Clavius, Christoph, In Sphaeram Ioannis de Sacro Bosco commentarius

Table of contents

< >
[51.] COMMENTARIVS.
[52.] COMMENTARIVS.
[53.] COMMENTARIVS,
[54.] DENVMERO ORBIVM CAELESTIVM.
[55.] DE MOTIBVS ORBIVM CÆLESTIVM.
[56.] DEPERIODIS MOTVVM CÆLESTIVM.
[57.] QVOMODO DEPREHENSVM SIT OMNES cælos ſimpliciter ab ortu in occaſum moueri.
[58.] QVA RATIONE COLLECTVS SIT MOTVS Cælorum ab occaſu in ortum.
[59.] QVA INDVSTRIA CAELOS INFERIORES ab Occaſu in Ortum ſuper diuerſos polos à polis mundi moueri obſeruatum ſit.
[60.] PROPTER QV AE PHAENOMENA ASTROMI motum trepidationis ſtellis fixis attribuerint.
[61.] DE ORDINE SPÆRARVM CÆLESTIVM.
[62.] COELVM MOVERI AB ORTV IN OCCASVM.
[63.] COMMENTARIVS.
[64.] COMMENTARIVS.
[65.] COELVM ESSE FIGVRÆ SPHÆRICÆ.
[66.] COMMENT ARIVS,
[67.] COMMENTARIVS.
[68.] DE FIGVRIS ISOPERIMETRIS. DEFINITIONES. I.
[70.] III.
[71.] IIII.
[73.] THEOR. 1. PROPOS. 1.
[74.] THEOR. 2. PROPOS. 2.
[75.] THEOR. 3. PROPOS. 3.
[76.] THEOR. 4. PROPOS. 4.
[77.] THEOR. 5. PROPOS. 5.
[78.] THEOR. 6. PROPOS. 6.
[79.] THEOR. 1. PROPOS. 7.
[80.] SCHOLIVM.
< >
page |< < (16) of 525 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div64" type="section" level="1" n="41">
          <pb o="16" file="052" n="53" rhead="Comment. in I. Cap. Sphæræ"/>
          <p>
            <s xml:id="echoid-s728" xml:space="preserve">
              <emph style="sc">Vervm</emph>
            dicet aliquis, cum circunferentia ſemicirculi ſit linea quædam
              <lb/>
              <note position="left" xlink:label="note-052-01" xlink:href="note-052-01a" xml:space="preserve">Dubitatio
                <lb/>
              eõtra ſupe-
                <lb/>
              riorem de-
                <lb/>
              finitionem
                <lb/>
              auctoris.</note>
            curua omnis latitudinis expers, ex ductu autẽ, ſeu motu cuiuſuis lineæ imagi-
              <lb/>
            nario, omnium Mathematicorum conſenſu, non efficiatur niſi ſuperficies, qui
              <lb/>
            fieri poteſt, ut ſphæra, quæ eſt ſolidum quippam, vt & </s>
            <s xml:id="echoid-s729" xml:space="preserve">auctor ipſe in declaratio
              <lb/>
            ne ſuæ definitionis aſſeruit, & </s>
            <s xml:id="echoid-s730" xml:space="preserve">mox iterum ex Theodoſio ſubiungetur, gignatur
              <lb/>
            ex ductu, ſeu reuolutione, circumactione ve circunferentię ſemicirculi? </s>
            <s xml:id="echoid-s731" xml:space="preserve">nam
              <lb/>
              <note position="left" xlink:label="note-052-02" xlink:href="note-052-02a" xml:space="preserve">Solutio du-
                <lb/>
              bitationis.</note>
            ex tali circũductu ſola ſuperficies extima ſphæræ procreatur. </s>
            <s xml:id="echoid-s732" xml:space="preserve">Cui oecurrendũ
              <lb/>
            eſt, definitionem hanc Euclidis non eſſe fideliterab auctore recitatam. </s>
            <s xml:id="echoid-s733" xml:space="preserve">Eucli-
              <lb/>
            des enim in lib. </s>
            <s xml:id="echoid-s734" xml:space="preserve">11. </s>
