History of use of the term "organism"

Solution 1:

The OED’s 1701 citation (the earliest) is from Nehemiah Grew’s Cosmologia sacra: or a discourse of the universe. It reads:

It is the advantagious Organism of the Eye, by which that is procured.

At the time, it meant Organic structure.

The 1834 citation is from Philosophical transactions of the Royal Society of London and reads:

The introduction of new powers into an organism necessarily requires a modification in its mode of development.

The meaning there is An individual animal, plant, or single-celled life form. Also: the material structure of such an individual; an instance of this.

Solution 2:

First of all, etymoline.com says:

1660s, "organic structure, organization," from organize (q.v.). Sense of "living animal or plant" first recorded 1842.

The earliest I found in Google Books is 1715's Philosophical Principles of Religion: Natural and Revealed: in Two Parts, Parts 1-2 by George Cheyne: