Clavius, Christoph, In Sphaeram Ioannis de Sacro Bosco commentarius

Table of contents

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[111.] Omnes ſtellæ 12. Tertiæ magnit. 2. Quartæ 6. Quintæ 4.
[112.] IN PLAGA ERGO AVSTRALI STELLÆ omnes 316. Primæ magnitud. 7. Secundæ 18. Tertiæ 60. Quar-tæ 168. Quintæ 53. Sextæ 9. Neb. 1. IN TOTO AVTEM FIRMAMENTO STELLÆ omnes, præter tres in cincinno. 1022. vt ſupra dictum eſt.
[113.] VSVS PRÆCEDENTIS TABVLAE.
[114.] DE STELLARVM DECLINATIONIBVS inueſtigandis.
[115.] DE QVANTITATE STELLARVM.
[116.] Proportiones diametrorum ſtellarum omnium ad diametrum terræ.
[117.] Quoties diameter cuiuſuis ſtellæ diametrum terræ, uel diameter terræ diametrum ſtellæ in ſe contineat.
[118.] Proportiones magnitudinum ftellarum omnium ad magnitudinem terrę.
[119.] Quoties magnitudo cuiuſuis ſtellæ magnitudinem terræ, uel magnitu-do terrę magnitudinem ſtellæ in ſe contineat.
[120.] TERRAM ESSE IMMOBILEM.
[121.] COMMENTARIVS.
[122.] COMMENTARIVS.
[123.] DE AMBITV TERRAE.
[124.] COMMENTARIVS.
[125.] COMMENTARIVS.
[126.] VIÆ AD INVESTIGANDVM AMBITVM TERRÆ commodiores, quàm ea, quæ ab auctore tradita eſt.
[127.] COMMENTARIVS.
[128.] REGVLA, QVA DI AMETER EX CIRCVNFE-rentia, & circumferentia ex diametro inueniatur.
[129.] REGVLAE, QVIBVSET SVPERFICIES MA-ximi circuli in orbe terreno, uel etiam in quacunque ſphæra, & ſuperficies conuexa eiuſdem orbis terreni, uel etiam cuiuſque ſpære, immo, & tota ſoliditas inueniatur.
[130.] DE VARIIS MENSVRIS Mathematicorum.
[131.] VARIÆ SENTENTIÆ AVCTORVM in ambitu terræ præfiniendo.
[132.] DISTANTIÆ COELORVM A TERRA, craſſitudinesq́ue, & Ambitus eorundem.
[133.] DIGRESSIO DE ARENAE NVMERO.
[134.] PRIMI CAPITIS FINIS.
[135.] CAPVT SECVNDVM DE CIRCVLIS, EX QVIBVS SPHAERA materialis componitur, & illa ſupercæleſtis, quæ per iſtam repræſentatur, componi intelligitur.
[136.] COMMENTARIVS.
[138.] II.
[139.] III.
[140.] IIII.
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        <div xml:id="echoid-div425" type="section" level="1" n="132">
          <p>
            <s xml:id="echoid-s8767" xml:space="preserve">
              <pb o="217" file="253" n="254" rhead="Ioan. de Sacro Boſco."/>
            colligetur. </s>
            <s xml:id="echoid-s8768" xml:space="preserve">Quoniam ſemidiameter conuexi Firmamenti continet ſemidia-
              <lb/>
            metros terræ 45225. </s>
            <s xml:id="echoid-s8769" xml:space="preserve">ſi fiat, ut ſinus totus 100000. </s>
            <s xml:id="echoid-s8770" xml:space="preserve">ad 45225. </s>
            <s xml:id="echoid-s8771" xml:space="preserve">ſemidiametrum
              <lb/>
            Firmamenti, ita 12208. </s>
            <s xml:id="echoid-s8772" xml:space="preserve">chorda graduum 7. </s>
            <s xml:id="echoid-s8773" xml:space="preserve">quibus diameter dicti circuli ſtellę
              <lb/>
            polaris ſubtenditur; </s>
            <s xml:id="echoid-s8774" xml:space="preserve">inuenietur dicta chorda, ſiue diameter illius circuli conti
              <lb/>
            nere 5521. </s>
            <s xml:id="echoid-s8775" xml:space="preserve">ſemidiametros terræ. </s>
            <s xml:id="echoid-s8776" xml:space="preserve">Cum ergo diameter conuexi ſphæræ Solaris
              <lb/>
            cõplectatur ſemidiametros terræ duntaxat 2432. </s>
            <s xml:id="echoid-s8777" xml:space="preserve">& </s>
            <s xml:id="echoid-s8778" xml:space="preserve">paulo amplius, perſpicuum
              <lb/>
            eſt, diametrum ſphæræ Solis non efficere dimidium diametri prædicti circuli.
