Hello One Shot
Hermetic Geometry use the rules of ceremonial casting. 15 minutes per magnitude. If you want to fast cast the spell, we can forget it.
It is true for standard Ring/Circle spell.
With Hermetic Geometry we can affect a remote circle/ring with sympathetic connection. The magus trace a circle, he incant the spell, calculate the target point and
the remote sympathétic identical circle "appear" at the calculate point and the spell take place at this circle (which is invisible). The remote circle don't need to pre-exist.
With a range of touch the magus touch the first circle he traces during his incantation (like normal ring/circle spells) and with the sympathetic connection the spell affect everyone into the remote circle.
I think it is the only way to explain the only example in Magi Of Hermes p101. Unless the author comes to us.
You can affect a remote circle with arcane ring or arcane circle i think. If you need arcane ring and arcane circle you will have +2 magnitudes compare to standard ring/circle. The bonus of +3 to the incantation will not be very usefull. Add the rules of ceremonial casting and the virtue will not be very attractive.
The range Line could be use with any target and duration...
I think the virtue is not clearly explain with only one exemple with false calculation.
With your help I think i understand better this virtue.
Cheers