808404v
[Commentary:
For Diophantus see the edition of Xylander,
(Diophantus 1575)
]
The doctrine of Algebraycall nombers is but
the doctrined of such continuall proportionalles of
which a unite is the
the doctrined of such continuall proportionalles of
which a unite is the
A unite being the first of continuall proportionalles; the second is
called a roote: because the third wilbe always a square: & the fourth
third a cube, as Euclide The names of the other proportionalles
following are all compounded of squares, or cubes or both according
to Diophantus & others which follow Some or other of the most parte of the later
writers gave the name of surdsolidus, of which the first or simple sursolid
is the sixt proportionall. &
called a roote: because the third wilbe always a square: & the fourth
third a cube, as Euclide The names of the other proportionalles
following are all compounded of squares, or cubes or both according
to Diophantus & others which follow Some or other of the most parte of the later
writers gave the name of surdsolidus, of which the first or simple sursolid
is the sixt proportionall. &
Any nomber may be any terme proportinall in a continuall progression
from a If the nomber terme be the second, the third is gotten by
multiplying the nomber into him & the fourth by multiplying the
third by the second & so as also by the doctrine of progression
any terme that is found another may be gotten compendiously
without continuall
from a If the nomber terme be the second, the third is gotten by
multiplying the nomber into him & the fourth by multiplying the
third by the second & so as also by the doctrine of progression
any terme that is found another may be gotten compendiously
without continuall
If a nomber that is known & designed to be the third, fourth,
or fifth or any other proportinall of another denomination: the
doctrine to find the second is that which is called the extraction
of the roote, which is taught in these
or fifth or any other proportinall of another denomination: the
doctrine to find the second is that which is called the extraction
of the roote, which is taught in these
The second proportionall is also called the first dignity, & the third the
second dignity, & the fourth the third dignity &
second dignity, & the fourth the third dignity &
The third is also called the first power; the 4th the second power &
The first proportionall
is a
is a
The first dignity is
the second proportionall,
called a
the second proportionall,
called a
The first power is the
third proportionall
called a square
or second Dignity
called a
third proportionall
called a square
or second Dignity
called a
The first solid is the
fourth proprtionall:
The third dignity: &
The second power,
called a
fourth proprtionall:
The third dignity: &
The second power,
called a
The pythagoreans
did call 4 the first solid
as Boethius
The nomber serveth to be, because pyramides are prime solids
& 4 amongst nombers is the first
did call 4 the first solid
as Boethius
The nomber serveth to be, because pyramides are prime solids
& 4 amongst nombers is the first