Alberti, Leone Battista
,
Architecture
,
1755
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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. </
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<
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>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. </
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<
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>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. </
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<
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>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. </
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<
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>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. </
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<
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>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. </
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<
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>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. </
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<
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>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. </
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<
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>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. </
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<
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>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. </
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<
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>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. </
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<
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>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. </
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<
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>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. </
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<
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>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. </
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<
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>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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