1ſuſpition of Arrogance ſay, that thither alſo doth the recourſe to
the defects of the matter (able to blemiſh the perfecteſt Mathe
matical Demonſtrations) ſuffice to excuſe the diſobedience of
Machines in concrete, to the ſame abſtracted and Ideal: yet not
withſtanding I will ſpeak it, affirming, That abſtracting all imper
fections from the Matter, and ſuppoſing it moſt perfect, and unal
terable, and from all accidental mutation exempt, yet neverthe
leſſe its only being Material, cauſeth, that the greater Machine,
made of the ſame matter, and with the ſame proportions, as the
leſſer; ſhall anſwer in all other conditions to the leſſer in exact
Symetry, except in ſtrength, and reſiſtance againſt violent invaſi
ons: but the greater it is, ſo much in proportion ſhall it be wea
ker. And becauſe I ſuppoſe the Matter to be unalterable, that is
alwaies the ſame, it is manifeſt, that one may produce Demonſtra
tions of it, no leſſe ſimply and purely Mathematical, then of eter
nal, and neceſſary Affections: Therefore, Sagredus, Revoke the
opinion which you, and, it may be, all the reſt hold, that have ſtu
died the Mechanicks; that Machines, and Frames compoſed of the
ſame Matter, with punctual obſervation of the ſelf ſame proporti
on between their parts, ought to be equally, or to ſay better, pro
portionally diſpoſed to Reſiſt; and to yield to External injuries
and aſſaults: For if it may be Geometrically demonſtrated, that
the greater are alwaies in proportion leſs able to reſiſt, than the
leſſe; ſo that in fine there is not only in all Machines & Fabricks
Artiſicial, but Natural alſo, a term neceſſarily aſcribed, beyond
which neither Art, nor Nature may paſſe; may paſſe, I ſay, al
waies obſerving the ſame proportions with the Identity of the
Matter.
the defects of the matter (able to blemiſh the perfecteſt Mathe
matical Demonſtrations) ſuffice to excuſe the diſobedience of
Machines in concrete, to the ſame abſtracted and Ideal: yet not
withſtanding I will ſpeak it, affirming, That abſtracting all imper
fections from the Matter, and ſuppoſing it moſt perfect, and unal
terable, and from all accidental mutation exempt, yet neverthe
leſſe its only being Material, cauſeth, that the greater Machine,
made of the ſame matter, and with the ſame proportions, as the
leſſer; ſhall anſwer in all other conditions to the leſſer in exact
Symetry, except in ſtrength, and reſiſtance againſt violent invaſi
ons: but the greater it is, ſo much in proportion ſhall it be wea
ker. And becauſe I ſuppoſe the Matter to be unalterable, that is
alwaies the ſame, it is manifeſt, that one may produce Demonſtra
tions of it, no leſſe ſimply and purely Mathematical, then of eter
nal, and neceſſary Affections: Therefore, Sagredus, Revoke the
opinion which you, and, it may be, all the reſt hold, that have ſtu
died the Mechanicks; that Machines, and Frames compoſed of the
ſame Matter, with punctual obſervation of the ſelf ſame proporti
on between their parts, ought to be equally, or to ſay better, pro
portionally diſpoſed to Reſiſt; and to yield to External injuries
and aſſaults: For if it may be Geometrically demonſtrated, that
the greater are alwaies in proportion leſs able to reſiſt, than the
leſſe; ſo that in fine there is not only in all Machines & Fabricks
Artiſicial, but Natural alſo, a term neceſſarily aſcribed, beyond
which neither Art, nor Nature may paſſe; may paſſe, I ſay, al
waies obſerving the ſame proportions with the Identity of the
Matter.
Many Machines
may be made more
exact in great than
in little.
may be made more
exact in great than
in little.
Great Material
Machines, al
though framed In
the ſame proportion
as others of the
ſame Matter that
are leſſer, are leſſe
ſtrong and able to
reſiſt external Im
petuſs's than the
leſſer.
Machines, al
though framed In
the ſame proportion
as others of the
ſame Matter that
are leſſer, are leſſe
ſtrong and able to
reſiſt external Im
petuſs's than the
leſſer.
SAGR. I already feel my Brains to turn round, and my Mind,
(like a Cloud unwillingly opened by the Lightning,) I perceive
to be ſurprized with a tranſcient, and unuſual Light, which from
affar off twinkleth, and ſuddenly aſtoniſheth me; and with ab
ſtruce, ſtrange, and indigeſted imaginations. And from what hath
been ſpoken, it ſeems to follow, that, it is a thing impoſſible to
frame two Fabricks of the ſame Matter, alike, and unequal, and
between themſelves in proportion equally able to Reſiſt; and
were it to be done, yet it would be impoſſible to find two only
Launces of the ſame wood, alike between themſelves in ſtrength,
and toughneſſe, but unequal in bigneſſe.
(like a Cloud unwillingly opened by the Lightning,) I perceive
to be ſurprized with a tranſcient, and unuſual Light, which from
affar off twinkleth, and ſuddenly aſtoniſheth me; and with ab
ſtruce, ſtrange, and indigeſted imaginations. And from what hath
been ſpoken, it ſeems to follow, that, it is a thing impoſſible to
frame two Fabricks of the ſame Matter, alike, and unequal, and
between themſelves in proportion equally able to Reſiſt; and
were it to be done, yet it would be impoſſible to find two only
Launces of the ſame wood, alike between themſelves in ſtrength,
and toughneſſe, but unequal in bigneſſe.
A Wooden Launce
fixed in a Wall at
Right-Angles, and
reduced to ſuch a
length and thick
neſſe as that it may
endure, but made a
hairs breadth big
ger, breaketh with
its own weight, is
ſingly one and no
more.
fixed in a Wall at
Right-Angles, and
reduced to ſuch a
length and thick
neſſe as that it may
endure, but made a
hairs breadth big
ger, breaketh with
its own weight, is
ſingly one and no
more.
SALV. So it is Sir; and the better to aſſure you that we con
cur in opinion, I ſay, that if we take a Launce of wood of ſuch a
length and thickneſſe, that being fixed faſt (v. g.) in a Wall at
Right Angles, that is parallel to the Horizon, it is reduced to the
utmoſt length, that it will hold at, ſo that lengthened never
ſo-little more, it would break, being over-burthened with its own
cur in opinion, I ſay, that if we take a Launce of wood of ſuch a
length and thickneſſe, that being fixed faſt (v. g.) in a Wall at
Right Angles, that is parallel to the Horizon, it is reduced to the
utmoſt length, that it will hold at, ſo that lengthened never
ſo-little more, it would break, being over-burthened with its own