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

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1
Of the SCREW of ARCHIMEDES
to draw Waier.
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

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.
Theſe things underſtood, let us infold the Triangle about the
Column, and let us make the Screw B A E F G, &c.
which if it
ſhall be placed at Right Angles with the end B in the Water, turn­
ing it about, it ſhall not this way draw up the Water, the Chanel
about the Column being elevated, as may be ſeen by the part B A.