in 1846 this planet was discovered by the frenchman urbain le verrier, as well as by the german gottfried galle, and was given the name neptune. bouvard's hypothesis had thus been proved correct, but he did not live to see its triumph as he died three years before le verrier's discovery.

How would the previous sentence be correctly capitalized?
Answer: In 1846 this planet was discovered by the Frenchman Urbain Le Verrier, as well as by the German Gottfried Galle, and was given the name Neptune. Bouvard's hypothesis had thus been proved correct, but he did not live to see its triumph as he died three years before Le Verrier's discovery.
he pressed for it to buy four slum properties in the town which they renovated so that the poorest families of dundee could live there.

How would the previous sentence be correctly capitalized?
Answer: He pressed for it to buy four slum properties in the town which they renovated so that the poorest families of Dundee could live there.
an ovarian cyst while pregnant should not cause any issues to your unborn baby.

How would the previous sentence be correctly capitalized?
Answer: An ovarian cyst while pregnant should not cause any issues to your unborn baby.
the gallery application is activated automatically.

How would the previous sentence be correctly capitalized?
Answer: The Gallery application is activated automatically.