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Not sure about any actual relationship, but in my records I have a Martha Noggle who married Frederick (spelled Fredrick) on 8 Sept 1850 in Henry County, Indiana. Given the location and time period, Martha may be a sibling or cousin of Cornelia.
Also, some relatives on my branch lived in Henry County, Indiana, but I have no info on Cornelia (or the Martha mentioned above) as a direct relation. Calvin Noggle (b.1800-1810 in Ohio), married Sarah Arnett in 1828 in Warren County, Ohio, and they moved to Henry County, Indiana prior to 1840. Calvin's parents were Jacob Noggle (1768-1841) and Nancy Venard (d.1849). No Cornelia listed as a child of Jacob and Nancy, either, unfortunately. However, it is possible there is some distant relationship between these families.