1of the Portion of the Sphære is N M; and of the Portion B G C the Axis is G M: Wherefore
the Centre of Gravity of them both ſhall be in the Line N M: And becauſe that from the Por
tion B N C the Portion B G C, not having the ſame Centre of Gravity, is cut off, the Centre
of Gravity of the remainder of the Magnitude that is above the Surface of the Liquid ſhall be
in the Line N K; namely, in the Line which conjoyneth the Centres of Gravity of the ſaid
Portions by the foreſaid 8 of Archimedis de Centro Gravitatis Planorum.
the Centre of Gravity of them both ſhall be in the Line N M: And becauſe that from the Por
tion B N C the Portion B G C, not having the ſame Centre of Gravity, is cut off, the Centre
of Gravity of the remainder of the Magnitude that is above the Surface of the Liquid ſhall be
in the Line N K; namely, in the Line which conjoyneth the Centres of Gravity of the ſaid
Portions by the foreſaid 8 of Archimedis de Centro Gravitatis Planorum.
NIC. Truth is, that in ſome of theſe Figures C is put for X, and ſo it was in
the Greek Copy that I followed.
the Greek Copy that I followed.
RIC. This Demoſtration is very difficult, to my thinking; but I believe that
it is becauſe I have not in memory the Propoſitions of that Book entituled De Cen
tris Gravium.
it is becauſe I have not in memory the Propoſitions of that Book entituled De Cen
tris Gravium.
RIC. We will take a more convenient time to diſcourſe of that, and now return
to ſpeak of the two laſt Propoſitions. And I ſay that the Figures incerted in the
demonſtration would in my opinion, have been better and more intelligble unto
me, drawing the Axis according to its proper Poſition; that is in the half Arch of
theſe Figures, and then, to ſecond the Objection of the Adverſary, to ſuppoſe
that the ſaid Figures ſtood ſomewhat Obliquely, to the end that the ſaid Axis, if it
were poſſible, did not ſtand according to the Perpendicular ſo often mentioned,
which doing, the Propoſition would be proved in the ſame manner as before:
and this way would be more naturall and clear.
to ſpeak of the two laſt Propoſitions. And I ſay that the Figures incerted in the
demonſtration would in my opinion, have been better and more intelligble unto
me, drawing the Axis according to its proper Poſition; that is in the half Arch of
theſe Figures, and then, to ſecond the Objection of the Adverſary, to ſuppoſe
that the ſaid Figures ſtood ſomewhat Obliquely, to the end that the ſaid Axis, if it
were poſſible, did not ſtand according to the Perpendicular ſo often mentioned,
which doing, the Propoſition would be proved in the ſame manner as before:
and this way would be more naturall and clear.
NIC. You are in the right, but becauſe thus they were in the Greek Copy,
I thought not fit to alter them, although unto the better.
I thought not fit to alter them, although unto the better.
RIC. Companion, you have thorowly ſatisfied me in all that in the beginning
of our Diſcourſe I asked of you, to morrow, God permitting, we will treat of
ſome other ingenious Novelties.
of our Diſcourſe I asked of you, to morrow, God permitting, we will treat of
ſome other ingenious Novelties.
me, drawing the Axis Z T according to its proper Poſition, that
is in the half Arch of theſe Figures.] And in this conſideration I have followed
the Schemes of Commandine, who being the Reſtorer of the Demonſtrations of theſe two laſt
Propoſitions, hath well conſidered what Ricardo here propoſeth, and therefore hath drawn the
ſaid Axis (which in the Manuſcripts that he had by him is lettered F T, and not as in that of
Tartaylia Z T,) according to that its proper Poſition.
But becauſe thus they were in the Greek Copy, I thought not
fit to alter them although unto the better.] The Schemes of thoſe Manu-
18[Figure 18]
ſcripts that Tartaylia had ſeen were more imperfect then thoſe
in Commandines Copies; but for variety ſake, take here one
of Tartaylia, it being that of the Portion of a Sphære, equall
to an Hemiſphære, with its Axis oblique, and its Baſe dimitted
into the Liquid, and Lettered as in this Edition.
fit to alter them although unto the better.] The Schemes of thoſe Manu-
18[Figure 18]ſcripts that Tartaylia had ſeen were more imperfect then thoſe
in Commandines Copies; but for variety ſake, take here one
of Tartaylia, it being that of the Portion of a Sphære, equall
to an Hemiſphære, with its Axis oblique, and its Baſe dimitted
into the Liquid, and Lettered as in this Edition.
Now Courteous Readers, I hope that you may, amidſt the
great Obſcurity of the Originall in the Demonſtrations of theſe
two laſt Propoſitions, be able from the joynt light of theſe two Famous Commentators of our
more famous Author, to diſcern the truth of the Doctrine affirmed, namely, That Solids of the
Figure of Portions of Sphæres demitted into the Liquid with their Baſes upwards ſhall ſtand
erectly, that is, with their Axis according to the Perpendicular drawn from the Centre of the
Earth unto its Circumference: And that if the ſaid Portions be demitted with their Baſes
oblique and touching the Liquid in one Point, they ſhall not rest in that Obliquity, but ſhall
return to Rectitude: And that laſtly, if theſe Portions be demitted with their Baſes downwards,
they ſhall continue erect with their Axis according to the Perpendicular aforeſaid: ſo that no
more remains to be done, but that weſet before you the 2 Books of this our Admirable Author.
great Obſcurity of the Originall in the Demonſtrations of theſe
two laſt Propoſitions, be able from the joynt light of theſe two Famous Commentators of our
more famous Author, to diſcern the truth of the Doctrine affirmed, namely, That Solids of the
Figure of Portions of Sphæres demitted into the Liquid with their Baſes upwards ſhall ſtand
erectly, that is, with their Axis according to the Perpendicular drawn from the Centre of the
Earth unto its Circumference: And that if the ſaid Portions be demitted with their Baſes
oblique and touching the Liquid in one Point, they ſhall not rest in that Obliquity, but ſhall
return to Rectitude: And that laſtly, if theſe Portions be demitted with their Baſes downwards,
they ſhall continue erect with their Axis according to the Perpendicular aforeſaid: ſo that no
more remains to be done, but that weſet before you the 2 Books of this our Admirable Author.