III.

Dic, Heliconiadum decus, O sublime Sororum
Pythagora! tua quot tyrones tecta frequentent,
Qui, sub te, sophiæ sudant iu agone magistro ?
Dicam; tuque animo mea dicta, Polycrates hauri :
Dimidia horum pars præclara mathemata discit,
Quarta immortalem naturum nosse laborat,
Tres sunt foeminei sexus.

The question here is, to find a number, the,,,, and of which+3, shall be equal to that number. It may be easily replied that this number is 18.

IV.

Dic quota nunc hora est? Superest tantum ecce diei
Quantum bis gimini exacta de luce trientes.

If we divide the day, as the ancients did, into 12 equal portions, the question will be to divide that number into two such parts, that of the first may be equal to the second: in this case the result 54 for the number of the hours elapsed; and consequently, for the remainder of the day 6 hours.

V.

Hic Diophantus habet tumulum, qui tempora vitæ
Illius mira denotat arte tibi.

Egit sextantem juvenis, languine malus

Vestire hinc cœpit parte duodecima.

Septante uxori post hæc sociater et anno

Formosus quinto nasciter inde puer.

Semissem ætatis postquam attigit ille paternæ,

Infelix subita morte peremptus obit.

Quatuor æstates genitor lugere superstes

Cogitur, hinc annos illius assequere.

To resolve this problem, we must find a number, the, of which+5+4, shall be equal to the number This number is 84.

12, 4, and

itself.

VI.

Qui jaculamur aquas tres hic adstamus Amores;
Sed varie liquidas Euripo immittimus undas :
Dexter ego, summis et quæ mihi manat ob alis
Ipsum lympha replet solo sextante dici;
Quatuor est horis lævus versa influit urna;
Dimidiatque diem medius dum fundit ab arca:
Dic, age, quam paucis Euripum implebimus horis,
Ex arca simul atque alis urnaque fluentes?

If we suppose the day to be divided into 12 hours, the 3 cupids can fill the bason in, of a day, or a little more than an hour.