Ceva, Giovanni, Geometria motus, 1692

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              Pr.
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              13.
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              huius.
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              Pr.
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              . </s>
              <s id="s.000533">prima.
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              Pr.
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              2.
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              prima.
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              Pr.
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              8.
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              huius &
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              Cor. </s>
              <s id="s.000536">pr.
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              13.</s>
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              Pr.
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              2.
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              huius.
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            <p type="main">
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              Corollarium.
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              Hinc aparet, ſpiralem DB ad ſpiralem DBG eandem habe­
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              re rationem, quam quadrilineum QIKN ad quadrilineum
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              HIKP; pariterque rectam DA ad eandem ſpiralem DCB ha­
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              bere ipſam rationem, ac rectangulum HIKL ad dictum qua­
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              drilineum HIKP. </s>
              <s id="s.000540">Eodem ferè modo exhiberi pißet ratio ſpi­
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              ralis ad ſpiralem, licèt plurium interſe circulationum, eritque
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              prorſus ea, quam habet vnum ad alterum eiuſdem illius na­
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              turæ, quadrilineorum.
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              PROP. XV. THEOR. XI.
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              Tab.
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              5.
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              Fig.
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              4.</s>
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              <s id="s.000543">SPiralis orta ex motu naturaliter accelerato per
                <expan abbr="radiũ">radium</expan>
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              circuli comprehendentis ſpiralem ipſam, & ex motu
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              æquabili circa
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              eiuſdem circuli, æqualis eſt
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              ei curuæ parabolicæ natæ ex motu compoſito, cuius vnum
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              latus curritur iuxta imaginem trianguli, nempe motu gra­
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              uium, alterum verò latus iuxta imaginem trilinei ſecundi,
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              habebitque parabola ipſa axim æqualem radio, & baſim̨
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              tertiæ parti circunferentiæ eiuſdem circuli ſpiralem com­
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              prehendentis. </s>
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            <p type="main">
              <s id="s.000544">Eſto ſpiralis ACB, quæ ſignatur ex motu
                <expan abbr="pũcti">puncti</expan>
              A æqua
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              biliter lati circa circumferentiam ADA, dum nempe
                <expan abbr="eodẽ">eodem</expan>
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              tempore IF, punctum B currit à quiete lineam BA motu
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              grauium deſcendentium; ſit verò imago velocitatum dicti
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              motus æquabilis per ADA rectangulum HGFI, & alte­
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              rius motus imago, (quæ triangulum erit) eſto FEIM. Pa­
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              tet, quia ipſæ imagines ponuntur homogeneæ, eſſe rectan­
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              gulum HGFI ad triangulum IFM vt ADA circumferentia
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              ad radium BA, & propterea IM ad IH erit vt BA ad dimi­
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              dium circunferentiæ AEDA. </s>
              <s id="s.000546">Sumatur quodlibet
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                tum</expan>
              K, & ducatur ONKL æquidiſtans HM, puteturque </s>
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