【Educe】 , 【evoke】 , 【elicit】 ,  【extract】 ,  【extort】  mean to bring or draw out what is hidden, latent, or reserved.

【Educe】 usually implies the development and outward manifestation of something potential or latent.

【Evoke】 basically suggests the voice or the words of a magician compelling spirits to leave the other world or the dead to arise from their graves.

In current use the term ordinarily implies the operation of a powerful agency that produces an effect instantly or that serves as a stimulus in arousing an emotion, a passion, or an interest.

【Elicit】 usually implies pains, trouble, or skill in drawing something forth or out; it often implies resistance either in the person or thing that is the object of effort.

【Extract】 implies the action of a force (as pressure or suction).

【Extort】 implies a wringing or wresting especially from one who is reluctant or resisting.