To complete the sentences correctly, you would drag and drop the historic figures as follows:
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For the first part of the sentence: "During Roman rule of Egypt, Claudius Ptolemy studied astronomy, geography, optics, and mathematics."
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For the second part of the sentence: "Elsewhere in the empire, the Roman physician Galen studied anatomy and medicine."
So the completed sentences would read:
"During Roman rule of Egypt, Claudius Ptolemy studied astronomy, geography, optics, and mathematics. Elsewhere in the empire, the Roman physician Galen studied anatomy and medicine."