The House of _Borghese_ descended from _Paul_ the Fifth, who succeeded _Clement_ (though _Leo_ the Eleventh, who liv’d but five and twenty days, was betwixt them) ran the same fortune; but being of a later Plantation in _Rome_, it conserves still some weak and decrepit Branches. One of the principal designs _Alexander_ had, to marry _Don Agostin_ with the young Princess _Borghosa_, was to unite the Estate and Patrimony of that tottering and declining House, with the House of _Chigi_, which at that time was rising to great Emminence, though for a while they came not to _Rome_. There was but one sprig left of the House of the _Borghesi_, and which was worse, even that of a weak temper, and much subject to infirmities: which _Alexander_ considering, and what accidents the vicissitudes of the world might bring upon the house of the _Borghesi_, he applyed all his endeavours to make a match (which succeeded well) with his Nephew, and gave him fair hopes of seeing the Patrimony of the _Borghesi_ in his own house. And this is the state of the _Borghesi_ at present, who in the time of _Paul_ the fifth, had above a dozen males of that name, of which there were not above six married; which was very considerable. But I return to speak how squares go in the world. The Families of the _Ludovisi_, _Barbarini_, _Panfili_, and _Chigi_, who yielded the four last _Popes_, I shall speak nothing of; because they have not enjoy’d the Benefits of the Papacy full out thirty years: so as it behoving us to let them rest in peace, I shall leave the observations of their Catastrophe to them which come after us. One thing only I shall insert, that the _Aldobrandini_ had at one time many more males alive, than are at present left of all these four houses together. God Almighty bless them according to their own desire; which I do heartily pray, as having no animosity against those that are good. Some have observ’d, and not with much difficulty, that the greatest part of the _Popes_ Families were, before their advancement to the Papacy, of great antiquity and grandeur; but for many that rais’d themselves by the treasure of the Triple Crown, it is not so easie to finde; for instead of attaining to a perpetuation of their Families, they have not been prolifique enough to defend them against a perpetual annihilation. The house of the _Medici_ in _Milan_ was of above two hundred years antiquity, maintaining it self in great Honour and Magnificence: But after _Pius_ the fourth was elected _Pope_ out of it, it grew worse and worse, declining with much more speed than it was rais’d, and that after so extravagant a manner, they could discern themselves rise, but could not perceive their decay.