given this fact, it is highly unlikely that any perpetrators of a hoax in 1st century judea would elect women to be their primary witnesses.

How would the previous sentence be correctly capitalized?
Answer: Given this fact, it is highly unlikely that any perpetrators of a hoax in 1st Century Judea would elect women to be their primary witnesses.
4 but the multitude of the city was divided: and part held with the jews, and part with the apostles.

How would the previous sentence be correctly capitalized?
Answer: 4 But the multitude of the city was divided: and part held with the Jews, and part with the apostles.
this end-user license agreement including its annex (“eula”) applies to you and teamviewer gmbh (“teamviewer” or “we”) for the licensing and use of our software, which includes the teamviewer software and all versions, features, applications and modules thereto (“software”).

How would the previous sentence be correctly capitalized?
Answer: This End-user License Agreement including its Annex (“EULA”) applies to you and TeamViewer GmbH (“TeamViewer” or “We”) for the licensing and use of our software, which includes the TeamViewer software and all versions, features, applications and modules thereto (“Software”).
this word includes the vast universe, not just this earth’s atmosphere.

How would the previous sentence be correctly capitalized?
Answer: This word includes the vast universe, not just this earth’s atmosphere.