71[vi]
Pappus, in his preface to the ſeventh Book of Matbematical
Collections, tells us that this Tract of Apollonius was divided into
two Books; that the firſt Book contained ſix Problems, and the
ſecond three: now Snellius' whole work contains but four; and
it ſeemed to me difficult to ſhew how thoſe could contain the ſub-
ſtance of nine, and yet the ſix firſt have ſixteen Epitagmas, or ge-
neral Caſes, and the three laſt nine. I firſt, therefore began with
inquiring whether, or no, other Problems could not be found,
wherein the ſection of an indefinite ſtraight line is propoſed to be
effected, “So, that of the ſegments contained between the point of
ſection ſought, and given points in the ſaid line, either the ſquare
on one of them, or the rectangle contained by two of them, may
have a given ratio to the rectangle contained by one of them and a
given external line, or to the rectangle contained by two of them; “
as is deſcribed by PAPPUS.
Collections, tells us that this Tract of Apollonius was divided into
two Books; that the firſt Book contained ſix Problems, and the
ſecond three: now Snellius' whole work contains but four; and
it ſeemed to me difficult to ſhew how thoſe could contain the ſub-
ſtance of nine, and yet the ſix firſt have ſixteen Epitagmas, or ge-
neral Caſes, and the three laſt nine. I firſt, therefore began with
inquiring whether, or no, other Problems could not be found,
wherein the ſection of an indefinite ſtraight line is propoſed to be
effected, “So, that of the ſegments contained between the point of
ſection ſought, and given points in the ſaid line, either the ſquare
on one of them, or the rectangle contained by two of them, may
have a given ratio to the rectangle contained by one of them and a
given external line, or to the rectangle contained by two of them; “
as is deſcribed by PAPPUS.
In this inquiry it ſoon occurred to me, that the three problems
which make my firſt, ſecond and fourth, come within the account
given by PAPPUS; and therefore are properly Problems in Determi-
ate Section, to be added to the four given by Snellius: and it does
not appear to me that more can be found which ſhould. Hence I
concluded, that there were in theſe, ſome, more general than thoſe
of Apollonius, which ought therefore to be divided.
which make my firſt, ſecond and fourth, come within the account
given by PAPPUS; and therefore are properly Problems in Determi-
ate Section, to be added to the four given by Snellius: and it does
not appear to me that more can be found which ſhould. Hence I
concluded, that there were in theſe, ſome, more general than thoſe
of Apollonius, which ought therefore to be divided.
My next buſineſs was, if poſſible, to find out the order in which
Apollonius had arranged them: and here, with reſpect to the
firſt Book, I had no other information to guide me, but what is
Apollonius had arranged them: and here, with reſpect to the
firſt Book, I had no other information to guide me, but what is