Clavius, Christoph, In Sphaeram Ioannis de Sacro Bosco commentarius

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          <p>
            <s xml:id="echoid-s647" xml:space="preserve">
              <pb o="14" file="050" n="51" rhead="Comment. in I. Cap. Sphæræ"/>
            re, quod apud paucos reperiatur bene explicata.</s>
            <s xml:id="echoid-s648" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s649" xml:space="preserve">
              <emph style="sc">Sciendvm</emph>
            eſt igitur, omnia commenſurari linea perpendiculari à
              <unsure/>
              <lb/>
              <note position="left" xlink:label="note-050-01" xlink:href="note-050-01a" xml:space="preserve">Mat
                <unsure/>
              hema-
                <lb/>
              tici omnia
                <lb/>
              metiuntur
                <lb/>
              linea perpẽ
                <lb/>
              diculari.</note>
            Mathematicis, ita vt tam longa dicatur eſſe quælibet magnitudo, quanta eſt
              <lb/>
            perpendicularis ducta ab vno extremo figuræ ad aliud extremũ; </s>
            <s xml:id="echoid-s650" xml:space="preserve">Vt in hoc pro
              <lb/>
              <figure xlink:label="fig-050-01" xlink:href="fig-050-01a" number="5">
                <image file="050-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/050-01"/>
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            poſito parallelogrammo A B C D,
              <lb/>
            longitudo erit linea perpendicula-
              <lb/>
            ris L M, ducta à puncto L, lateris
              <lb/>
            A D, ad latus oppoſitum B C, pro-
              <lb/>
            tractum, vel perpendicularis A F.
              <lb/>
            </s>
            <s xml:id="echoid-s651" xml:space="preserve">Pari ratione latitudinem cuiuſuis
              <lb/>
            quantitatis tantã dicunt eſſe, quan-
              <lb/>
            ta eſt perpendicularis educta ab v-
              <lb/>
            no latere ad aliud; </s>
            <s xml:id="echoid-s652" xml:space="preserve">Vt propoſiti pa-
              <lb/>
            rallelogrammi latitudo erit perpen
              <lb/>
            dicularis B E, alatere A B, ad latus
              <lb/>
            D C, protractum extenſa. </s>
            <s xml:id="echoid-s653" xml:space="preserve">Profundi-
              <lb/>
            tas denique ſeu craſſities, altitudove cuiuſcunque corporis tanta eſſe iudica-
              <lb/>
            tor, quanta eſt perpendicularis producta ab vna parte ad aliã. </s>
            <s xml:id="echoid-s654" xml:space="preserve">Quamobrem Eu
              <lb/>
            clides pulcherrime ad initium ſexti lib. </s>
            <s xml:id="echoid-s655" xml:space="preserve">deſiniens altitudinem cuiuſq; </s>
            <s xml:id="echoid-s656" xml:space="preserve">figuræ
              <lb/>
            dixit: </s>
            <s xml:id="echoid-s657" xml:space="preserve">Eam eſſe lineam perpendicularem à vertice ad baſim deductam.</s>
            <s xml:id="echoid-s658" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s659" xml:space="preserve">
              <emph style="sc">Ratio</emph>
            vero, cur omnia Mathematici metiantur linea perpendiculari,
              <lb/>
              <note position="left" xlink:label="note-050-02" xlink:href="note-050-02a" xml:space="preserve">@ur a Ma-
                <lb/>
              thematicis
                <lb/>
              omnia mẽ-
                <lb/>
              ſurentur li
                <lb/>
              n
                <unsure/>
              ea perpen
                <lb/>
              diculari.</note>
            ea eſt, quà
              <unsure/>
            m Ptolemæus aſſerit in libello, quem de Analemmate conſcripſit, & </s>
            <s xml:id="echoid-s660" xml:space="preserve">
              <lb/>
            quam Simplicius accepit ex libro eiuſdem Ptolemæi de Dimenſiones: </s>
            <s xml:id="echoid-s661" xml:space="preserve">quoniã