            <s xml:id="echoid-s735" xml:space="preserve">defin. </s>
            <s xml:id="echoid-s736" xml:space="preserve">4. </s>
            <s xml:id="echoid-s737" xml:space="preserve">non dixit, Sphęram effici ex conuerſione circunfe
              <lb/>
            rentiæ ſemicirculi circa diametrũ, ſed ex ductu. </s>
            <s xml:id="echoid-s738" xml:space="preserve">ac reuolutione totius ſemicir-
              <lb/>
              <note position="left" xlink:label="note-052-03" xlink:href="note-052-03a" xml:space="preserve">Definitio
                <lb/>
              ſphęrę ab
                <lb/>
              Eucl. tradi-
                <lb/>
              ta.</note>
            culi, quem quidem conſtat eſſe ſu perficiem. </s>
            <s xml:id="echoid-s739" xml:space="preserve">Quamobrem ſicut ex reuolutione
              <lb/>
            lineę rectæ finitæ circa alterũ extremum fixum deſcribitur circulus, ita vt ipſa
              <lb/>
            linea ſuperficiem efficiat, punctum vero alterum extremum circunferentiam
              <lb/>
            deſignet: </s>
            <s xml:id="echoid-s740" xml:space="preserve">ſic quoque ex circumactione quidem ſuperficiei ſemicirculi procrea-
              <lb/>
            bitur ſolidita@ ſphæræ, ex reuolutione uero ſemicircunferentiæ ſuperficies ex-
              <lb/>
            tima rotunda; </s>
            <s xml:id="echoid-s741" xml:space="preserve">atque hac ratione perfectum corpus ſphæricum naſcitur.</s>
            <s xml:id="echoid-s742" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s743" xml:space="preserve">
              <emph style="sc">Sphaera</emph>
            etiam à Theodoſio ſic deſcribitur; </s>
            <s xml:id="echoid-s744" xml:space="preserve">Sphæra eſt ſolidum
              <lb/>
              <note position="left" xlink:label="note-052-04" xlink:href="note-052-04a" xml:space="preserve">Alia ſphę-
                <lb/>
              ræ defini-
                <lb/>
              tio tradita
                <lb/>
              à Thedo-
                <lb/>
              ſio.</note>
            quoddam una ſuperficie cotentum, in cuius medio punctus eſt, à quo omnes
              <lb/>
            lineæ ductæ ad circunferentiam ſunt æquales.</s>
            <s xml:id="echoid-s745" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div73" type="section" level="1" n="42">
          <head xml:id="echoid-head46" xml:space="preserve">COMMENTARIVS.</head>
          <p>
            <s xml:id="echoid-s746" xml:space="preserve">
              <emph style="sc">Haec</emph>
            eſt ſecunda ſphæræ definitio deſumpta ex Theodoſio de ſphæri-
              <lb/>
            cis elementis; </s>
            <s xml:id="echoid-s747" xml:space="preserve">in aqua quidem tres particulæ continentur. </s>
            <s xml:id="echoid-s748" xml:space="preserve">Prima eſt [ſolidum]
              <lb/>
              <note position="left" xlink:label="note-052-05" xlink:href="note-052-05a" xml:space="preserve">Explicatio
                <lb/>
              definitio-
                <lb/>
              nis ſphærę
                <lb/>
              à Theodoſ.
