Cardano, Geronimo, Opvs novvm de proportionibvs nvmerorvm, motvvm, pondervm, sonorvm, aliarvmqv'e rervm mensurandarum, non solùm geometrico more stabilitum, sed etiam uarijs experimentis & observationibus rerum in natura, solerti demonstratione illustratum, ad multiplices usus accommodatum, & in V libros digestum. Praeterea Artis Magnae, sive de regvlis algebraicis, liber vnvs abstrvsissimvs & inexhaustus planetotius Ariothmeticae thesaurus ... Item De Aliza Regvla Liber, hoc est, algebraicae logisticae suae, numeros recondita numerandi subtilitate, secundum Geometricas quantitates inquirentis ...

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s id="id002716">
                <pb pagenum="154" xlink:href="015/01/173.jpg"/>
              dat à dextra parte, et circumuoluatur h cochleę rediens ad ſiniſtram
                <lb/>
              ibique deſcendens connectatur trochleæ in inferiori in o, cuius imæ
                <lb/>
              parti annectatur pondus remorans in imo annexum parte troch­
                <lb/>
              leæ p. </s>
              <s id="id002717">Cum ergo trahitur n trochlea, trahitur funis adeò ut pon­
                <lb/>
              dus m, tandem aſcendat cum trochlea l prope k: quia ergo in duo­
                <lb/>
              decim horis pondus m deſcenderet per k l funem reuolutionibus
                <lb/>
              circa d rotam dicamus uiginti, ergo ſi debet deſcendere à k ad l, per
                <lb/>
              funem duplicatam k l cum ipſam neceſſe ſit obequitantem d reuo­
                <lb/>
              lutionibus quadraginta circumuolui d, nam tota o h n d m g l k lon
                <lb/>
              gè maior eſt duplo k l, neceſſe eſt m deſcendere tardius quàm in du
                <lb/>
              plo temporis, quo deſcenderet per rectum funem k l, quod erat de­
                <lb/>
              monſtrandum. </s>
              <s id="id002718">Et hanc appendicem uidi apud Cæſarem Odonum
                <lb/>
              Apulum medicum, uirum elegantem lepidique ingenij. </s>
              <s id="id002719">Memento
                <lb/>
              uerò quod ubi orbiculi non cederent funi, uel quia duriores in cir
                <lb/>
              cumuolutione, uel quia latius exciperent illum reduplicato fune
                <lb/>
              circa illos omnin o circumducuntur, ſed difficilius ideò egent gra­
                <lb/>
              uiori pondere.</s>
            </p>
            <p type="main">
              <s id="id002720">Propoſitio centeſima quinquageſima ſeptima.</s>
            </p>
            <p type="main">
              <s id="id002721">Horologiorum molarium rationem oſtendere.</s>
            </p>
            <p type="main">
              <s id="id002722">
                <arrow.to.target n="marg523"/>
              </s>
            </p>
            <p type="margin">
              <s id="id002723">
                <margin.target id="marg523"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id002724">Sunt horum duo genera primum, & anti
                <lb/>
                <figure id="id.015.01.173.1.jpg" xlink:href="015/01/173/1.jpg" number="178"/>
                <lb/>
              quius licet multo poſterius eo quod pon­
                <lb/>
              deribus ducitur, quod funiculo ex inteſti­
                <lb/>
              nis ouium ſeu fidibus liræ agitur. </s>
              <s id="id002725">Sit igitur
                <lb/>
              axis f k erectus ſuper plano, cui per longum
                <lb/>
              coniuncta mola multiplicis ſpiræ in fine, cu
                <lb/>
              ius c annectatur ferreo circulo, qui habeatur loco capſulæ b c, quæ
                <lb/>
              circumuolui poſsit: huic
                <expan abbr="circũductus">circunductus</expan>
              funis d e multipliciter in pun
                <lb/>
              cto g, ſit autem e h in modum pyramidis ſenſim in acutum, ſed non
                <lb/>
              ualde per
                <expan abbr="ſpirã">ſpiram</expan>
              exculptam deſinentis, cui rota in uertice inſerta den
                <lb/>
              ſiculo, & uertatur h e, colligens funiculum tractum in ſpira uerſus
                <lb/>
              apicem: unde funiculus circumuoluet b g d,
                <expan abbr="capſulã">capſulam</expan>
              uerſus c, trahet
                <lb/>
              ergo molam, & conſtringet uiolenter
                <expan abbr="quãtum">quantum</expan>
              fert longitudo funis
                <lb/>
              quæ circumuolui poteſt a b e ad h: & cum trahitur in d eremittitur,
                <lb/>
              non poteſt mola ſtatim retrahere reluctantibus denticulis h l rotæ,
                <lb/>
              & alijs quæ implicantur curriculo m, a igitur mola conſtructa uio­
                <lb/>
              lenter mouet b g d, capſulam motu contrario à c in d & in g & in b,
                <lb/>
              quare funis d e trahitur, & trahit e h illum circumuoluendo contra­
                <lb/>
              rio motu priori, is mouet denticulo rotam h l, illa per curriculum in
                <lb/>
              aliam
                <expan abbr="rotã">rotam</expan>
              , & ſic deinceps donec tempus moueatur, & rota indicis.
                <lb/>
              </s>
              <s id="id002726">Hic adeſt capſula, & quod circumuertitur à claue non eſt axis molę
                <lb/>
              ſed extra molam, ſcilicet e h. </s>
              <s id="id002727">Et quoniam hac ratione quanto mola a </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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