Cardano, Girolamo, De subtilitate, 1663

Table of figures

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              <s id="s.010869">
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              æqualis. </s>
              <s id="s.010870">Quadrilaterum quod illi inſcribitur,
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              duos angulos ex aduerſo collocatos, duobus
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              rectis æquales ſemper habet. </s>
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              <s id="s.010871">Duóque eiuſdem rectangula ex oppoſi­
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              tis lateribus conſtantia, rectangulo diame­
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              trorum quadrilateri pariter accepta ſunt
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              æqualia. </s>
              <s id="s.010872">Quadrilateri verò quòd circulo
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              circumſcribitur, duo latera oppoſita duobus
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              reliquis ſibi inuicem oppoſitis ſunt æqua­
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              lia. </s>
              <s id="s.010873">Eſt verò capaciſſima figurarum pro am­
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              bitus ratione. </s>
              <s id="s.010874">Omnéſque figuræ in eo con­
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              tentæ, capaciſſimæ earum quæ ſub eiſdem
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              lateribus contineri poſſunt: figuræ verò in
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              illo æquilatere etiam ſunt æquiangulæ. </s>
              <s id="s.010875">Pun­
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              ctum habet in medio, à quo omnes lineæ,
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              vſque ad circumferentiam ductæ, æquales
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              ſunt. </s>
              <s id="s.010876">Si extra ipſum punctus figatur, lineæ
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              quotquot ad aduerſam circumferentiæ par­
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              tem ducentur, ductæ in partem exteriorem
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              rectangulum efficient æquale quadrato con­
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              tingentis ex eodem puncto. </s>
              <s id="s.010877">Quod ſi diame­
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              ter producatur extrà quantumlibet, alia ve­
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              rò diametro in centro ſecetur ad rectos, ex
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              huius fine diuiſa portione quarta circumfe­
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              rentiæ in quotquot æquales partes, per ea­
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              rum vltimam recta ducatur ad eam quæ ex­
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              terius in directo diametri adiacet, erit ipſa
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              diametro adiacens æqualis omnibus rectis
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              ex diuiſionum periferiæ punctis ductis per­
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              pendicularibus in ſubiectam diametrum, vſ­
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              que ad aduerſam circumferentiæ partem,
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              quæ quidem lineæ omnes, vt palam eſt dia­
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              metro, quæ exterius eſt productæ æquidi­
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              ſtant. </s>
              <s id="s.010878">Quod ſi ab eadem extremitate diame­
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              tros lineæ quotquot, ſeu intrà, ſeu extrà, ad
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              adiacentem quidam extrà, ad circumferen­
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              tiæ verò partem alteram intrà ducantur,
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              erunt in exterioribus rectangula ex tota li­
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              nea in partem intercluſam periferia circuli
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              & in interioribus ex tota in partem reliqua
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              diametro ad rectos ſtante intercluſam qua­
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              drato circulo inſcripto ſemper æqualia. </s>
              <s id="s.010879">Quę
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              verò circulo, hyperboli, & defectioni com­
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              munes ſunt, hæ ſunt. </s>
              <s id="s.010880">Ducta ex contingente
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              perpendicularis ſuper diametrum iacentem
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              in directo puncti, ex quo contingens ducta
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              eſt, partes diametros ſub eadem proportione
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              diuidit, ſub qua tota linea ex puncto è quo
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              contingens producta eſt ad centrum circuli
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              veniens, vſque ad alteram circumferentiæ
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              partem, ad partem exteriorem ſe habet. </s>
              <s id="s.010881">Se­
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              midiametros quoque proportione media eſt,
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              inter eam quæ à centro ad punctum exte­
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              rius, & eam quę à centro ad locum vbi cadit
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              perpendicularis ex loco contingentis ſuper
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              eandem diametrum. </s>
              <s id="s.010882">Cùm verò à terminis
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              diametri duæ contingentes ducuntur, ab eiſ­
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              dem verò punctis per idem punctum cir­
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              cumferentiæ mutuò ad alteram contingen­
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              tem, erit quod ſub partibus contingentium
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              his poſtremis lineis terminatarum rectan­
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              gulum continetur æquale quadrato dia­
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              metri.
