大般涅槃經義記 1.93

1.93

帝釋獻中，先標供主，釋提桓因忉利天王，此翻名為能為天王。三十三天兼列其眾，須彌頂上有其三十三處之別，當中釋居，面各八國，臣民所住，故通說為三十三天。次明獻供，倍過前者，倍過四王，亦可倍前一切所設。如來不受，不果同前。乃至第六「所設」已下是其欲界空天獻供，始從夜摩乃至他化皆來獻奉，文相可知。

In Śakra's offering, the maker of the offering is first designated: Śakra Devānām Indra, the king of the Trāyastriṃśa Heaven, whose name is translated as "Able to Be Heavenly King." The thirty-three heavens also include his retinue. At the summit of Mount Sumeru there are thirty-three distinct places: in the center resides Śakra, and on each of the four sides are eight states inhabited by subjects and ministers; hence they are collectively called the Thirty-Three Heavens. Next, his presenting offerings is clarified: "doubled beyond the previous" means doubled beyond the Four Kings, or it may mean doubled beyond all that had been prepared before. The Tathāgata does not accept it, and his failing in his aim is the same as before. Through to the sixth, from "what was prepared" downward, are the offerings presented by the celestial devas of the desire realm: beginning from the Yāma Heaven down to the Paranirmitavaśavartin Heaven, all came to present offerings, the textual details of which can be understood.