Salusbury, Thomas, Mathematical collections and translations (Tome I), 1667

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1
I Do not think it ſit in this place to paſs over with Silence the
Invention
of Archimedes to raiſe Wa er with the Screw, which
is
not only marvellous, but miraculous: for we ſhall find that
the
Water aſcendeth in the Screw continually deſcending; and in
a
given Time, with a given Force doth raiſe an unſpeakable quan­
tity
therof.
But before we proceed any farther, let us declare the uſe
of
the Screw in making Water to riſe: And in the enſuing Figure,
let
us conſider the Line I L O P Q
205[Figure 205]
R
S H being wrapped or twined
about
the Collumn M I K H,
which
Line you are to ſuppoſe to
be
a Chanel thorow which the
Water
may run: If we ſhall put
the
end I into the Water, making
the
Screw to ſtand leaning, ſo as
the
point L may be lower than
the
firſt I, as the Diagram ſhew­
eth
, and ſhall turn it round about
on
the two Axes, T and V, the Water ſhall run thorow the Cha­
nel
, till that in the end it ſhall diſcharge ſorth at the mouth H.
Now I ſay, that the Water, in its conveyance from the point I to
the
point H, doth go all the way deſcending, although the point H
be
higher than the point I.
Which that it is ſo, we will declare
in
this manner.
We will deſcribe the Triangle A C B, which is
that
of which the Screw H I is generated, in ſuch ſort that the
Chanel
of the Screw is repreſented by the Line A C, whoſe
Aſcent
and Elevation is determined by the Angle C A B; that is
to
ſay, if ſo be, that that Angle ſhall be the third or fourth part of a
Right
Angle, then the Elevation of the Chanel A C ſhall be ac­
cording
to 1/3, or 1/4 of a Right Angle.
And it is manifeſt; that the
Riſe
of that ſame Chanel A C will be taken away debaſing the
point
C as far as to B: for then the Chanel A C ſhall have no
Elevation
.
And debaſing the point C a little below B, the Water
will
naturally run along the Chanel A C downwards from the
point
A towards C.
Let us therefore conclude, that the Angle A
being
1/3 of a Right Angle, the Chanel A C ſhall no longer have any
Riſe
, debaſing it on the part C for 1/3 of a Right Angle.

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