1pieces, according to the Lines E F, G H, &c. making ſeven Segments,
we muſt adde to the twenty ſix Palmes of the circuit of the whole
Board, ſeventy others; whereupon the eight little pieces ſo cut and
ſeperated, have to cut ninty ſix Palmes of water. And, if moreover,
we cur each of the ſaid pieces into five parts,
19[Figure 19]
ducing them into Squares, to the circuit of ninty
ſix Palmes, with four cuts of eight Palmes apiece;
we ſhall adde alſo ſixty four Palmes, whereupon
the ſaid Squares to deſcend in the water, muſt
divide one hundred and ſixty Palmes of water,
but the Reſiſtance is much greater than that of
twenty ſix; therefore to the leſſer Superficies,
we ſhall reduce them, ſo much the more eaſily
will they float: and the ſame will happen in all
other Figures, whoſe Superficies are ſimular amongſt themſelves, but
different in bigneſs: becauſe the ſaid Superficies, being either
ſhed or encreaſed, always diminiſh or encreaſe their Perimeters in
ſubduple proportion; to wit, the Reſiſtance that they find in
trating the water; therefore the little pieces gradually ſwim, with more
and more facility as their breadth is leſſened.
we muſt adde to the twenty ſix Palmes of the circuit of the whole
Board, ſeventy others; whereupon the eight little pieces ſo cut and
ſeperated, have to cut ninty ſix Palmes of water. And, if moreover,
we cur each of the ſaid pieces into five parts,
ducing them into Squares, to the circuit of ninty
ſix Palmes, with four cuts of eight Palmes apiece;
we ſhall adde alſo ſixty four Palmes, whereupon
the ſaid Squares to deſcend in the water, muſt
divide one hundred and ſixty Palmes of water,
but the Reſiſtance is much greater than that of
twenty ſix; therefore to the leſſer Superficies,
we ſhall reduce them, ſo much the more eaſily
will they float: and the ſame will happen in all
other Figures, whoſe Superficies are ſimular amongſt themſelves, but
different in bigneſs: becauſe the ſaid Superficies, being either
ſhed or encreaſed, always diminiſh or encreaſe their Perimeters in
ſubduple proportion; to wit, the Reſiſtance that they find in
trating the water; therefore the little pieces gradually ſwim, with more
and more facility as their breadth is leſſened.
This is manifeſt; for keeping ſtill the ſame height of the Solid, with
the ſame proportion as the Baſe encreaſeth or deminiſheth, doth the ſaid
Solid alſo encreaſe or diminiſh; whereupon the Solid more diminiſhing
than the Circuit, the Cauſe of Submerſion more diminiſheth than the Cauſe
of Natation: And on the contrary, the Solid more encreaſing than the
Circuit, the Cauſe of Submerſion encreaſeth more, that of Natation
leſs.
the ſame proportion as the Baſe encreaſeth or deminiſheth, doth the ſaid
Solid alſo encreaſe or diminiſh; whereupon the Solid more diminiſhing
than the Circuit, the Cauſe of Submerſion more diminiſheth than the Cauſe
of Natation: And on the contrary, the Solid more encreaſing than the
Circuit, the Cauſe of Submerſion encreaſeth more, that of Natation
leſs.
Laſtly, to that which we read in the latter part of the Text, that
is to ſay, that we muſt compare the Gravity of the Moveable with
the Reſiſtance of the Medium againſt Diviſion, becauſe if the force of
the Gravity exceed the Reſiſtance of the Medium, the Moveable will
deſcend, if not it will float. I need not make any other anſwer,
but that which hath been already delivered; namely, that its not
the Reſiſtance of abſolute Diviſion, (which neither is in Water nor
Air) but the Gravity of the Medium that muſt be compared with the
Gravity of the Moveables; and if that of the Medium be greater, the
Moveable ſhall not deſcend, nor ſo much as make a totall Submerſion,
but a partiall only: becauſe in the place which it would occupy in
the water, there muſt not remain a Body that weighs leſs than a like
quantity of water: but if the Moveable be more grave, it ſhall
cend to the bottom, and poſſeſs a place where it is more conformable
is to ſay, that we muſt compare the Gravity of the Moveable with
the Reſiſtance of the Medium againſt Diviſion, becauſe if the force of
the Gravity exceed the Reſiſtance of the Medium, the Moveable will
deſcend, if not it will float. I need not make any other anſwer,
but that which hath been already delivered; namely, that its not
the Reſiſtance of abſolute Diviſion, (which neither is in Water nor
Air) but the Gravity of the Medium that muſt be compared with the
Gravity of the Moveables; and if that of the Medium be greater, the
Moveable ſhall not deſcend, nor ſo much as make a totall Submerſion,
but a partiall only: becauſe in the place which it would occupy in
the water, there muſt not remain a Body that weighs leſs than a like
quantity of water: but if the Moveable be more grave, it ſhall
cend to the bottom, and poſſeſs a place where it is more conformable