Clavius, Christoph, In Sphaeram Ioannis de Sacro Bosco commentarius

Table of handwritten notes

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            <s xml:id="echoid-s3998" xml:space="preserve">
              <pb o="78" file="114" n="115" rhead="Comment. in I. Cap. Sphæræ"/>
            culo, quam ſphæræ & </s>
            <s xml:id="echoid-s3999" xml:space="preserve">motus facilitas, & </s>
            <s xml:id="echoid-s4000" xml:space="preserve">partium firmitas, nullo obſtante ex-
              <lb/>
            crinſeco, maxima cõceditur. </s>
            <s xml:id="echoid-s4001" xml:space="preserve">Sexto & </s>
            <s xml:id="echoid-s4002" xml:space="preserve">ultimo utraq. </s>
            <s xml:id="echoid-s4003" xml:space="preserve">figura tam circularis, quàm
              <lb/>
            ſphærica inter figuras iſoperimetras, planas quidem, ſi de circulo loquamur,
              <lb/>
            ſolidas uero, ſi de ſphæra ſermo habeatur, capaciſſima exiſtit, ut infra oſtende-
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            mus. </s>
            <s xml:id="echoid-s4004" xml:space="preserve">Accedit ẽt, ꝙ circulus lineam rectam, & </s>
            <s xml:id="echoid-s4005" xml:space="preserve">ſphæra ſuperficiem planã in pun-
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            cto tantum unico contingit, quorum illud ex 2. </s>
            <s xml:id="echoid-s4006" xml:space="preserve">& </s>
            <s xml:id="echoid-s4007" xml:space="preserve">16. </s>
            <s xml:id="echoid-s4008" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s4009" xml:space="preserve">tertij lib. </s>
            <s xml:id="echoid-s4010" xml:space="preserve">Eucl.
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            </s>
            <s xml:id="echoid-s4011" xml:space="preserve">euidenter colligitur, hoc autem a Theodoſio propoſ. </s>
            <s xml:id="echoid-s4012" xml:space="preserve">3. </s>
            <s xml:id="echoid-s4013" xml:space="preserve">primi lib. </s>
            <s xml:id="echoid-s4014" xml:space="preserve">ſphæricorum
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            elementorum clariſſime demonſtratur. </s>
            <s xml:id="echoid-s4015" xml:space="preserve">Cũ igitur ſphæricum corpus inter om-
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            nia alia tam nobile exiſtat, ob tam multas, tamque præclaras dignitates, ac ex-
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            cellentias, quis iam dubitare, aut hæſitare poterit, cœlum tali eſſe figura prædi-
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            tũ@ Præſertim cũ cœlum, ut d@ctum eſt in præcedenti concluſione, continue vol
              <lb/>
            uatur motu circulati, cui quidem motui corpus ſphæricum, inter reliqua, maxi
              <lb/>
            me eſt accommodatum, ob continuam, & </s>
            <s xml:id="echoid-s4016" xml:space="preserve">uniformem partium ſucceſſionem,
              <lb/>
            ita ut nihil extrinſecus eſſe poſſit impedimento, propterea quòd circa centrum
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            eiſdem ſemper loci limitibus cir cumagitatur; </s>
            <s xml:id="echoid-s4017" xml:space="preserve">Vnde & </s>
            <s xml:id="echoid-s4018" xml:space="preserve">facillime mouetur.</s>
            <s xml:id="echoid-s4019" xml:space="preserve"/>
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            <s xml:id="echoid-s4020" xml:space="preserve">
              <emph style="sc">Vt avtem</emph>
            ſecunda hæc auctoris ratio à commoditate deſumpta per-
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              <note position="left" xlink:label="note-114-01" xlink:href="note-114-01a" xml:space="preserve">Iſoperime-
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              træ figuræ
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              quæ.</note>
            fectius intelligatur, pauca dicenda erunt de figuris iſoperimetris. </s>
            <s xml:id="echoid-s4021" xml:space="preserve">Figurę igitur
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            Iſoperimetrę appellantur illæ, quæ habent circunferentias, ſiue linearum am-
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            bitus æquales inter ſe. </s>
            <s xml:id="echoid-s4022" xml:space="preserve">Vt quadratum ſex palmos habens in ambitu dicitur iſo-
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            perimetrum triangulo, aut cuicunq. </s>
            <s xml:id="echoid-s4023" xml:space="preserve">alteri figuræ (ſiue rectilinea ea ſit, ſiue cur-
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            uilinea, ſiue ex his mixta,) habenti in circuitu ſex etiam palmos: </s>
            <s xml:id="echoid-s4024" xml:space="preserve">ita ut qua-
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            tuor lineæ rectæ quadrati ambitum conſtituentes in vnam, eandemq́ue rectam
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              <note position="left" xlink:label="note-114-02" xlink:href="note-114-02a" xml:space="preserve">Inter figu-
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              @as Iſoperi-
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              metras re-
