72[vii]
be met with in the above mentioned Preface of Pappus;
where he
tells us that in the ſix Problems of Book I. there were “Sixteen
Epitagmas, or general Caſes, five Determinations; and of theſe,
four were Maxima, and one a minimum: That the maxima are at the
ſecond Epitagma of the ſecond Problem, at the third of the fourth,
the third of the fifth, and the third of the ſixth; but that the minimum
was at the third Epitagma of the third problem. ” It moreover ſeem- ed reaſonable to me, that theſe Problems wherein the feweſt points
are given, would be antecedent to thoſe wherein there were more;
and of theſe wherein the number of given points are the ſame, that
thoſe would be prior to the others, wherein there was a given ex-
ternal line concerned: and laſtly, that when the number of given
points were two, the ſecond Caſe, or Epitagma, would naturally
be when the required point O is ſought between the two given
ones.
tells us that in the ſix Problems of Book I. there were “Sixteen
Epitagmas, or general Caſes, five Determinations; and of theſe,
four were Maxima, and one a minimum: That the maxima are at the
ſecond Epitagma of the ſecond Problem, at the third of the fourth,
the third of the fifth, and the third of the ſixth; but that the minimum
was at the third Epitagma of the third problem. ” It moreover ſeem- ed reaſonable to me, that theſe Problems wherein the feweſt points
are given, would be antecedent to thoſe wherein there were more;
and of theſe wherein the number of given points are the ſame, that
thoſe would be prior to the others, wherein there was a given ex-
ternal line concerned: and laſtly, that when the number of given
points were two, the ſecond Caſe, or Epitagma, would naturally
be when the required point O is ſought between the two given
ones.
Now the three new Problems, together with the three firſt of
Snellius, making exactly ſixteen Epitagmas, viz. one in the firſt,
and three in each of the others; it ſeemed highly probable, that
theſe compoſed the firſt book. Alſo that the Problem, wherein
only one point was given, would be the firſt; and it ſeemed eaſy
to aſſign the ſecond, becauſe it is the only one wherein the limita-
1
Snellius, making exactly ſixteen Epitagmas, viz. one in the firſt,
and three in each of the others; it ſeemed highly probable, that
theſe compoſed the firſt book. Alſo that the Problem, wherein
only one point was given, would be the firſt; and it ſeemed eaſy
to aſſign the ſecond, becauſe it is the only one wherein the limita-
1
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