              <lb/>
            videlicet menſura alicuius rei debet eſſe ſtata, determinataq́; </s>
            <s xml:id="echoid-s662" xml:space="preserve">& </s>
            <s xml:id="echoid-s663" xml:space="preserve">non indeſini
              <lb/>
            ta: </s>
            <s xml:id="echoid-s664" xml:space="preserve">Inter cũctas autem lineas rectas, penes quas ſumitur omnis menſura, ſola
              <lb/>
            linea perpendicularis eſt certæ, determinatæq́; </s>
            <s xml:id="echoid-s665" xml:space="preserve">longitudinis, aliæ autem om-
              <lb/>
            nes indeterminatæ. </s>
            <s xml:id="echoid-s666" xml:space="preserve">Vt in ſuperiore parallelogrammo, linea perpendicularis
              <lb/>
            BE, penes quam ſumpſimus latitudinem figuræ, inter omnes lineas, quæ à late
              <lb/>
            re A B, duci poſſunt ad latus D C, ſiue vlterius protractum ſit, ſiue non, ſola
              <lb/>
            eſt ſtatæ, atq; </s>
            <s xml:id="echoid-s667" xml:space="preserve">inuariabilis quãtitatis; </s>
            <s xml:id="echoid-s668" xml:space="preserve">A quocunq. </s>
            <s xml:id="echoid-s669" xml:space="preserve">enim puncto lateris A B, du-
              <lb/>
            xeris ad latus D C, lineam perpendicularem, hæc prorſus eandem habebit lon
              <lb/>
            gitudinem, quàm perpendicularis B E, qualis eſt perpendicularis G H. </s>
            <s xml:id="echoid-s670" xml:space="preserve">Nam
              <lb/>
            cum G B F H, (vt manifeſto conſtat ex primo lib. </s>
            <s xml:id="echoid-s671" xml:space="preserve">Euclidis) ſit parallelogram-
              <lb/>
            mum, erunt latera oppoſita B E, G H, æqualia, & </s>
            <s xml:id="echoid-s672" xml:space="preserve">ſic de alijs; </s>
            <s xml:id="echoid-s673" xml:space="preserve">Quod minime
              <lb/>
              <note position="left" xlink:label="note-050-03" xlink:href="note-050-03a" xml:space="preserve">34. primi.</note>
            contingit in alijs lineis, quæ non perpendiculares ſunt: </s>
            <s xml:id="echoid-s674" xml:space="preserve">Ex quo cunque enim
              <lb/>
            puncto lateris A B, ad latus D C, duci poſſunt innumeræ lineę non perpendi-
              <lb/>
            culares, quarum vna altera maior eſt, & </s>
            <s xml:id="echoid-s675" xml:space="preserve">omnibus minor exiſtit perpendicula-
              <lb/>
            ris ab eodem puncto deducta, vt manifeſtum eſt in lineis G H, G I, G K. </s>
            <s xml:id="echoid-s676" xml:space="preserve">Quod
              <lb/>
              <note position="left" xlink:label="note-050-04" xlink:href="note-050-04a" xml:space="preserve">19. primi.</note>
            cum ita ſit, non ſine magno cõſilio, immo ipſa Natura duce, mẽſuræ quantia-
              <lb/>
              <figure xlink:label="fig-050-02" xlink:href="fig-050-02a" number="6">
                <image file="050-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/050-02"/>
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            tum capiuntur penes lineas parpendicula-
              <lb/>
            res, quæ ſolæ terminatæ ſunt, atque inuaria
              <lb/>
            biles: </s>
            <s xml:id="echoid-s677" xml:space="preserve">non autẽ ſecundum alias, quæ infini-
              <lb/>
            tis modis poſſunt duci, modo breuiores,
              <lb/>
            modo longiores; </s>
            <s xml:id="echoid-s678" xml:space="preserve">Sicut etiam non ſolum
              <lb/>
            apud Mathematicos, verum etiam apud
              <lb/>
            vulgus ſpacia, & </s>
            <s xml:id="echoid-s679" xml:space="preserve">itinerum interualla iux-
              <lb/>
            ta lineas rectas ſumuntur, quæ breuiſſimæ
              <lb/>
            ſunt, & </s>
            <s xml:id="echoid-s680" xml:space="preserve">non penes circulares, quæ </s>
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