Arithmetic and geometry were taught on floors, which were strewed with dust, or sand; in which the numbers and diagrams were made and drawn, which they might strike out at pleasure. THE SECOND SATIRE OF PERSIUS. DEDICATED TO HIS FRIEND PLOTIUS MACRINUS, ON HIS BIRTH-DAY. THE ARGUMENT. _This Satire contains a most grave and philosophical argument, concerning prayers and wishes. Undoubtedly it gave occasion to Juvenal's tenth satire; and both of them had their original from one of Plato's dialogues, called the "Second Alcibiades." Our author has induced it with great mystery of art, by taking his rise from the birth-day of his friend; on which occasions, prayers were made, and sacrifices offered by the native. Persius, commending, first, the purity of his friend's vows, descends to the impious and immoral requests of others. The satire is divided into three parts. The first is the exordium to Macrinus, which the poet confines within the compass of four verses: the second relates to the matter of the prayers and vows, and an enumeration of those things, wherein men commonly sinned against right reason, and offended in their requests: the third part consists in showing the repugnances of those prayers and wishes, to those of other men, and inconsistencies with themselves. He shows the original of these vows, and sharply inveighs against them; and, lastly, not only corrects the false opinion of mankind concerning them, but gives the true doctrine of all addresses made to heaven, and how they may be made acceptable to the powers above, in excellent precepts, and more worthy of a Christian than a Heathen._