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

Table of figures

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                <pb xlink:href="040/01/854.jpg" pagenum="161"/>
              of Time from the aſſigned point, and the Velocities of them all
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              being equal, there ſhall conſequently be deſcribed by thoſe move­
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              able points Circumferences of Circles alwayes bigger and bigger,
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              all concentrick about the firſt point aſſigned: juſt in the ſame
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              manner as we ſee it done in the Undulations of ſtanding Water,
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              when a ſtone is dropt into it; the percuſſion of which ſerveth to
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              give the beginning to the Motion on every ſide, and remaineth
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              as the Center of all the Circles that happen to be deſigned ſucceſ­
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              ſively bigger and bigger by the ſaid Undulations. </s>
              <s>But if we ima­
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              gine a Plane erect unto the Horizon, and a point be noted in the
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              ſame on high, from which infinite Lines are drawn inclined, ac­
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              cording to all inclinations, along which we fancy grave Movea­
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              bles to deſcend, each with a Motion naturally Accelerate
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              with thoſe Velocities that agree with the ſeveral Inclinations;
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              ſuppoſing that thoſe deſcending Moveables were continually viſi­
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              ble, in what kind of Lines ſhould we ſee them continually diſpoſed?
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              </s>
              <s>Hence my wonder ariſeth, ſince that the precedent Demonſtrati­
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              ons aſſure me, that they ſhall all be alwayes ſeen in one and the
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              ſame Circumference of Circles ſucceſſively encreaſing, according
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              as the Moveables in deſcending go more and more ſucceſſively re­
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              ceding from the higheſt point in which their Fall began: And the
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              better to declare my ſelf, let the chiefeſt point A be marked, from
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              which Lines deſcend according to any Inclinations A F, A H, and
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              the Perpendicular A B, in which taking the points C and D, de­
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              ſcribe Circles about them that paſs by
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                <figure id="id.040.01.854.1.jpg" xlink:href="040/01/854/1.jpg" number="96"/>
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              the point A, interſecting the inclined
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              Lines in the points F, H, B, and E, G,
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              I. </s>
              <s>It is manifeſt, by the fore-going
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              Demonſtrations, that Moveables de­
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              ſcendent along thoſe Lines departing
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              at the ſame Time from the term A,
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              one ſhall be in E, the other ſhall be in
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              G, and the other in I; and ſo con­
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              tinuing to deſcend they ſhall arrive
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              in the ſame moment of Time at F, H,
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              and B: and theſe and infinite others continuing to move along the
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              infinite differing Inclinations, they ſhall alwayes ſucceſſively arrive
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              at the ſelf-ſame Circumferences made bigger & bigger
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              in infinitum.
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              From the two Species, therefore, of Motion of which Nature makes
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              uſe, ariſeth, with admirable harmonious variety, the generation of in­
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              ſinite Circles. </s>
              <s>She placeth the one as in her Seat, and original be­
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              ginning, in the Center of infinite concentrick Circles; the other
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              is conſtituted in the ſublime or higheſt Contact of infinite Circum­
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              ferences of Circles, all excentrick to one another: Thoſe proceed
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              from Motions all equal and Equable; Theſe from Motions all al­</s>
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