in book one the relations satisfied by the diameters and tangents of conics are studied while in book two apollonius investigates how hyperbolas are related to their asymptotes , and he also studies how to draw tangents to given conics.

How would the previous sentence be correctly capitalized?
Answer: In book one the relations satisfied by the diameters and tangents of conics are studied while in book two Apollonius investigates how hyperbolas are related to their asymptotes , and he also studies how to draw tangents to given conics.
this monday a new record was set by to players when they played a hand on full tilt poker that will as from now on be known as history's largest poker pot until a new record is set.

How would the previous sentence be correctly capitalized?
Answer: This Monday a new record was set by to players when they played a hand on Full Tilt Poker that will as from now on be known as history's largest poker pot until a new record is set.
it only takes about 35 minutes to travel from anundgard sundsvall by car.

How would the previous sentence be correctly capitalized?
Answer: It only takes about 35 minutes to travel from Anundgard Sundsvall by car.
diving in the similan islands is also possible from krabi by daytrip or liveaboard cruises.

How would the previous sentence be correctly capitalized?
Answer: Diving in the Similan islands is also possible from Krabi by daytrip or liveaboard cruises.