Schweikart, son of an attorney in Hesse, was educated in the school of his town.

He went to the high school in Hanau and Waldeck before entering in 1796 to study law in the university of Marburg, where he attended lectures of the mathematics professor J.K.F.

After practicing as a lawyer for a few years in Erbach, he was, from 1803 to 1807, instructor of the youngest prince of Hohenlohe-Ingelfingen.

[3] But Schweikart is best remembered for his works on mathematics: in 1807 he published Die Theorie der Parallellinien, nebst dem Vorschlage ihrer Verbannung aus der Geometrie (The theory of parallel lines, along with the suggestions of their banishment from geometry).

[5] He influenced the work of his nephew, the mathematician Franz Taurinus.