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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            <p type="main">
              <s id="id001824">
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              in proportionibus notiſsimis angulorum ſed etiam in coniuncti­
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              one & detractione. </s>
              <s id="id001825">Et eſt ex ſubtiliſsimis operationibus, quæ ho­
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              mini in hoc genere eueniant.</s>
            </p>
            <p type="main">
              <s id="id001826">Propoſitio centeſima ſeptima.</s>
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            <p type="main">
              <s id="id001827">Si in circulo duo diametri ad rectum angulum ſe ſecauer int: alię
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              uerò ad perpendiculum ex diametro exierint ad circumferentiam,
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              ſingulæ ſupra diametrum erunt maiores portionibus reliquis dia­
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              metri ſuperioribus, infra autem minores. </s>
              <s id="id001828">Dimidium autem porti­
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              onis ſuperioris reſiduum ad centrum maius ſagitta habebit. </s>
              <s id="id001829">In ali­
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              qua præterea portionis ſuperioris parte, quæ uerſus diametrum
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              tranſuerſum poſita eſt, maior eſt differentia partis diametri ei cor­
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              reſpondentis, quam lineæ tranſuerſæ.</s>
            </p>
            <figure id="id.015.01.119.1.jpg" xlink:href="015/01/119/1.jpg" number="114"/>
            <p type="main">
              <s id="id001830">Sint duę diametri a b, c d ad perpendi
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              culum ſecantes ſe in centro, &
                <expan abbr="ducũtur">ducuntur</expan>
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              ſupr f g k h, & infra m l ad perpendicu­
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              lum ſupra a b: dico f g eſſe maiorem f a,
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              & k h k a, & contrà minorem m l, quàm
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              m a. </s>
              <s id="id001831">Per octauam enim ſexti, quod fit ex
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                <arrow.to.target n="marg374"/>
                <lb/>
              b f in f a æquale eſt
                <expan abbr="q̃drato">quadrato</expan>
              f g, ſed b f eſt
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              maior f g, quia b f eſt maior c b, & ideo
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              e c g f, ergo f g maior eſt f a, m l
                <expan abbr="aũt">aut</expan>
              minor eſt per
                <expan abbr="eadẽ">eadem</expan>
              e c, quare e a,
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              multo igitur minor m a, quod eſt primum. </s>
              <s id="id001832">Suppoſito etiam, quòd
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                <arrow.to.target n="marg375"/>
                <lb/>
              a g arcus ſit dimidium a c, dico a f
                <expan abbr="minorẽ">minorem</expan>
              eſſe f e, nam quadratum e
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                <arrow.to.target n="marg376"/>
                <lb/>
              g æquale eſt quadratis f e, & f g, &
                <expan abbr="quadratũ">quadratum</expan>
              a g quadratis f g & f a
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              & e g eſt ęqualis lateri exagoni, & a g latus octogoni, igitur e g ma­
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                <arrow.to.target n="marg377"/>
                <lb/>
              ior g a, & duo quadrata e f & f g maiora duobus quadratis f g &
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              f a, detracto igitur communi f g quadrato, patet propoſitum.
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                <arrow.to.target n="marg378"/>
              </s>
            </p>
            <p type="margin">
              <s id="id001833">
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              P
                <emph type="italics"/>
              er
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              31.
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              ter­
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              tij
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              lement.
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              </s>
            </p>
            <p type="margin">
              <s id="id001834">
                <margin.target id="marg375"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              7.
                <emph type="italics"/>
              tertij
                <emph.end type="italics"/>
                <lb/>
              E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
              C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="margin">
              <s id="id001835">
                <margin.target id="marg376"/>
              1.
                <emph type="italics"/>
              eiuſdem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id001836">
                <margin.target id="marg377"/>
              P
                <emph type="italics"/>
              er
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              47.
                <emph type="italics"/>
              pri
                <lb/>
              mi
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id001837">
                <margin.target id="marg378"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              ^{m}.
                <lb/>
              15.
                <emph type="italics"/>
              quarti
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                <lb/>
              E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="id001838">Cum rurſus ex prima parte huius lineę f g & k h ſint maiores f a,
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              & k a & ea ſit æqualis e c, neceſſe eſt ut iuxta punctum c augeatur </s>
            </p>
            <p type="main">
              <s id="id001839">
                <arrow.to.target n="marg379"/>
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              magis linea in ea, quam ſit differentia lineæ tranſuerſæ ad lineam
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              tranſuerſam per communem animi ſententiam, quod eſt tertium.</s>
            </p>
            <p type="margin">
              <s id="id001840">
                <margin.target id="marg379"/>
              P
                <emph type="italics"/>
              er
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              28.
                <emph type="italics"/>
              ter­
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              tij
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="id001841">Propoſitio centeſima octaua.</s>
            </p>
            <p type="main">
              <s id="id001842">Punctum ęqualitatis differentię deſcenſus, & remotionis à cen­
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              tro inuenire.</s>
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            <p type="main">
              <s id="id001843">Per præcedentem moto puncto a uerſus c ſemper uſ que ad e, c ma
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                <arrow.to.target n="marg380"/>
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              gis diſtat
                <expan abbr="pũctum">punctum</expan>
              a linea a e, quàm à puncto a uerſus, quia linea n h
                <lb/>
              maior eſt n a, & per eandem dum appropinquat ad c cum e c fiat
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              ęqualis ea, maius fit in crementum in a e, quàm reſpectu lineæ tranſ­
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              uerſalis. </s>
              <s id="id001844">Volo ergo inuenire punctum hoc in quo fit mutatio: &
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              diuido arcum ac per æqualia in f, & dico illum eſſe punctum quæ­
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              ſitum: accepto quouis puncto in e f, puta k, duco g o h p ęquidiſtan</s>
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          </chap>
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    </archimedes>
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