"against, over against, opposite, on the opposite side; on the contrary, contrariwise," mid-14c., from Latin contra (prep. and adv.) "against," originally "in comparison with," ablative singular feminine of *com-teros, from Old Latin com "with, together" (see com-) + -tr, zero-degree form of the comparative suffix -ter-.
early 14c., "act of conceiving in the womb," from Old French concepcion (Modern French conception) "conception, grasp, comprehension," from Latin conceptionem (nominative conceptio) "a comprehending, conception," noun of action from past-participle stem of concipere "to take in and hold; become pregnant," from con-, here perhaps an intensive prefix (see con-), + combining form of capere"to take" (from PIE root *kap- "to grasp").
Originally of pregnancy (also with reference to Conception Day in the Church calendar); mental sense of "process of forming concepts, act or power of conceiving in the mind" is from late 14c. Meaning "that which is conceived in the mind" is from 1520s; that of "general notion" is from 1785.