Avodah Zarah, Chapter One, Mishnah Seven
This mishnah teaches that one is forbidden to assist a non-Jew in any way that may injure the public.
1) One should not sell them bears, lions or anything which may injure the public.
2) One should not join them in building a basilica, a scaffold, a stadium, or a platform.
3) But one may join them in building public or private bathhouses.
a) When however he reaches the cupola in which the idol is placed he must not build.
Section one: A Jew is not allowed to sell bears or lions to non-Jews, lest the non-Jew not take proper care of the animal and the animal cause damage to the public. This section may also be understood as referring to the gladiator exhibitions which often involved lions and bears. The Rabbis were opposed to these violent exhibitions and to the culture that encouraged the enjoyment of bloodshed. A Jew should certainly not attend such events nor sell animals to non-Jews that might be used in these events.
Section two: A Jew may not join non-Jews in building any of the structures listed in this section. The basilica served as a courtroom. The scaffold was used for executions. The platform was used for judges to make speeches. We can see from this mishnah that the Jews had a deep distrust for the non-Jewish law system. This law system is considered damaging to the public and therefore a Jew should not aid in building this system.
Section three: A Jew is allowed to join non-Jews in building bathhouses, since bathhouses are for the public good. Indeed in other Talmudic sources the Romans are praised for building bathhouses, marketplaces, roads and bridges. From other stories in the Talmud and a famous story that will appear in our tractate, it is clear that Jews and non-Jews shared public bathhouses.
[Note: the version of the mishnah upon which my interpretation is based is dimasaot and not bimasaot, as recommended by Albeck.]
A Jew may not aid in building the cupola of the bathhouse since that is the place where the idol is placed. As we have learned already in the previous mishnayoth, a Jew may not perform any action which would aid in idolatrous practice.