Alberti, Leone Battista, Architecture, 1755

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              <s>
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              would have you conſider three Places, which
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              I call Points; the two Ends, that is the Steel
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              and the Peathers, and the third is the Loop in
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              the Middle for throwing the Dart by; and the
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              two Spaces between the two Ends and the
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              Loop, I ſhall call the Radii. </s>
              <s>I ſhall not diſ­
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              pute about the Reaſons of theſe Names, which
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              will appear better from the Conſideration of
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              the Thing itſelf. </s>
              <s>If the Loop be placed ex­
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              actly in the Middle of the Dart, and the Fea­
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              ther End be juſt equal in Weight to the Steel,
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              both Ends of the Dart will certainly hang even
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              and be equally poiſed; if the ſteel End be the
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              Heavieſt, the Feather will be thrown up, but
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              yet there will be a certain Point in the Dart
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              further towards the heavy End, to which if
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              you ſlip the Loop, the Weight will be imme­
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              diately brought to an equal Poiſe again; and
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              this will be the Point by which the larger Ra­
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              dius exceeds the ſmaller juſt as much as the
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              ſmaller Weight is exceeded by the larger. </s>
              <s>For
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              thoſe who apply themſelves to the Study of
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              theſe Matters, tell us, that unequal Radii may
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              be made equal to unequal Weights, provided
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              the Number of the Parts of the Radius and
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              Weight of the right Side, multiplied together,
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              be equal to the Number of thoſe Parts on the
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              oppoſite left Side: Thus if the Steel be three
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              Parts, and the Feather two, the Radius be­
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              tween the Loop and the Steel muſt be two, and
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              the other Radius between the Loop and the
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              Feather muſt be three. </s>
              <s>By which Means, as
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              this Number five will anſwer to the five on the
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              oppoſite Side, the Radii and the Weights an­
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              ſwering equally to one another, they will hang
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              even and be equally poiſed. </s>
              <s>If the Number
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              on each Side do not anſwer to one another,
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              that Side will overcome on which that Inequa­
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              lity of Numbers lies. </s>
              <s>I will not omit one Ob­
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              ſervation, namely, that if equal Radii run out
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              from both Sides of the Loop, and you give the
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              Ends a twirl round in the Air they will de­
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              ſeribe equal Circles; but if the Radii be un­
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              equal, the Circles which they deſcribe, will be
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              unequal alſo. </s>
              <s>We have already ſaid that a
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              Wheel is made up of a Number of Circles:
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              Whence it is evident, that if two Wheels let
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              into the ſame Axis be turned by one and the
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              ſame Motion, ſo as when one moves the
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              other cannot ſtand ſtill, or when one ſtands
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              ſtill the other cannot move; from the Length
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              of the Radii or Spokes in each Wheel we may
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              come at the Knowledge of the Force which is
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              in that Wheel, remembring always to take the
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              Length of the Radius ſrom the very Center of
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              the Axis. </s>
              <s>If theſe Principles are ſufficiently
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              underſtood, the whole Secret of all theſe En­
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              gines of which we are here treating, will be
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              maniſeſt; eſpecially with Relation to Wheels
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              and Leavers. </s>
              <s>In Pullies indeed we may con­
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              ſider ſome ſurther Particulars: For both the
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              Rope which runs in the Pully and the little
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              Wheel in the Pully are as the Plain, whereon
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              the Weight is to be carried with the middle
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              Motion, which we obſerved in the laſt Chapter
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              was between the moſt Eaſy and the moſt Dif­
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              ficult, inaſmuch as it is neither to be raiſed up
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              nor let down, but to be drawn along upon the
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              Plain keeping always to one Center. </s>
              <s>But that
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              you may underſtand the Reaſon of the Thing
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              more clearly, take a Statue of a thouſand
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              Weight; if you hang this to the Trunk of a
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              Tree by one ſingle Rope, it is evident this Rope
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              muſt bear the whole thouſand Weight. </s>
              <s>Faſten
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              a Pully to the Statue, and into this Pully let
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              the Rope by which the Statute hangs, and bring
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              this Rope up again to the Trunk of the Tree,
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              ſo as the Statue may hang upon the double
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              Rope, it is plain the Weight of the Statue is
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              then divided between two Ropes, and that the
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              Pully in the Middle divides the Weight equal­
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              ly between them. </s>
              <s>Let us go on yet further,
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              and to the Trunk of the Tree faſten another
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              Pully and bring the Rope up through this
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              likewiſe. </s>
              <s>I ask you what Weight this Part of
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              the Rope thus brought up and put through
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              the Pully will take upon itſelf: You will ſay
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              five hundred; do you not perceive from hence
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              that no greater Weight can be thrown upon
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              this ſecond Pully by the Rope, than what the
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              Rope has itſelf; and that is five hundred. </s>
              <s>I
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              ſhall therefore go no farther, having, I think,
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              demonſtrated that a Weight is divided by Pul­
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              lies, by which means a greater Weight may be
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              moved by a ſmaller; and the more Pullies
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              there are, the more ſtill the Weight is divided;
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              from whence it follows that the more Wheels
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              there are in them, ſo many more Parts the
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              Weight is ſplit into and may ſo much the more
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              eaſily be managed.
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              </s>
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