New Liturgical Movements has a picture of a thirteenth century chasuble from Toledo. I used to have one in this shape, I gave it away to a priest who liked I it, I must admit I did too.
It was the ancient shape of the cape or over coat worn over the tunic, it should come down to the knees. It is made from a semi-circle of fabric, with orphrey uniting the straight edge and giving a little extra movement so it isn't exactly 90 degrees.
In the West it was gathered up in the crook of the arms, giving it rather beautiful folds, with more or less an equal amount of fabric front and back, in the East in was worn so the back looked more like a cope and the front had less bulk. But East and West used the same vestment.
This is the vestment that the traditional Roman presumes the priest is wearing, hence he is supposed to be helped with it when his hands drop below the elbow, for example at the incensation. Worse problems are encountered at the elevation of the host and chalice, the server literally has to lift the fabric of the chasuble to enable the priest to raise his hands so the host might appear above his head.
- Once the elevation was introduced two developments took place to ease things for the priest, those who thought the conical shape, little hutness, was important cut the sides of the chasuble from the curved edge to the shoulder, hence the Roman or "fiddleback" chasuble.
- Those who thought the fullness was important eased the 90 degree angle sometimes to the 180 degree point, where there was a straight edge along the shoulder and the garment became, rather than a semi-circle, a full circle, especially in the late twentieth century when it could be made of cheap polyester. It is what is commonly call the Gothic chasuble.
The 90 degree angle and the circularity was previously significant in so far as it was related to the square, a symbol of the universe, of perfection: the three corneredness to the Trinity.