Coincide, v. i. [imp. & p. p. Coincided; p. pr. & vb. n. Coinciding.]
Etymology: [L. co- + incidere to fall on; in + cadere to fall: cf. F. coïncider. See Chance, n.]
1. To occupy the same place in space, as two equal triangles, when placed one on the other. If the equator and the ecliptic had coincided, it would have rendered the annual revoluton of the earth useless. Cheyne.
2. To occur at the same time; to be contemporaneous; as, the fall of Granada coincided with the discovery of America.
3. To correspond exactly; to agree; to concur; as, our aims coincide. The rules of right jugdment and of good ratiocination often coincide with each other. Watts.
Shades of meaning
Fernald has no entry of its own for coincide; he lists it under agree.
Where he writes about it:
To concur is to agree in general; to coincide is to agree in every particular. — from agree
Whether in application to persons or things, concur tends to expression in action more than coincide; we may either concur or coincide in an opinion, but concur in a decision; views coincide, causes concur. — from agree