And the celebrated doctor expounded his plan of treatment with Soden waters, a remedy obviously prescribed primarily on the ground that they could do no harm.
He was a believer, who was interested in religion primarily in its political aspect, and the new doctrine which ventured upon several new interpretations, just because it paved the way to discussion and analysis, was in principle disagreeable to him.
There are no more uses of "primarily" in the book.
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Did the author mention multiple companies primarily to demonstrate diversity of solutions or to show that interest in the industry is widespread?
The second paragraph is primarily concerned with showing how the colleges are different.