Heron Alexandrinus, Mechanica, 1999

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    <archimedes>
      <text>
        <body>
          <chap n="2">
            <pb n="3">
              <s id="A18-2.03.01">3 The third power.</s>
              <s id="A18-2.03.02">The third power is the one that is called block and tackle.</s>
              <s id="A18-2.03.03">For if we want to lift any load, we tie ropes to this load and want to pull the ropes tight, until we lift it.</s>
              <s id="A18-2.03.04">Therefore we need a force equal to the load to be lifted.</s>
              <s id="A18-2.03.05">But if we remove the rope from the load, tie one of its ends to a firm crossbeam, put the other one over a pulley that is attached to the middle of the load, and pull the rope, then it is easier to move that load.</s>
              <s id="A18-2.03.06">If we now attach another pulley to the firm crossbeam, put the end of the rope over it and pull it, then the moving of the load is even easier for us.</s>
              <s id="A18-2.03.07">If we further fasten a second pulley to that load and pull the end of the rope over it, then this increases for us the ease in moving the load.</s>
              <s id="A18-2.03.08">In this manner we continue to attach pulleys to the firm crossbeam and to the load that we want to lift and to put the one end of the rope over the pulley tied to the firm crossbeam and the load and let the rope run back to it again and again, then through this the ease to lift that load increases for us.</s>
              <s id="A18-2.03.09">The more numerous the pulleys are that the rope runs on, the easier can that load be lifted.</s>
              <s id="A18-2.03.10">The one end of the rope has to be firmly tied to the firm crossbeam and the rope has to run from this towards the load.</s>
              <s id="A18-2.03.11">The pulleys on the firm crossbeam have to be attached to another [piece of] wood and rotate around the same axle.</s>
              <s id="A18-2.03.12">This axle is called Manganon.</s>
              <s id="A18-2.03.13">The [piece of] wood is fastened to the firm crossbeam by means of other ropes.</s>
              <s id="A18-2.03.14">The pulleys on the load sit on another axle, equal to that first one and fastened to the load.</s>
              <s id="A18-2.03.15">The pulleys have to be attached to the axle in such a manner that they cannot come in contact with one another; for if they can come in contact the rotation is impeded.</s>
              <s id="A18-2.03.16">Why now the ease in lifting is increased for us, when the number of pulleys is increased and why the one end of the rope is tied to the crossbeam, we are going to explain later.</s>
            </pb>
          </chap>
        </body>
      </text>
    </archimedes>