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

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1Rectangle F H deſcribeth whilſt it draweth the Weight D along
the Plane B A, by the means of a Chord parallel to this Plane, and
paſſing about the Pulley E, in ſuch ſort, that H G, that is the height
of this Rectangle, is equal to B A, along which the Weight D is to
move, whilſt it mounteth to the height of the Line C A.
And N O
repreſents the firſt Dimenſion of ſuch another Force, that is de­
ſcribed by the Rectan­
gle N P, in the time that
220[Figure 220]
it is raiſing the Weight
L to M.
And I ſuppoſe
that L M is equal to B A,
or double to C A; and
that N O is to F G, as
O P is to G H.
This
done, I conſider that at
ſuch time as the Weight
D is moved from B to­
wards A, one may ima­
gine its Motion to be
compoſed of two others, of which the one carrieth it from B R to­
wards C A, (to which operation there is no Force required, as all
thoſe ſuppoſe who treat of the Mechanicks) and the other raiſeth
it from B C towards R A, for which alone the Force is required:
inſomuch that it needs neither more nor leſs Force to move it
along the Inclined Plane B A, than along the Perpendicular C A.
For I ſuppoſe that the unevenneſſes, &c. of the Plane do not
at all hinder it, like as it is alwaies ſuppoſed in treating of this
matter.
So then the whole Force F H is employed only about the raiſing
of D to the height of C A: and foraſmuch as it is exactly equal to
the Force N P, that is required for the raiſing of L to the Height
of L M, double to C A, I conclude by my Principle that the
Weight D is double to the Weight L.
For in regard that it is
neceſſary to employ as much Force for the one as for the other,
there is as much to be raiſed in the one as in the other; and no
more knowledge is required than to count unto two for the
knowing that it is alike facile to raiſe 200 pounds from C to A,
as to raiſe 100 pounds from L to M: ſince that L M is double
to C A.
You tell me, moreover, that I ought more particularly to ex­
plain the nature of the Spiral Line that repreſenteth the Plane
equally enclined, which hath many qualities that render it ſuffi­
ciently knowable.

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