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            <p type="margin">
              <s id="s.010883">
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              Circulo, &
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              hyperboli, ac
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              defectioni
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              communes
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              proprietates.</s>
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              <s id="s.010884">
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              Corporum
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              creatio.</s>
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              <s id="s.010885">Cùm ſemicirculus fixa diametro circum­
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              ducitur donec ad locum ſuum redeat, fit cor­
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              pus quod Sphæra vocatur. </s>
              <s id="s.010886">Quòd ſi ſit por­
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              tio ſemicirculo minor, fit corpus ouo ſimile,
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              quódque ouale dici poteſt. </s>
              <s id="s.010887">A maiore autem
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              portione factum nomen non habet. </s>
              <s id="s.010888">Sed ſi
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              rectangulum quadrilaterum eodem modo
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              circumducatur, fit cylindrus, quem colum­
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              nam appellare licet. </s>
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              <s id="s.010889">At ſi rectangulus trigonus eodem modo
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              altero laterum rectum angulum continen­
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              tium fixo, reliquo ſuper planum extenſo, fit
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              conus rectus, ſeu pyramis. </s>
              <s id="s.010890">Huius tres ſunt
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              ſpecies, iuxta laterum rectum angulum con­
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              tinentium totidem differentias. </s>
              <s id="s.010891">Nam ſi la­
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              tera ſint æqualia, fit rectus rectangulus co­
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              nus. </s>
              <s id="s.010892">Si maius quod fixum eſt latus, acutus
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              rectus conus. </s>
              <s id="s.010893">Quòd ſi maius ſit latus quod
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              circumuoluitur, fit rectus obtuſus conus.
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              </s>
              <s id="s.010894">Rectum conum voco ad differentiam illo­
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              rum, quorum inclinata eſt ſummitas, nec ba­
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              ſis circulus eſt. </s>
              <s id="s.010895">Omnis igitur coni recti pri­
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              mùm baſis eſt circulus, quo plano inſidet,
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              ſeu obtuſus, ſeu rectangulus ſit, ſeu acutus,
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              oxygoniuſve. </s>
              <s id="s.010896">Punctus autem coni ſupremus,
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              vertex dicitur. </s>
              <s id="s.010897">Ex vertice ad centrum baſis
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              ducta, vocatur coni axis. </s>
              <s id="s.010898">Quòd ſi ſuper axem
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              conus plana ſuperficie, ſeu plano (vt breuius
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              dicam) diuidatur, figura ex plano, quæ intra
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              conum continetur, ſemper eſt iſoſceles trian­
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              gulus, quem axis coni ſemper per æqualia
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              in duos trigonos diuidit: quorum quilibet eſt
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              orthogonius: æquilaterus verò æqualis, &
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              æquiangulus triangulo illi à quo conus fa­
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              bricatus eſt. </s>
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              <s id="s.010899">In prima igitur figura ſit orthogonius tri­
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              gonus ADC, ex cuius circumductu fiat co­
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              nus rectus A B C, cuius baſis eſt circulus
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              BECF, ex illius centro D A linea, quæ fuit
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              latus fixum trigoni, vocatur axis coni, eiúſ­
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              que extremitas ſuperior punctus, videlicet
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              A vocatur vertex coni. </s>
              <s id="s.010900">Si igitur planum di­
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              uidat conum ſuper axe AD, pars plani ABC
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              intra conum contenta, erit triangulus iſoſ­
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              celes A B C quem palam diuidere conum
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              per æqualia. </s>
              <s id="s.010901">Ipſum verò triangulum ab
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              axe coni AD, diuidi in duos triangulos or­
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              thogonios A D B, & A C D, quorum qui­
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              libet æqualis eſt æquilaterúſque, atque
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              æquiangulus trigono A D C primo, ex cu­
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              ius circumductu factus eſt conus. </s>
              <s id="s.010902">Si igitur
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              latus A D, æquale ſit lateri DC, vocabitur
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              conus rectus rectangulus: & ſi A D maior
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              eſt DC, vocabitur conus acutus rectus: &
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              AD ſit minor DC, vocabitur conus rectus
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              obtuſus. </s>
              <s id="s.010903">Quanquam hæc diuiſio fermè ſit ſu­
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              perflua: nam quæcunque dicuntur, com­
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              munia erunt omni cono, dummodo re­
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              ctus ſit, ſeu ſit rectangulus, ſeu acutus, ſeu
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              obtuſus. </s>
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              <s id="s.010904">Cum verò conus rectus (deinceps
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              bre­
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              uitatis cauſa conum dixiſſe ſufficiat,
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              </s>
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