Harriot, Thomas, Mss. 6782

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      <text xml:lang="eng" type="free">
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          <pb file="add_6782_f363" o="363" n="726"/>
          <head xml:space="preserve" xml:lang="lat"> De Infinitis
            <lb/>
          [
            <emph style="bf">Translation: </emph>
          On infinite ]</head>
          <p>
            <s xml:space="preserve"> In progressions that be infinite be they increasing or decreasing.
              <lb/>
            </s>
            <s xml:space="preserve"> There are these </s>
            <s xml:space="preserve"> First to a quantity that haveth
              <emph style="st">proportion</emph>
            rate
              <lb/>
            to the first quantity given, or rather because betwixt positive quantityes
              <lb/>
            there is a positive rate, I may call that rate infinite either in great-
              <lb/>
            ness or litle
              <emph style="super">nes</emph>
            s according to
              <emph style="st">proportion</emph>
              <emph style="super">progression</emph>
            , in respect of the first quantity
              <lb/>
            </s>
            <s xml:space="preserve"> Yet in respecte of the progression following it is divisible or mul-
              <lb/>
            tiplicable till the progression being infinite hath for his second passe
              <lb/>
            also a quantity
              <emph style="super">of an[???]</emph>
            infinite </s>
            <s xml:space="preserve"> Which is not only infinite in respecte of
              <lb/>
            the first quantity of the last progression; but infinitely infinite in respect
              <lb/>
            of
              <emph style="st">of</emph>
            the first in the first </s>
            <s xml:space="preserve"> And also the summe of the second pro-
              <lb/>
            gression is infinite
              <emph style="st">infi</emph>
            in respect of the first summe of the first pro-
              <lb/>
            gression, or the first quantity of </s>
          </p>
          <p>
            <s xml:space="preserve"> And so a third, fourth & infinite other progressions and passes; of which
              <lb/>
            any quantity or the summe of all infinitely all, is of an infinite
              <lb/>
            quantity in greatness of litleness in respect, of the summe or
              <lb/>
            first quantity of the first </s>
            <lb/>
            <s xml:space="preserve"> And yet
              <emph style="st">at</emph>
              <emph style="super">for a</emph>
            last in decreasing progressions we must needes under-
              <lb/>
            stand a quantity absolutely indivisible; but multiplicable infinitely
              <lb/>
            infinite
              <emph style="st">to make the [¿]prime[?] from where the rest are issued</emph>
            till a quantity
              <lb/>
            absolutely immultiplicable be produced which I may call universally </s>
            <lb/>
            <s xml:space="preserve"> And in increasing progressions we must needes understand that
              <lb/>
              <emph style="st">at</emph>
              <emph style="super">for a</emph>
            last there must be a quantity immultiplicable absolute, but
              <lb/>
            divisible infinitely infinite till that quantity be issued that is
              <lb/>
            absolutely </s>
          </p>
          <p>
            <s xml:space="preserve"> That such
              <emph style="st">a</emph>
            quantity which I call universally infinite: hath not only
              <lb/>
            act rationall, by supposition, or by consequence
              <emph style="super">mere</emph>
            supposition: but
              <lb/>
            also act reall, or existence: in an instant,
              <emph style="super">[???] perfect</emph>
            actuall being,
              <lb/>
            or in time, passed by motion
              <emph style="st">fini</emph>
            both finite & infinite: with many reall
              <lb/>
            consequences or properties consequent; & accidents adioyning:
              <lb/>
            shalbe declared in the papers </s>
          </p>
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