282141v
[Commentary:
The reference on this page is to Stevin's L'arithmétique ... aussi l'algebre
(Stevin , page 289. ]
The Theorem of this proposition
If the summe of the second & third be double: & unto that double
added the half of the first magnitude: & betwixt that aggregate
& half of the first magnitude be gotten a meane proportionall:
& from that meane proportionall be taken the sayd half of the
first magnitude: The remayne is the second
If the summe of the second & third be double: & unto that double
added the half of the first magnitude: & betwixt that aggregate
& half of the first magnitude be gotten a meane proportionall:
& from that meane proportionall be taken the sayd half of the
first magnitude: The remayne is the second
The theorem is found by resolving of an æquation
which was the second sorte in Stevin pag. 289; & then after by composition
I made the problem above on the other
which was the second sorte in Stevin pag. 289; & then after by composition
I made the problem above on the other
The worke to bring it to an æquation is this.
Let the second be . then the third must be .
Let the second be . then the third must be .
per species
it is done
in the next
it is done
in the next
So that if it be considered the absolutes wilbe always the
the oblong made of the summe of the second & and the first magnitude: & the nomber of roots wilbe always so many
as therebe unites in the
the oblong made of the summe of the second & and the first magnitude: & the nomber of roots wilbe always so many
as therebe unites in the