1 Mechanical RECREATIONS. CHA P. I. Of Engines, by help of which we may Raife a very great Weight, with Small Strength. T HE invention of all these Engines depend upon one Sole That, The fame Force that can lift up a Weight (for Example of 100 Pounds) to the height of one Foot; can lift up one of 200 Pounds to the height of half a Foot: Or one of 400 Pounds to the height of a fourth part of a Foot; And fo of the Reft, be there never fo much applyed to it. And this Principle cannot be denied, if we confider that the Effect ought to be proportioned to the Action that is neceffary for the Production of it: So that, if it be neceffary to employ an Action by which we may raise a Weight of 100 Pounds, to the height of two Foot; for to raise one fuch to the height of one Foot only, this fame ought to weigh 200 Pounds: For, it's the fame thing to raise 100 Pounds to the height of one Foot; and again yet another 100 Pounds to the height of one Foot, as to raife one of 200 Pounds to the height of one Foot, and the fame alfo, as to raise 100 Pounds to the height of two Feet. Now the Engines which ferve to make this Application of a Force which acteth at a Great Space upon a Weight which it caufeth to be raised by a Leffer, are Trochela, the Pulley. Cuneus, the Wedge. Axis in Peritrochio, the Crane, Capften, or Wheel. Cochlea, the Screw. Vectis, the Leaver. And fome others: For, if we will not apply, or compare them one to another, we cannot well number more: And if we will apply them; we need not inftance in fo many. A CHAP 1 LE СНАР. II. Of the Pulley PROCLEA. ET A, B, C, be bear but the half of it. Afterwards, let us fuppofe thit A, one of the Ends of this Cord, being made faft to fome Nail, the other C be again fuftained by a Man; and it is manifeft, that this Man in C needs not (no more than before) for the fuftaining the Weight E, more Force than is requifite for the fuftaining of 100 Pounds; because the Nail at A, doth the fame Office as the Man which we fuppofed there before. In fine, let us fuppofe that this Man in C do put the Cord to make the Weight E to Rife; and it is manifeft, that if he there employeth the Force which is requifite for the Raifing of an hundred pound to the height of two Foot, he shall Raife this Weight E of 200 Pounds to the height of one Foot; for the Cord A B C being doubled, as it is, it must be pulled two Foot by the end C, to make the Weight E rife as much, as if two Men did draw it, the one by the end A, and the other by the end C, each of them the length of one Foot only. There is always one thing that hinders the exactness of the Calculation, that is the ponderofity of the Cord or Pulley, and the difficul ty that we meet with in making the Cord to flip, and in bearing it: But But this is very small in comparison of that which raiseth it, and cannot be estimated fave within a small matter. Moreover, it is necessary to obferve, that it is nothing but the redoubling of the Cord, and not the Pulley, that caufeth this Force; for if we faften yet another Pulley towards A, about which we pass the Cord A B CH, there will be required no less Force to draw H towards K, and fo to lift up the Weight E, than there was before to draw C towards G. But if to these two Pulleys we add yet another towards D, to which we faften the Weight, and in which we make the Cord to run or flip, juft as we did in the firft, then we shall need no more force to lift up this Weight of 200 Pounds, than to lift up 50 pounds without the Pulley; because that in drawing four Feet of Cord we lift it up but one Foot. And fo in multiplying of the Pulleys, one may raise the greatest Weights with the leaft Forces. It is requifite allo to obferve, that a little more Force is always neceffary for the raifing of a Weight, than for the fuftaining of it; which is the Reafon why I have spoken here diftinctly of the one and of the other. IF CHAP. III. A NE. Of the Inclined PLAN F not having more force than fufficeth to raise an hundred Pounds, one would nevertheless raise this Body F, that weigheth 200 Pounds, to the height of the Line B A, there needs no more, but to draw or rowl it along A F B 1 the Inclined Plane C A, which I fuppofe to be twice as long as the Line A B, for by this means, for to make it arrive at the Point A, we mult there employ the Force that is neceffary for the railing too Pounds twice as high, and the more enclin'd this Plane fhall be made, fo much the lefs force fhall need to raise the Weight F: But there is to be rebated from this Calculation, the difficulty there is in moving the Body F, along the Plane A C, if that Plane were laid down upon the Line B C, all the parts of which I fuppofe to be equidiftant from the Center of the Earth. It is true, that this impediment being fo much lefs as the Plane is more united, more hard, more even, and more polite, it cannot be likewise estimated but by guefs, and it is not very confiderable. We need not neither much to regard that the Line BC, being a part of Circle that hath the fame Center with the Earth, the Plane AC ought to be (though but very little) Curved, and to have the Figure of part of a Spiral, described between two Circles, which like A Ź Wife wife have for their Center that of the Earth; for that it is not any way fenfible. T CHAP. IV. Of the WEDGE Cuneus. HE force of the Wedge A B CD, is cafily understood after that which hath been spoken above of the enclined Plane, for the force wherewith we strike downwards, acts as if it were to make it move according to the Line BD; and the Wood, or other thing and body that it cleaveth, openeth not, or the Weight that it raiseth doth not raise, fave only according to the Line A C, infomuch, that the force wherewith one driveth or ftriketh this Wedge, ought to have the fame proportion to the refiftance of this Wood or Weight, that AC hath to AB: Or elfe again, to be exact, it would be convenient that BD were a part of a Circle, and AD and CD two portions of Spirals that had the fame Center with the Earth, and that the Wedge were of a matter fo perfectly hard and polite, and of fo fmall Weight, as that any little force would fuffice to move it. CHAP. V. Of the CRANE, CAPSTEN, or WHEEL, Axis in Peritrochio. force defcribeth,or that the Diameter of the one hath to the Diameter of the other, for that the Circumferences have the fame proportions as the Diameters: Infomuch, as the Cylinder C having no more but one Foot in Diameter, if the Wheel A B be fix Feet in its Diameter, and the Weight D do weigh 600 pounds, it fhall fuffice that the force in B fhall be capable to raise an 100 Pounds, and fo of others. One may alfo, instead of the Cord that rolleth about the Cylinder C, place there a small Wheel with Teeth or Cogs, that may turn another greater, and by that means multiply the Power of the force as much as one shall pleafe, without having any thing to deduct of the fame, fave only the difficulty of moving the Machine, as in the others. › Unto this Faculty of the Wheel, may be referred the Force of all thofe Engines which confift of Wheels with Teeth in them: And from hence alfo may be difcerned the Reafon why fundry Inftruments in com mon use are framed, as Hand-Mills, the Piercer, the Gimlet, &c. as in the Figure. All which are but feveral kinds, of this fourth Faculty the Wheel; in all which Inftruments, the Points A B C do represent the Places of the Power Fulfiment and the the Weight. The Power being in the fame proportion unto the Weight as BC is unto B A. A CB H W CHAP VI. Of the SCREW Cochlea. Hen once the force of the Capften, and of the inclined Plane is understood, that of the Screw is eafie to be computed, for it is compofed only of a Plane much inclined, which windeth about the Cylinder; and if this Plane be in fuch manner inclined, as that the Cylinder ought to make v. gr. ten turns, to advance forwards the length of a Foot in a Screw, and that the |