              <lb/>
            </s>
            <s xml:id="echoid-s8779" xml:space="preserve">Quare cum circuli habeant proportionem diametrorum duplicatam, nempe
              <lb/>
            eam, quam diametrorum quadrata habent; </s>
            <s xml:id="echoid-s8780" xml:space="preserve">erit circulus maximus in ſphęra So
              <lb/>
              <note position="right" xlink:label="note-253-01" xlink:href="note-253-01a" xml:space="preserve">2. duod.</note>
            lis minor quàm {1/4}. </s>
            <s xml:id="echoid-s8781" xml:space="preserve">dicti circuli. </s>
            <s xml:id="echoid-s8782" xml:space="preserve">Ex quo ſequitur, ſphæram Solis intra illum
              <lb/>
            circulum poſitum dictum circulum nequaquam tangere poſſe.</s>
            <s xml:id="echoid-s8783" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div428" type="section" level="1" n="133">
          <head xml:id="echoid-head138" xml:space="preserve">DIGRESSIO DE ARENAE NVMERO.</head>
          <p>
            <s xml:id="echoid-s8784" xml:space="preserve">ARCHIMEDIS tempore (vt ipſemet in lib. </s>
            <s xml:id="echoid-s8785" xml:space="preserve">de arenæ numero refert)
              <lb/>
              <note position="right" xlink:label="note-253-02" xlink:href="note-253-02a" xml:space="preserve">Arenæ nu-
                <lb/>
              merum ſe-
                <lb/>
              cũdũ quoſ
                <lb/>
              dam eſſe in
                <unsure/>
                <lb/>
              finitum, ſe-
                <lb/>
              cũ dũ quoſ-
                <lb/>
              dã uero fi-
                <lb/>
              nitũ quidẽ,
                <lb/>
              ſed ab om-
                <lb/>
              ni dato nu-
                <lb/>
              mero ſupe-
                <lb/>
              rari.</note>
            arbitrabantur nonnulli, numerum arenæ, non quidem ſolum eius, quæ circa
              <lb/>
            Syracuſas, & </s>
            <s xml:id="echoid-s8786" xml:space="preserve">reliquam Siciliam, ſed & </s>
            <s xml:id="echoid-s8787" xml:space="preserve">illius, quæ in omni regione habitabili,
              <lb/>
            pariter atque in habitabili continetur, infinitum eſſe. </s>
            <s xml:id="echoid-s8788" xml:space="preserve">Alij uero, non quidẽ eſſe
              <lb/>
            inſinitum dicebant eum arenæ numerum, propterea quòd infinitum dari non
              <lb/>
            poſſit, ſed nullum dari poſſe determinatũ numerum credebant, qui illius mul-
              <lb/>
            titudinem exuperaret, aut ei par eſſet; </s>
            <s xml:id="echoid-s8789" xml:space="preserve">immo uero potius è contrario, nume-
              <lb/>
            rum quemcunque propoſitum, & </s>
            <s xml:id="echoid-s8790" xml:space="preserve">determinatum, à numero illo arenæ ſupera-
              <lb/>
            tum it
              <unsure/>
            i. </s>
            <s xml:id="echoid-s8791" xml:space="preserve">Ex quo infert Archimedes, eos, qui ita opinantur, ſi eiuſmodi aerenæ
              <lb/>
            aceruum animo comprehenderent, cuiuſmodi eſſet, ſi uniuerſæ terra, reple-
              <lb/>
            to in ea mari, & </s>
            <s xml:id="echoid-s8792" xml:space="preserve">cauitatibus omnibus, altiſſimorum montium uertices exæ-
              <lb/>
            quaret, atque huius ipſius rurſus alterum multiplicem excogitarent, ſine ul-
              <lb/>
