You should read Gauss' book (General theory of curves and surfaces). It is written in a fairly unenlightening manner (back then, people did not trust pictures, so Gauss just does pages and pages of horrible computations), but if you read it carefully, you will see that he had a very geometric view of things. Secondary sources (e.g., Spivak) are based entirely on Gauss' book, since Gauss did not write an autobiography, to the best of my knowledge), so you should go to the source.

You should read Gauss' book (General theory of curves and surfaces). It is written in a fairly unenlightening manner (back then, people did not trust pictures, so Gauss just does pages and pages of horrible computations), but if you read it carefully, you will see that he had a very geometric view of things. Secondary sources (e.g., Spivak) are based entirely on Gauss' book and since Gauss did not write an autobiography (to the best of my knowledge) you should go to the said book of his.