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[ Etymonline :]  [...] invitare "invite, treat, entertain," originally "be pleasant toward,"
from in- "toward" (see in- (2)).   [...]

I am conjecturing that entry by an object in a target necessitates the object's approach TOWARD the target; but the meaning of 'toward' still appears to suit the prefix ad- more than in-.

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    Good question: why is the same word used for "inside" and "into"? There is some shared notion of insideness, but still. It may be interesting to know that in can also be used both to indicate "inside" and "into" in Dutch. And also in German, where "inside" takes the dative case and "into" the accusative. (In Dutch, cases have mostly died, but they are still used in idiom.) – Cerberus Mar 13 '16 at 02:35

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I think part of the issue here is that "toward" isn't particularly accurate as a a description of the meaning of "in"; "into" would be much more appropriate. Consider that in English you can be in a building or you can go in(to) a building. You may be interested in this question and its answers for further information.

Joel Derfner
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  • I would as well argue for the meaning of inside. Anybody can come towards, but for inside, you need to give them the permission. – Eleshar Nov 27 '16 at 12:51