In this lesson we will study Mishnah 7 in the first chapter of Maseches Avodah Zarah. The Mishnah's starting point is the prohibition against selling dangerous items to non-Jews - weapons and the like.
The commentators differ as to the reason for this prohibition:
The concern is that they may come to kill a Jew.
The concern is that they may kill non-Jews unlawfully, in violation of the seven Noahide laws, and the Jew turns out to be assisting them.
Whatever the reason may be, the Mishnah rules that one does not sell non-Jews bears, lions, or anything that can cause harm to the public - weapons such as swords and spears - out of concern that they will harm Jews or kill non-Jews unlawfully.
Building for non-Jews and together with them:
For the same reason, one may not assist them in carrying out executions, and therefore a Jew may not build together with them, nor even for them, the following structures:
Basilica - a large, ornate building used for public events and civic affairs, such as a town assembly or a serious, high profile trial in which a person might face the death penalty.
Gardom - a kind of courthouse in which capital cases are judged; building it helps the non-Jew to kill, and that is not permitted.
Stadium - an arena in which bullfights and gladiator contests were held, in which people are killed.
Bamah - a sort of platform from which a person was thrown as part of the execution process, similar to what we today call a gallows.
Here too the concern is twofold: that Jews may be thrown into the stadium, or that non-Jews may be killed unlawfully. In any event, these are places of killing, and such structures serve directly to facilitate executions - and a Jew may take no part in them.
What may be built together with them:
By contrast, it is permitted to build together with them, and even for them, public structures intended for beauty and decoration. These do not serve idolatry, even though idols are sometimes depicted in them: for example, an ornate fountain in the town square with idolatrous statues and images incorporated into it. Since these are not set up for the worship of the idol but purely for decoration, a Jew is permitted to be involved in erecting the site itself - the fountain - but not in erecting the idol.
The bathhouse:
The bathhouse is a public bathing facility. The custom was to place an image of an idol in public bathhouses, and generally, as the commentators put it, a statue of Aphrodite - the Greek goddess of love, beauty, fertility and pleasure. In the Roman version, and this is indeed the Roman period, the reference is to Venus, who as it were took Aphrodite's place. But the statue was set up purely for decoration, and not for the worship of the idol as such, and therefore it is permitted to build the bathhouse together with idolaters or for them.
"Higi'u lakipah":
But "higi'u lakipah" - once they reach the niche in which the idol will be set. A "kipah" is a kind of arch or alcove inside which the image is stood up. Here the purpose of the alcove is specific: to house the idolatry. In this it differs from a bathhouse, which stands essentially so that people can bathe in it. The kipah is made for the idol itself, and making something for idolatry is forbidden even when it does not involve worshiping the idol.
Therefore, "mah she'ma'amidin bah avodah zarah" - the place in which the idol will be set - "assur livnos". A Jew may not build the alcove of the idol itself, but the bathhouse in which the image will be placed he is permitted to build. The same applies to a public square containing a fountain and the like: the identical rules govern it.
In summary: In this Mishnah we learned the prohibition against selling to gentiles items that endanger the public, whether out of concern for the killing of Jews or out of concern for assisting in unlawful killing. From this follows the prohibition against building together with them or for them a basilica, a scaffold, a stadium or a platform - structures used for carrying out executions. In contrast, decorative and public structures such as a fountain and a bathhouse are permitted, even though idolatrous images are set up in them for ornamentation. The test is the purpose of the structure: anything designed from the outset to house the idolatry, such as the kipah, is forbidden to build.