at the same time the various visual impressions are grounded by a soundtrack that is propagated through the body via speakers placed beneath a long bench on which you can sit in the installation.

How would the previous sentence be correctly capitalized?
Answer: At the same time the various visual impressions are grounded by a soundtrack that is propagated through the body via speakers placed beneath a long bench on which you can sit in the installation.
the romans rebuilt the town on the island and it prospered and grew beyond the boundaries of the old celtic city. the island town was known by the latin name lutetia, which was latin for midwater-dwelling.

How would the previous sentence be correctly capitalized?
Answer: The Romans rebuilt the town on the island and it prospered and grew beyond the boundaries of the old Celtic city. The island town was known by the Latin name Lutetia, which was Latin for Midwater-Dwelling.
the theorems then follow a fairly similar pattern to the two-dimensional analogues previously given in books one and four.

How would the previous sentence be correctly capitalized?
Answer: The theorems then follow a fairly similar pattern to the two-dimensional analogues previously given in books one and four.
it is also no secret that there are members and groups of members in enhedslisten who are not agreed with sap on what constitutes a strength or a weakness and are likely to oppose the proposals that sap are making in this text and will defend the status quo.

How would the previous sentence be correctly capitalized?
Answer: It is also no secret that there are members and groups of members in Enhedslisten who are not agreed with SAP on what constitutes a strength or a weakness and are likely to oppose the proposals that SAP are making in this text and will defend the status quo.