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The pre-1910 birth records are quite scarce and would normally contain:
only the name of the child's parents
the sex of the child
the date of birth and residence of the parents
possibly not even the child's name if the child hadn't been named yet.
There are, of course, exceptions. For example, the state of Virginia has birth records since the 1850's and Vermont has records since 1770. Prior to about 1910, records are found in the individual counties (or towns in the New England states).