The phrase "and corrected the first" is grammatically correct and can be used in written English.
It can be used when referring to making a correction to the first item in a series or list.
Example: "After reviewing the document, I found several errors and corrected the first."
Alternatives: "and amended the first" or "and fixed the first".
Except on rare occasions where time or distance precluded review, Cooper always examined and corrected the first proofs himself.
LB designed the ad hoc software and corrected the first draft.
Z Culig designed the study, supervised and coordinated research, analyzed data, and corrected the first draft of the manuscript.
GG participated in the design of the case report and review of literature and corrected the first draft.
F R Santer is responsible for day-to-day supervision, coordinated research, analyzed data, and corrected the first draft of the manuscript.
Zhijun Bao conceived the initial idea, contributed to each stage of the study development, analysis, reporting, reviewed the analysis and interpretation of data, corrected the first draft, co-designed the contents and revised the manuscript.
CL conceived the initial idea, contributed to each stage of the study development, analysis, reporting, reviewed the analysis and interpretation of data, corrected the first draft, co-designed the contents and revised together with EO the manuscript.
CL contributed to each stage of the study development, analysis, reporting, reviewed the analysis and interpretation of data, corrected the first draft, co-designed the contents of the manuscript.
In two cases I agreed, and corrected the sentences; in the third I didn't, for reasons I'll explain.
She published a catalogue of stars in 1798 through the Royal Society, which significantly updated and corrected the one published by the first astronomer royal, John Flamsteed, in 1725.
And after correcting the first error waited a year before forced by the IRS to correct the other.