            lo dubio exiſtimaturos, illius multitudinem numeros omnes longe, multũq́;
              <lb/>
            </s>
            <s xml:id="echoid-s8793" xml:space="preserve">ſuperare. </s>
            <s xml:id="echoid-s8794" xml:space="preserve">Horum omnium errorem Archimedes in eo lib. </s>
            <s xml:id="echoid-s8795" xml:space="preserve">quem de Arenæ nu
              <lb/>
            mero inſcripſit, Geometrice, & </s>
            <s xml:id="echoid-s8796" xml:space="preserve">quidem acutiſſime reſellit, inueſtigãs numerũ,
              <lb/>
            qui non ſolum arenæ multitudinem ſuperet, quæ terræ undique repletæ, ut di
              <lb/>
            ximus, æqualis eſſet, ſed etiam quæ ipſi mundo (poſito etiam mundo multo
              <lb/>
            maiore, quàm re ipſa eſt) parem haberet magnitudinem. </s>
            <s xml:id="echoid-s8797" xml:space="preserve">Atque hoc eſt Archi-
              <lb/>
              <note position="right" xlink:label="note-253-03" xlink:href="note-253-03a" xml:space="preserve">Archime-
                <lb/>
              dis propoſi
                <lb/>
              tum in lib.
                <lb/>
              de arenæ
                <lb/>
              numero.</note>
            medi propoſitum in lib. </s>
            <s xml:id="echoid-s8798" xml:space="preserve">de arenæ numero, ubi prius ſubtili quadam ratione de
              <lb/>
            monſtrat, quanam uia diſtantia Solis à terra ſit inueſtiganda, inuento prius an
              <lb/>
            gulo, qui minor ſit angulo, quem duæ lineæ rectę à centro uiſus egredientes,
              <lb/>
            Solemq́ue tangentes comprehendunt, qua de re conſule eius ſcripta, & </s>
            <s xml:id="echoid-s8799" xml:space="preserve">com-
              <lb/>
            mentarios Federici Commandini.</s>
            <s xml:id="echoid-s8800" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8801" xml:space="preserve">Nos igitur ueſtigiis Archimedis inh ærentes, numerum quoque inquire-
              <lb/>
            mus, qui longe maior ſit numero arenæ, etiam minutiſſimæ, quæ totum mun-
              <lb/>
            dum uſque ad Firmamentum repleret. </s>
            <s xml:id="echoid-s8802" xml:space="preserve">Multi enim à me contenderunt, ut hoc
              <lb/>
            loco rem hanc explicarem. </s>
            <s xml:id="echoid-s8803" xml:space="preserve">Quod quidem eo libentius feci, quod ſciam, id mul
              <lb/>
            tis fore iucundiſſimum; </s>
            <s xml:id="echoid-s8804" xml:space="preserve">præſertim uero quòd negotium hoc non ſit prorſus à
              <lb/>
            noſtro inſtituto alienum: </s>
            <s xml:id="echoid-s8805" xml:space="preserve">quando quidem multa hoc loco adduximus de diftã
              <lb/>
            tiis, ac magnitudinibus cœlorum, ex quibus facili negotio id, quod propoſui-
              <lb/>
            mus, colligere poſſumus. </s>
            <s xml:id="echoid-s8806" xml:space="preserve">Vt autem illuſtrior, atque admirabilior diſputatio
              <lb/>
            noſtra euadat, ponamus totum mundum ad Firmamentum uſque longe maio
              <lb/>
            rem eſſe, quàm ab Aſtronomis deprehenſus eſt; </s>
            <s xml:id="echoid-s8807" xml:space="preserve">Item arenulas mundum uniuer
              <lb/>
            ſum replentes multò eſſe maiores, quàm vſpiam reperiuntur. </s>
            <s xml:id="echoid-s8808" xml:space="preserve">Nam ſi </s>
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