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              cti lineas ca
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              pacior eſt,
                <lb/>
              quæ plures
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              angulos ha
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              bet; ac pro-
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              inde circu-
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              lus capaciſ-
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              ſimus.</note>
            lineam coaptatę adęquentur ad amuſſim tribus lineis rectis trianguli, aut la-
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            teribus omnibus cuiuſcunque alterius figuræ in rectum quoque, atque conti-
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            nuum poſitis. </s>
            <s xml:id="echoid-s4025" xml:space="preserve">Quod idem intelligendum erit de corporibus quibuſcunque iſ@
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            perimetris, ſumendo ſuperficies pro lineis.</s>
            <s xml:id="echoid-s4026" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s4027" xml:space="preserve">
              <emph style="sc">Inter</emph>
            omnes autem figuras rectilineas iſoperimetsas ea, quę plures
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            continet an gulos, maior, capaciorq́ue exiſtit. </s>
            <s xml:id="echoid-s4028" xml:space="preserve">Quod breuiter, & </s>
            <s xml:id="echoid-s4029" xml:space="preserve">rudi quadam
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            mineua confirmabimus in triangulo æquilatero, ſiue Iſoſcele, & </s>
            <s xml:id="echoid-s4030" xml:space="preserve">figura altera
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            parte longiore. </s>
            <s xml:id="echoid-s4031" xml:space="preserve">Accuratius enim hoc ipſum mox in tractatione figurarum Iſo-
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            perimetrarum demonſtrabimus. </s>
            <s xml:id="echoid-s4032" xml:space="preserve">Sit triangulum ęquilaterum, uel Iſoſceles
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            A B C, cuius latus B C, diuidatur in partes ęquales in puncto D, & </s>
            <s xml:id="echoid-s4033" xml:space="preserve">ducatur li-
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            nea recta D A, quę perpendicularis erit ad B C. </s>
            <s xml:id="echoid-s4034" xml:space="preserve">Nam duo latera A D, D B,
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            trianguli A D B, ęqualia ſunt duobus lateribus A D, D C, trianguli A D C,
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            & </s>
            <s xml:id="echoid-s4035" xml:space="preserve">baſis A B, baſi A C, ęqualis ponitur. </s>
            <s xml:id="echoid-s4036" xml:space="preserve">Igitur duo anguli A D B, A D C, æ-
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              <note position="left" xlink:label="note-114-03" xlink:href="note-114-03a" xml:space="preserve">8. primi.</note>
              <figure xlink:label="fig-114-01" xlink:href="fig-114-01a" number="15">
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            quales erunt, & </s>
            <s xml:id="echoid-s4037" xml:space="preserve">ob id (per definitionem)
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            uterque rectus. </s>
            <s xml:id="echoid-s4038" xml:space="preserve">Perficiatur parallelogram
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            mum rectangulum A D C E. </s>
            <s xml:id="echoid-s4039" xml:space="preserve">Quoniam
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              <note position="left" xlink:label="note-114-04" xlink:href="note-114-04a" xml:space="preserve">4. uel 38.
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              primi.</note>
            igitur triangulum A D B, triangulo
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            A D C, eſt æqualæ, eidemque triangu-
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            lo A D C, ęquale eſt triãgulum A C E,
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              <note position="left" xlink:label="note-114-05" xlink:href="note-114-05a" xml:space="preserve">34. primi.</note>
            erunt (per communem ſententiam) trian
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            gula A D B, A C E, inter ſe æqualia.
              <lb/>
            </s>
            <s xml:id="echoid-s4040" xml:space="preserve">Quare, addito cõmuni triangulo A D C,
              <lb/>
            erit parallelogrammum A D C E, ęqua-
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            le triangulo A B C. </s>
            <s xml:id="echoid-s4041" xml:space="preserve">Et quia duo latera
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            A E, D C, parallelogrammi, cum inter
              <lb/>
              <note position="left" xlink:label="note-114-06" xlink:href="note-114-06a" xml:space="preserve">34. primi.</note>
            ſe ęqualia ſint, ſimul ſumpta æqualia ſunt lateri B C, trianguli A B B; </s>
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