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Aeuitas age/lifetime indeed can be said, but it is rare. In usage, perpetuitas perpetuity or aeternitas eternity is said more. Aeuum age/time, however, is of the neuter gender.
Auus grandfather is the father of the father. Proauus great-grandfather is the father of the grandfather. Atauus great-great-grandfather is the father of the great-grandfather. Tritauus great-great-great-grandfather is the father of the atauus.
Alterutrum one or the other signifies either this or that, or both. But it has more to do with two sides.
Alii others we write in the singular in the dative case, as Sallust says concerning Catiline: 'He was enticing many of the youths with diverse allurements: to some alii he provided prostitutes, to others alii he bought horses, to others alii dogs for hunting.'
Aruina fat/grease, tallow.
Altilitate from nourishing, from alere to nourish, that is, the very thing which is nourished.
Acti driven/compelled, forced, compelled.
Autumant they assert/claim, they assert, confirm, or aver.
Auspicium divination/auspice is the beginning of some thing, from which it first takes its start, that is, it is begun so that it may be done. Moreover, auspicium is that which birds or animals demonstrate to pagan augurs, whence future things are known. Therefore, there are good auspices, which urge things to be begun; there are bad ones, which forbid them.
Actae shores/beaches are called secret places near the sea, that is, on the shore, pleasant and delightful.