C70) 
Multiplying ihe Antecedents together , and! alfo the 
Confequents, and thofe two Produ£ls give the Com- 
pound Ration, as to add 4 to 3, and 6 to 5. 4 x 6=^24, 
and 3 X f =1 So 24 to 15-, that is, 8 to 5: is the Sum 
of thofe two Rations; that is, a 3d. nnnor added to a 
4tb. makes a 6th. minor : Thus 3 to 2 added to 4 to 3 
makes x to i, that is, a Diapente added to a DiateJJaron 
makes a Diapafon. So Subftradlion of Rations one Irom 
another is performed by Divifion ; that is, as Divificn 
of Fraftions is performed by crcfs MulripUcation, foalfo 
the doubUog.treblingjquadrupUng, of Rations is per- 
formed by IquaringjCubingjbiquadrating.S'c.of the terms. 
So the halving, tnfeding, quartering, ^c. is performed 
by extradling the Square Root, theCubick Biquadratick 
Roots, ®c. of the Terms, or by Crofs Multiplications, 
as in the dividing Fra£tions ; by which Method he fliews 
how 'twill be eafie to find how many lefTer Rations are 
contained in a greater, ^c, as Merfennus found i^o\Com- 
nt^'s' in an OSave, But Mercator working by Logarithms 
finds 55" ^h. And fuppofing a Comma to be a 5'3d. part 
of a Dkpafont he thereby accommodates the exprelTing 
of alJ the Intervals by Commas pretty near, of which 
here is 106.) aTable added. The Ancients owned 
only 8th. jth. and 4th. for fimple Confonant Intervals 
expreft by 12. 9. 8. and 6. whence 'twas (aid, Mercurius 
his Lyre was firurjg with four Chords. After this the Do- 
ctor (hews an eafie Method of finding Intermediate Ra^ 
tions, and exprefTing them in whole Numbers, and has 
in />. 122. given a Table of them, but obferv^es that all 
the Intervals are not Harmonica). 
In the Sixth Chapter he treats of Difcords and De- 
grees, meaning thereby only fuch Difcords as fall with- 
in the Degrees of the Scale of Mufick (for there ar^ 
infinite other, all proportions of Tones not Harmonick, 
being Difcordant. ) Now there are three varieties of 
thefe Dc^grees in the ScUes ol Mufick, which are as it 
were 
