Spinoza Ethica Prop. 15 Scholium

[vir_litterarum]

Denique, si ex uno puncto infinitae cuiusdam quantitatis concipiatur, duas lineas, ut AB, AC, certa ac determinata in initio distantia in infinitum protendi; certum est, distantiam inter B et C continuo augeri, et tandem ex determinata indeterminabilem fore.

I am confused as to what “a point of a certain infinite quanity” means. I take Spinoza to be referring here to a scenario in which at first the distance between lines AB and AC is zero but then gradually extends to infinity, so how does the “infinite quantity” of the point affect this?

[adrianus]

Sic verto:

Finally, if from one point in a certain infinite quantity [a point in/of an infinite plane or space or body, say, // > res punctum infiniti superficiei spatiive seu corporis spectat> ] it were to be imagined that two lines, AB AC, at a fixed and determinate distance [between B and C] initially were to be infinitely extended, certainly the distance between B and C would continually increase, and in the end there would be an indeterminable distance from a determinate one.

[modus.irrealis]

@vir litterarum

I am confused as to what “a point of a certain infinite quanity” means. I take Spinoza to be referring here to a scenario in which at first the distance between lines AB and AC is zero but then gradually extends to infinity, so how does the “infinite quantity” of the point affect this?

I agree with adrianus’s translation – my understanding of the point is that only in an infinite body could you extend the lines to infinity and arrive at the supposed contradiction.