BINARY arithmetick, that wherein unity, or 1 and 0 are only used.
This was the invention of M. Leibnitz, who sheweth it to be very expeditious in discovering the properties of numbers, and in constructing tables: and Dangecourt, in the history of the royal academy of sciences, gives a specimen of it concerning arithmetical progressions; where he shews, that because, in binary arithmetick, only two characters are used, therefore the laws of progression may be more easily discovered by it than by common arithmetic.
All the characters used in binary arithmetick are 0 and 1, and the cipher multiplies every thing by 2, as in the common arithmetic by 10. Thus 1 is one; 10, two; 11, three; 100, four; 101, five; 110, six; 111, seven; 1000, eight; 1001, nine; 1010, ten; which is built on the same principles with common arithmetick.
The author, however, does not recommend this method for common use, because of the great number of figures required to express a number; and adds, that if the common progression were from 12 to 12, or from 16 to 16, it would be still more expeditious.