Introduction to Arithmetic. Trans. into English by Martin Luther D'Ooge. With studies in Greek arithmetic by Frank Egleston Robbins and Louis Charles Karpinsky

The English translation of Nicomachus of Gerasa’s Introduction to Arithmetic by Martin Luther D'Ooge, with studies by Robbins and Karpinsky, illuminates ancient Greek numerical philosophy. Nicomachus presents arithmetic as a foundational science intertwined with metaphysics, emphasizing the mystical properties of numbers. The supplementary studies enhance understanding by situating Nicomachus within Greek mathematical tradition, bridging ancient and modern perspectives.

Though less rigorous than Euclid, Nicomachus’ work influenced medieval mathematics and philosophy. This edition provides valuable insights into historical numeration and the cultural significance of arithmetic, making it a must-read for historians of mathematics and philosophy enthusiasts.

pp.237/238:

"... the sum of nothing added to nothing, which makes nothing."

(D'Ooge, M. L., Robbins, F. E., & Karpinsky, L. C. (1926). Nicomachus of Gerasa Introduction to Arithmetic with Studies in Greek Arithmetic. Trans, into English by Martin Luther D'Ooge, with studies in Greek arithmetic by Robbins and Karpinsky. New York: Macmillan.)  see also: HathiTrust

In other words, it is:  0 +0 +0 + ... = +0.

However, even if not completely incorrect, this is not correct.  Peano axioms of the multiplication by zero are not correct. Much more, it is

1+1+1+ ... = +n

Multiplying by zero, it is

(+1+1+1+...)*0 = +n*0 = n_0

or

0+0+0+... = n_0

see also: Barukčić, I. (2020). Zero and infinity: Mathematics without frontiers. Hamburg: BoD–Books on Demand. Page: 90-91, Theorem 3.25.