                <lb/>
              @aditæ.</note>
            id eſt, corpus, poniturq́; </s>
            <s xml:id="echoid-s749" xml:space="preserve">ad differentiam figurarum planarum, cuiuſmodi eſt
              <lb/>
            circulus, quadratum, &</s>
            <s xml:id="echoid-s750" xml:space="preserve">c. </s>
            <s xml:id="echoid-s751" xml:space="preserve">Secunda [una ſuperficie contentum] apponitur ad ex-
              <lb/>
            cludendas figuras ſolidas pluribus ſuperficiebus comprehenſas, qualis eſt rota
              <lb/>
            currus, lapis molaris, pyramis, cubus, &</s>
            <s xml:id="echoid-s752" xml:space="preserve">c. </s>
            <s xml:id="echoid-s753" xml:space="preserve">Sed quoniam duplex eſt ſuperficies,
              <lb/>
            una plana, quæ ex omni parte linea recta adæquate poteſt cõmenſurari, ut eſt
              <lb/>
            ſuperficies alicuius muri bene cõplanati, uel tabulæ uel papyri bene extenſæ:
              <lb/>
            </s>
            <s xml:id="echoid-s754" xml:space="preserve">Altera curua, quæ undique linea recta menſurari nequit; </s>
            <s xml:id="echoid-s755" xml:space="preserve">Atq; </s>
            <s xml:id="echoid-s756" xml:space="preserve">hæc uel eſt con
              <lb/>
            caua, ut eſt interior ſuperficies alicuius hydriæ; </s>
            <s xml:id="echoid-s757" xml:space="preserve">uel conuexa, cuiuſmodi eſt
              <lb/>
            exterior ſuperficies hydriæ, uel pilæ; </s>
            <s xml:id="echoid-s758" xml:space="preserve">Sphæra ſuperficie curua, eaq́; </s>
            <s xml:id="echoid-s759" xml:space="preserve">conuexa & </s>
            <s xml:id="echoid-s760" xml:space="preserve">
              <lb/>
            unica continetur. </s>
            <s xml:id="echoid-s761" xml:space="preserve">Tertia denique particula eſt [in cuius medio, &</s>
            <s xml:id="echoid-s762" xml:space="preserve">c.</s>
            <s xml:id="echoid-s763" xml:space="preserve">] adiungi-
              <lb/>
            turq́ue ad differentiam plurimorum ſolidorum una quidem ſuperficie conten
              <lb/>
            torum, in quibus tamen tale punctum aſſignari minime poteſt: </s>
            <s xml:id="echoid-s764" xml:space="preserve">quale eſt cor-
              <lb/>
            pus ouale, lenticulare, & </s>
            <s xml:id="echoid-s765" xml:space="preserve">alia huiuſmodi.</s>
            <s xml:id="echoid-s766" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s767" xml:space="preserve">
              <emph style="sc">Qvod</emph>
            ſi hanc deſinitionem cum priore conferamus, reperiemus illam fa-
              <lb/>
            bricandæ ſphærę modum, induſtriamq́; </s>
            <s xml:id="echoid-s768" xml:space="preserve">nobis præbere: </s>
            <s xml:id="echoid-s769" xml:space="preserve">hanc uero ſphæræ iam
              <lb/>
              <note position="left" xlink:label="note-052-06" xlink:href="note-052-06a" xml:space="preserve">Cõparatio
                <lb/>
              duarũ ſphæ
                <lb/>
              ræ definitio
                <lb/>
              nũ interſe.</note>
            ſabricatæ ſubſtantiam explicare, ob idq́; </s>
            <s xml:id="echoid-s770" xml:space="preserve">illã potius deſcriptionẽ, hanc uero de
              <lb/>
            finitionem dicẽdã eſſe. </s>
            <s xml:id="echoid-s771" xml:space="preserve">Quam quidem definitionem Theodoſij deſumptam ex
              <lb/>
            Tymęo Platonis eleganter expreſſit Cicero in lib. </s>
            <s xml:id="echoid-s772" xml:space="preserve">de Vniuerſitate his uerbis
              <lb/>
            de mundo loquens. </s>
            <s xml:id="echoid-s773" xml:space="preserve">Ergo globoſus eſt fabricatus, quod σ φ {αι}ρώ{ει}δες Græci vocant,
              <lb/>
            cuius omnis extremitas paribus à medio radijs attingitur. </s>
            <s xml:id="echoid-s774" xml:space="preserve">Conuenit enim hęc etiam
              <lb/>
            definitio uniuerſo mundo; </s>
            <s xml:id="echoid-s775" xml:space="preserve">Mundus ſiquidem eſt ſphęra ſolida, cum nihil in
              <lb/>
            ipſo uacuum exiſtat, ſed omnia corporibus ſint repleta à mundi </s>
          </p>
        </div>
      </text>
    </echo>