See a transcription for the manuscript

### Translation of Periodus numerorum (1705?)

$0_{512}1_{512}|0_{256}1_{256}|0_{128}1_{128}|0_{64}1_{64}|0_{32}1_{32}|0_{16}1_{16}|0_{8}1_{8}|0_{4}1_{4}|0_{2}1_{2}|0_{1}1_{1}=N$

$19\ \ \ \ \ \ \ \ \ \ 18\ \ \ \ \ \ \ \ \ 17\ \ \ \ \ \ \ \ \ 16\ \ \ \ \ \ \ 15\ \ \ \ \ \ \ 14\ \ \ \ \ \ 13\ \ \ \ \ 12\ \ \ \ 11\ \ \ 10$

$=$ Period of Natural Numbers in Dyadic Columns.

$0_{1024}1_{1024}|0_{512}1_{512}|0_{256}1_{256}|0_{128}1_{128}|0_{64}1_{64}|0_{32}1_{32}|0_{16}1_{16}|0_{8}1_{8}|0_{4}1_{4}|0_{2}1_{2}|0_{1}1_{1}=0$

$20\ \ \ \ \ \ \ 19\ \ \ \ \ \ \ \ \ \ 18\ \ \ \ \ \ \ \ \ 17\ \ \ \ \ \ \ \ \ 16\ \ \ \ \ \ \ \ 15\ \ \ \ \ \ \ \ 14\ \ \ \ \ \ 13\ \ \ \ \ 12\ \ \ \ 11\ \ \ 10$

$=0=$ Period of Natural Numbers written in a Dyadic form in single Columns.

Calculation RULES

1. In this case, the single characters are not multiplied

by every co-multiplier, as in other cases,

But rather the single characters [are multiplied] by the single corresponding ones

In this case in fact, it is not computed sideways and Number by Number

but descending Period by Period

2. If a corresponding Period doesn’t fill the whole place of the

next one, it shall be repeated as many times until it fills it.

For, once the same period is repeated, a Period of the

Same Column still remains

3. Multiplying by 0 returns 0 itself, 1 returns the co-multiplier

so that  is equal to 0˙ with a carry

0˙, by adding a carry of 1, gives 1 with a carry and by adding 1 to this one gives 0˙˙ etc.

4. Every carry adds a Unit [RK1] to the higher nearest Column

A double carry adds a unit to the higher column shifted by one place

A triple carry adds a unit in the same place and so

A unit to the analogous next place of the higher column

A quadruple carry adds a Unit to the higher Column shifted by two places etc.

See a transcription for the manuscript