( 8o ) 
Twelves. He gives no more than the outward 
Figure of the Machines, and fhews the Method of 
working them. But as by this every one, who has 
any Skiil in Mechanicks, will be able to guefs, how 
the inward Parts ought to be contrived ; fo it can- 
not be denied, that thefe are two different Machines, 
independent of one another 5 that the laft, which 
is for Multiplication , is nothing elfe but an Appli- 
cation of the Neipperian Bones on flat moveable 
Disks ; confequently that his Invention alone is not 
fit to perform juftly all Arithmetical Operations. 
After him the celebrated Baron de Leibnitz , the 
Marchefe Toleni , and Mr. Leupold took this Un- 
dertaking in hand, and attempted to perform it after 
different Methods. 
The firft publifhed his Scheme in the Year 1709, 
in the Mifcellanea Berolinenfia , but then he gave 
only the outward Figure of the Machine. Signor 
Foleni communicated his, but explaining at the 
fame time its inward Conftrudtion, in hi sMifcellanea 
of the fame Year, 1709. Mr. Leupold's Machine, 
together with thofe of Mr. de Leibnitz and Signor 
Toleni , were inferred 'mhisTheatrum Arithmetico- 
Geometricum , publifhed at Leipzig in 17x7, after 
the Author’s Death, yet imperfedt, as it is owned 
in the Book itfelf. 
Befides thefe, I learned from feveral French 
Journals, that Charles Fafcal invented one, which 
however I never had the fight of.* 
* The Defcription of this Machine is fince printed by M . Gallon in 
his Colle&ion of Machines and Inventions approved by the Academy 
of Sciences at Paris (publifhed in French at Paris, 1735. in Quarto, in 
Six Tomes) in Tom. IV. p. 137 ; and likewife another by Al. Lefpine , 
Tom , IV. p. 131 3 and three more by Al, Hellerin de Boijlijj'andeau , 
lorn, V. p. 103, nifC? J2T * 
I took 
