The "Magic Squares" and their corresponding symbols are definitely of Medieval origin. However, the numeric squares may have had their beginning in Rome and I have heard them linked to the mathemetician mystic Pythagoras and his followers. There is also a tradition of "magic squares" using "words," Abracadabra being one of the most famous. Abracadabra was used as a charm (long before is was parodied in stagecraft), by writing the word and then diminishing it by one letter in each successive line to form a triangle. It was carried to remove illness. As the word diminished, so to would the illness. This comes from Cabbalitic usage. There was also a tradition of demon traps in the Middle East wherein a spell was written in a bowl, spiralling from the rim to the bottom where the demon would be drawn and trapped as it read the words. This tradition may have given rise to the geometric yantras of India designed to draw the viewer inwards in contemplation.

So I don't think it can be said that the tradition of the "magic square" came from one specific place, but rather it has evolved from multiple sources. The Middle Ages were a time when many ideas came together to synthesize new traditions. The squares existed long before then, but "angelic script" and such sigils and spirits as you see associated with the squares are not evident in history until that time. The other correspondences -herbs, metals, stones, animals- come from ancient associations with the planets rather than the squares themselves.

As for Venus, I find it to be one of the most fascinating planets, tradition-wise. The pentagram and octogram are both derived from the transit of Venus, and it is both the Evening and Morning Star depending upon its course. Though now associated solely with Venus, the goddess of beauty and love, at other times it has been both a male and female deity or stood for the goddess of love or war, depending upon its position.