and infinity in general); for some reason the words "mathematical" and "infinity" were subsequently dropped, and we are left just with a generic term "analysis" which now requires context to be understood properly.