75[x]
The Limitations of the two former are ſaid by Pappus to have
been minimums, and that of the third a maximum, in conformity,
to which, I have here made them ſo; although I cannot ſee with
what propriety: each of them admitting, in ſome Caſes, of a maxi-
mum and in others of minimum, as I have intimated in a ſcbolium at
the end of each Problem. But notwithſtanding I have conformed to
the manner of Apollonius in dividing this Problem into three,
which it muſt be confeſſed contributes much to order in enumera-
ting ſuch a multitude of Caſes, yet have I previouſly ſhewn how
the whole may be generally conſtructed at once; and that by a me-
thod, which I flatter myſelf will not be found inferior to any that
hath heretofore been given of this very intricate and general
Problem.
been minimums, and that of the third a maximum, in conformity,
to which, I have here made them ſo; although I cannot ſee with
what propriety: each of them admitting, in ſome Caſes, of a maxi-
mum and in others of minimum, as I have intimated in a ſcbolium at
the end of each Problem. But notwithſtanding I have conformed to
the manner of Apollonius in dividing this Problem into three,
which it muſt be confeſſed contributes much to order in enumera-
ting ſuch a multitude of Caſes, yet have I previouſly ſhewn how
the whole may be generally conſtructed at once; and that by a me-
thod, which I flatter myſelf will not be found inferior to any that
hath heretofore been given of this very intricate and general
Problem.
Such are the things that I have attempted, and ſuch the reaſons
for what I have done in the following little Tract. The merit due
to each of them I chearfully ſubmit (where every one ought) to
the deciſion of the impartial Reader. In the Conſtructions, my
chief Aim was novelty and uniformity: I could have given more
ſimple conſtructions to one or two of them; in particular the ſixth
of Book I: but it was not my intention to give any thing that I
knew had been done before. I know of many imperfections, but
no falſe reaſonings, and hope none will be found; but if there
ſhould, I hope the candid Geometer will be more inclined to ex-
cuſe than exult, when I aſſure him the greateſt part of the work
has been executed at different times, amidſt the hurry and perplexi-
ties which it may eaſily be conceived attend the fitting out for a
three years Voyage to the ſouth ſeas.
for what I have done in the following little Tract. The merit due
to each of them I chearfully ſubmit (where every one ought) to
the deciſion of the impartial Reader. In the Conſtructions, my
chief Aim was novelty and uniformity: I could have given more
ſimple conſtructions to one or two of them; in particular the ſixth
of Book I: but it was not my intention to give any thing that I
knew had been done before. I know of many imperfections, but
no falſe reaſonings, and hope none will be found; but if there
ſhould, I hope the candid Geometer will be more inclined to ex-
cuſe than exult, when I aſſure him the greateſt part of the work
has been executed at different times, amidſt the hurry and perplexi-
ties which it may eaſily be conceived attend the fitting out for a
three years Voyage to the ſouth ſeas.