Placidus
Placidus de Tito (1601-1668)
most common modern · time-based division · controversial at high latitudes
How it divides the sky
Placidus determines house cusps by dividing time — thirds of the time it takes a planet to move from the birth point to the upper or lower meridian. So house sizes vary greatly with northern/southern latitude. At the equator all 12 houses are roughly equal; at 50° N some houses become tiny, others huge. Above 60° the system mathematically fails.
When to use it
The default of most modern Western astrologers. Tropical zodiac + Placidus is the most common combination. Works well near the equator and at mid-latitudes. If you're in Turkey (~38-40° N), Placidus is a safe choice. If you're in Norway/Canada, consider another system (Whole Sign, Equal).
History
Italian monk and mathematician Placidus de Tito published it in 1657; the method actually comes from 8th-century Arab astrologers. Its historical popularity came in the 19th century with the reprinting of William Lilly's tables.