Clavius, Christoph, In Sphaeram Ioannis de Sacro Bosco commentarius

Page concordance

< >
Scan Original
111 74
112 75
113 76
114 77
115 78
116 79
117 80
118 81
119 82
120 83
121 84
122 85
123 86
124 87
125 88
126 89
127 90
128 91
129 92
130 93
131 94
132 95
133 96
134 97
135 98
136 99
137 100
138 101
139 102
140 103
< >
page |< < (78) of 525 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div205" type="section" level="1" n="67">
          <p>
            <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-
              <lb/>
            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-
              <lb/>
            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.
              <lb/>
            </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
              <lb/>
            elementorum clariſſime demonſtratur. </s>
            <s xml:id="echoid-s4015" xml:space="preserve">Cũ igitur ſphæricum corpus inter om-
              <lb/>
            nia alia tam nobile exiſtat, ob tam multas, tamque præclaras dignitates, ac ex-
              <lb/>
            cellentias, quis iam dubitare, aut hæſitare poterit, cœlum tali eſſe figura prædi-
              <lb/>
            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
              <lb/>
            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"/>
          </p>
          <p>
            <s xml:id="echoid-s4020" xml:space="preserve">
              <emph style="sc">Vt avtem</emph>
            ſecunda hæc auctoris ratio à commoditate deſumpta per-
              <lb/>
              <note position="left" xlink:label="note-114-01" xlink:href="note-114-01a" xml:space="preserve">Iſoperime-
                <lb/>
              træ figuræ
                <lb/>
              quæ.</note>
            fectius intelligatur, pauca dicenda erunt de figuris iſoperimetris. </s>
            <s xml:id="echoid-s4021" xml:space="preserve">Figurę igitur
              <lb/>
            Iſoperimetrę appellantur illæ, quæ habent circunferentias, ſiue linearum am-
              <lb/>
            bitus æquales inter ſe. </s>
            <s xml:id="echoid-s4022" xml:space="preserve">Vt quadratum ſex palmos habens in ambitu dicitur iſo-
              <lb/>
            perimetrum triangulo, aut cuicunq. </s>
            <s xml:id="echoid-s4023" xml:space="preserve">alteri figuræ (ſiue rectilinea ea ſit, ſiue cur-
              <lb/>
            uilinea, ſiue ex his mixta,) habenti in circuitu ſex etiam palmos: </s>
            <s xml:id="echoid-s4024" xml:space="preserve">ita ut qua-
              <lb/>
            tuor lineæ rectæ quadrati ambitum conſtituentes in vnam, eandemq́ue rectam
              <lb/>
              <note position="left" xlink:label="note-114-02" xlink:href="note-114-02a" xml:space="preserve">Inter figu-
                <lb/>
              @as Iſoperi-
                <lb/>
              metras re-
                <lb/>
              cti lineas ca
                <lb/>
              pacior eſt,
                <lb/>
              quæ plures
                <lb/>
              angulos ha
                <lb/>
              bet; ac pro-
                <lb/>
              inde circu-
                <lb/>
              lus capaciſ-
                <lb/>
              ſimus.</note>
            lineam coaptatę adęquentur ad amuſſim tribus lineis rectis trianguli, aut la-
              <lb/>
            teribus omnibus cuiuſcunque alterius figuræ in rectum quoque, atque conti-
              <lb/>
            nuum poſitis. </s>
            <s xml:id="echoid-s4025" xml:space="preserve">Quod idem intelligendum erit de corporibus quibuſcunque iſ@
              <lb/>
            perimetris, ſumendo ſuperficies pro lineis.</s>
            <s xml:id="echoid-s4026" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4027" xml:space="preserve">
              <emph style="sc">Inter</emph>
            omnes autem figuras rectilineas iſoperimetsas ea, quę plures
              <lb/>
            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
              <lb/>
            mineua confirmabimus in triangulo æquilatero, ſiue Iſoſcele, & </s>
            <s xml:id="echoid-s4030" xml:space="preserve">figura altera
              <lb/>
            parte longiore. </s>
            <s xml:id="echoid-s4031" xml:space="preserve">Accuratius enim hoc ipſum mox in tractatione figurarum Iſo-
              <lb/>
            perimetrarum demonſtrabimus. </s>
            <s xml:id="echoid-s4032" xml:space="preserve">Sit triangulum ęquilaterum, uel Iſoſceles
              <lb/>
            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-
              <lb/>
            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,
              <lb/>
            trianguli A D B, ęqualia ſunt duobus lateribus A D, D C, trianguli A D C,
              <lb/>
            & </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-
              <lb/>
              <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">
                <image file="114-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/114-01"/>
              </figure>
            quales erunt, & </s>
            <s xml:id="echoid-s4037" xml:space="preserve">ob id (per definitionem)
              <lb/>
            uterque rectus. </s>
            <s xml:id="echoid-s4038" xml:space="preserve">Perficiatur parallelogram
              <lb/>
            mum rectangulum A D C E. </s>
            <s xml:id="echoid-s4039" xml:space="preserve">Quoniam
              <lb/>
              <note position="left" xlink:label="note-114-04" xlink:href="note-114-04a" xml:space="preserve">4. uel 38.
                <lb/>
              primi.</note>
            igitur triangulum A D B, triangulo
              <lb/>
            A D C, eſt æqualæ, eidemque triangu-
              <lb/>
            lo A D C, ęquale eſt triãgulum A C E,
              <lb/>
              <note position="left" xlink:label="note-114-05" xlink:href="note-114-05a" xml:space="preserve">34. primi.</note>
            erunt (per communem ſententiam) trian
              <lb/>
            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-
              <lb/>
            le triangulo A B C. </s>
            <s xml:id="echoid-s4041" xml:space="preserve">Et quia duo latera
              <lb/>
            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>
            <s xml:id="echoid-s4042" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum