Text: as it moves north it switches from having a westward movement relative to the earth's surface to having an eastward movement.

Correct capitalization: As it moves north it switches from having a westward movement relative to the Earth's surface to having an eastward movement.

Text: 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.

Correct capitalization: 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.

Text: wealth shouldn't be our end goal, it should be a means to a greater end. we also can't afford to

Correct capitalization: Wealth shouldn't be our end goal, it should be a means to a greater end. We also can't afford to

Text: discover our selection of vintage interior zinc items, and give them a new life in your own personal space.

Correct capitalization:
Discover our selection of vintage interior zinc items, and give them a new life in your own personal space.