gracheeha

I was taught that infinite described numerical bounds while infinitesimal described a quantity. Where infinite is a significant scope and infinitesimal is an insignificant quantity.

For example, if I manufactured an infinite amount of steel cups on a steel die there would be an infinitesimally small difference between any two adjacent cups (a few atoms). However, as the action of stamping the die causes a small amount of material to rub off both the die and press, comparing two cups thousands or millions of units apart will begin to yield a significant change as the die and press begin to wear out.

Therefore:

infinitely large means "very large" or describes the upper bound
infinitely small means "very small" or describes the lower bound
infinitesimally small means so small as to be insignificant
infinitesimally large has no logical meaning

Additionally, saying infinitesimally small is in effect, saying a small amount of insignificance. Infinitesimal should be regarded as an absolute Boolean.
This usage varies between different physical sciences as well as math and physics depending on the context used. This is because Infinity as a concept can be both paradoxical and rational. When taken out of the realm of scientific writing or engineering into common usage, the definitions tend to be a composite of the solved equation or problem in its own discipline.

вполне может быть, что такой книги в сети нет. это ж весьма специфичная тематика, да и наверняка старое издание.