Ptolemy's four quarters divide only the oikoumene, the inhabited world known in the second century, and the western hemisphere lies wholly outside it. No quarter, triplicity or planetary co-ruler was ever assigned to the Americas by the tradition that built the scheme, and nothing proposed since has acquired comparable standing. This is not a lost passage or a disputed reading; it is an absence created by the geographic horizon of the source.
What would resolve this A survey of the mundane astrological literature from the sixteenth century onward, when the Americas entered European awareness, establishing whether any author extended the chorography to the new hemisphere, on what reasoning, and whether the extension was taken up by anyone else. A negative result would settle the entry as firmly as a positive one, and either way the entry ceases to be an open absence.
OpenHistory of astrology; early modern intellectual history; history of geographic knowledgeNicholas Campion, A History of Western Astrology