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BOETIUS hath this Rule for it, where∣fore take his own words:* 1.1 saith he,
Differen∣tiam terminorum in mi∣norem terminum multi∣plica, & post junge ter∣minos, & juxta cum qui inde confectus est; com∣mitte illum numerum,
qui ex differentiis & ter∣mino minore productus est, cujus cum latitudi∣nem inveneris, addas eam minori termino, & quod inde colligitur me∣dium terminum pones.That is, Multiply the difference of the Terms, by the lesser term, and add likewise the same Terms together: this done if you divide the product, by the sum of the Terms, and to the Quotient thereof, add the lesser Term; the last Sum is the Musical mean desired: Examp. Admit the two numbers given be 6, and 12. I say that if the difference of the Terms which is 6, were Multiplied by the les∣ser Term 6, it would produce 36; then if you add the two terms 6, and 12, together: their sum would be 18, now if you divide 36, by 18, the Quotient is 2; lastly if to the Quotient 2, you add the lesser Term 6, the sum thereof will be 8, which is a Mean Musical proportional required.
In his second Book of his Arithmetick and the 38 Chapter; where he saith that this proportion hath, Magnam vim in Musici modulaminis tempera∣mentis, & in Speculatione naturalium questionum: i. e. Great force in Mu∣sical composition, (or in the Composure of Musick) and in the discovery of the Secrets of Nature.