Salusbury, Thomas, Mathematical collections and translations (Tome I), 1667

Table of figures

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              <s>
                <pb xlink:href="040/01/723.jpg" pagenum="31"/>
              is 2, and between the two Squares 9 and 4, 6 is the Mean. </s>
              <s>The
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              property of Cubes is to have neceſſarily between them two Num­
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              bers Mean-proportional. </s>
              <s>Suppoſe 8, and 27, the Means between
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              them are 12 and 18; and between the Unite and 8 the Means
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              are 2 and 4; betwixt the Unite and 27 there are 3, and 9. We
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              therefore conclude,
                <emph type="italics"/>
              That there is no other Infinite Number but the
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              Vnite.
                <emph.end type="italics"/>
              And theſe be ſome of thoſe Wonders, that ſurmount the
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              comprehenſion of our Imagination, and that advertize us how ex­
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              ceedingly they err, who diſcourſe about Infinites with thoſe very
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              Attributes, that are uſed about Finites; the Natures of which have
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              no congruity with each other. </s>
              <s>In which affair I will not conceal
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              from you an admirable accident, that I met with ſome time ſince,
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              explaining the vaſt difference, yea, repugnance and contrariety of
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              Nature, that a terminate quantity would incur by changing or paſ­
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              ſing into Infinite. </s>
              <s>We aſſign this Right Line A B, of any length at
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              pleaſure, and any point in the ſame, as C being taken, dividing it
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              into two unequal parts: I ſay, that many couples Lines, (hold­
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              ing the ſame proportion between themſelves as have the parts
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              A C, and B C,) departing from the terms A and B to meet with
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              one another; the points of their Interſection ſhall all fall in the
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              Circumference of one and the ſame Circle: as for example, A L
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              and B L departing [or
                <emph type="italics"/>
              being drawn
                <emph.end type="italics"/>
              ] from the Points A and B, and
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              having between themſelves the ſame proportion, as have the parts
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              A C and B C, and concurring in the point L: and the ſame pro­
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              portion being between two others A K, and B K, concurring in K,
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              alſo others as A I, and B I; A H, and B H; A G, and B G; A F,
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              and B F; A E, and B E: I ſay, that the points of their Interſecti­
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              on L, K, I, H, G, F, E, do all fall in the Circumference of one
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              and the ſame Semi-circle: ſo that we ſhould imagine the point
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              C to mve conti­
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                <figure id="id.040.01.723.1.jpg" xlink:href="040/01/723/1.jpg" number="58"/>
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              nuallyafter ſuch
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              a ſort, that the
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              Lines produced
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              from it to the fix­
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              ed terms A and
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              B retain alwaies
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              the ſame propor­
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              tion that is be­
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              tween the firſt
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              parts A C and C B, that point C ſhall decribe the Circumference
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              of a Circle, as we ſhall ſhew you preſently. </s>
              <s>And the Circle in ſuch
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              ſort deſcribed ſhall be alwaies greater and greater ſucceſſively,
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              according as the point C is taken nearer to the middle point
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              which is O; and the Circle ſhall be leſſer which ſhall be deſcribed
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              from a point nearer to the extremity B, inſomuch, that from the </s>
            </p>
          </chap>
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