275138
[Commentary:
For the edition of Apollonius used by Harriot see
(Apollonius . ]
Mesographa
Heronis.
Philonis Bizantij.
Heronis.
Philonis Bizantij.
Cum Annotatione nostra de
faciliori
[Translation: With my annotations for easier ]
faciliori
[Translation: With my annotations for easier ]
where is
double to
as
double to
as
Note:
whether these
lines be
whether these
lines be
then would be parallel to
& the problem performed nearly
and also other wayes &
& the problem performed nearly
and also other wayes &
Although Eutocius prefereth philo Bizantius his pratice of finding two
mean proportionalls Before that of Because the number being devided
into small æquall parts, it may now easily be seene when & be æquall,
then by often applying of the compasses to find & Yet in
my improvement the pratice would be better & more easy Let the figures
nombring the æquall parts beginne at . & let their numeration runne towards ;
& the like from towards Then will the shape of a rectangle or gnomon
keepe always at rectangles with the ruler . and then and moving
the ruler with the gnomon keeping the poynt also in the line till you find
and æquall; then is that performed whi also which they now have
& [???] thus easier in practice because that æquallity is sooner found
because the figures go in both wayes a like, which in philoes practice cannot
be observed but with with as much difficulty almost, if not so much as
that of her
mean proportionalls Before that of Because the number being devided
into small æquall parts, it may now easily be seene when & be æquall,
then by often applying of the compasses to find & Yet in
my improvement the pratice would be better & more easy Let the figures
nombring the æquall parts beginne at . & let their numeration runne towards ;
& the like from towards Then will the shape of a rectangle or gnomon
keepe always at rectangles with the ruler . and then and moving
the ruler with the gnomon keeping the poynt also in the line till you find
and æquall; then is that performed whi also which they now have
& [???] thus easier in practice because that æquallity is sooner found
because the figures go in both wayes a like, which in philoes practice cannot
be observed but with with as much difficulty almost, if not so much as
that of her