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

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1riſing or aſcending: it of neceſſity remaineth manifeſt, that in the
Superficies which is exactly equilibrated, the ſaid Ball remaineth in­
different and dubious between Motion and Reſt, ſo that every ſmall
Force is ſufficient to move it, as on the contrary, every ſmall Reſi­
ſtance, and no greater than that of the meer Air that environs it, is
able to hold it ſtill.
* Or along.
From whence we may take this Concluſion for indubitable, That
Crave Bodies, all Extern and Adventitious Impediments being re­
moved, may be moved along the Plane of the Horizon by any ne­
ver ſo ſmall Force: but when the ſame Grave is to be thrown along
an Aſcending Plane, then, it beginning to ſtrive againſt that aſcent,
having an inclination to the contrary Motion, there ſhall be requi­
red greater Violence, and ſtill greater the more Elevation that ſame
Plane ſhall have.
As for example, the Moveable G, being poſited
upon the Line A B parallel to the Horizon, it ſhall, as hath been
ſaid, be indifferent on it either to Motion or Reſt, ſo that it may
be moved by a very ſmall Force: But if we ſhall have the Planes
Elevated, they ſhall not be driven along without Violence; which

Violence will be required to be
greater to move it along the Line
A D, than along A C; and ſtill
greater along A E than along A D:
The which hapneth, becauſe it hath
greater Impetus of going down­
wards along A E than along A D,
and along A D than along A C.
So
that we may likewiſe conclude
Grave Bodies to have greater Reſiſtance upon Planes differently
Elevared, to their being moved along the ſame, according as one
ſhall be more or leſs elevated than the other; and, in fine, that the
greateſt Reſiſtance of the ſame Grave to its being raiſed is in the
Perpendicular A F.
But it will be neceſſary to declare exactly what
proportion the Force muſt have to the Weight, that it may be able
to carry it along ſeveral elevated Planes, before we proceed any
farther, to the end that we may perfectly underſtand all that which
remains to be ſpoken.
Letting, therefore, Perpendiculars fall from the points C, D,
and E unto the Horizontal Line A B, which let be C H, D I, and
E K: it ſhall be demonſtrated that the ſame Weight ſhall be mo­
ved along the Plane A C with leſſer Force than along the Perpendi­
cular A F, (where it is raiſed by a Force equal to it ſelf) accor­
ding to the proportion by which the Perpendicular C H is leſs than
A C: and that along the Plane A D, the Force hath the ſame pro­
portion to the Weight, that the Perpendicular I D hath to D A:
and, laſtly, that in the Plane A E the Force to the Weight obſer­
veth the proportion of E K and E A.