176 ON THE EARLY 



Mdl-i-Mdl-i-Cdb, and the eighth Mdl-i-Cdb-i-Cdb, in the ninth C a h-i-Cdb^ 

 Cdb, and so on. Ail these powers are in proportion, either ascending or 

 descending. Thus the ratio of Mdl-i-Mdl to Cdb is like the ratio of Cdb 

 to Mdl, Mdl to Shut, and Shai to one, and one to one divided by Shai; 

 and one divided by Shai to one divided by Mat; and one divided by Mdl 

 to one divided by Cab; and one divided by Cdb' to one divided by Mdl-i- 

 Mdl. To multiply one of these powers by another, if they are both oft 

 the same side, (viz. of unity) add the exponents of their powers to- 

 gether; the product will have the same denomination as this sum. For 

 example, to multiply Mdl-i-Cdb by Mdl-i-Mdl-i-Cdb, the first is the 5th 

 power and the 2d the 7th. The result then is Cdb-i-Cdb-i-Cab-i-Cab or 

 four Cabs, which is the 12th power. If the factors are on different sides, 

 the product will be the excess on the side of the greater. The product 

 of one divided by Mdl-i-Mdl into Mdl-i-Cab is Shai; and the product of 

 one divided by Cab-i-Cdb-Cdb into Cdb-i-Mdl-i-^Mdl , is one divided by 

 Mdl: and if the factors are at the same distance (from one,) the product 

 Is one. The particulars of the methods of division, and extraction of 

 roots and other rules, I have given in my greater book. The rules of 

 Algebra which have been discovered by learned men are six, and they 

 relate to number and Shai and Mdl. The following table will shew the 

 products and quotients of these, which are here given for the sake of 

 brevity. 



