Clavius, Christoph, In Sphaeram Ioannis de Sacro Bosco commentarius

Table of figures

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        <div xml:id="echoid-div236" type="section" level="1" n="81">
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            <s xml:id="echoid-s4380" xml:space="preserve">
              <pb o="89" file="125" n="126" rhead="Ioan. de Sacro Boſco."/>
            au em augulus D A C, dimidiũ anguli E D C; </s>
            <s xml:id="echoid-s4381" xml:space="preserve">propterea quòd anguli D A C,
              <lb/>
              <note position="right" xlink:label="note-125-01" xlink:href="note-125-01a" xml:space="preserve">5. primi.</note>
            D C A, æquales ſunt, & </s>
            <s xml:id="echoid-s4382" xml:space="preserve">his ſimul ſumptis æqualis quoque externus angulus
              <lb/>
              <note position="right" xlink:label="note-125-02" xlink:href="note-125-02a" xml:space="preserve">32. primi.</note>
            E D C. </s>
            <s xml:id="echoid-s4383" xml:space="preserve">Maior igitur erit angulus E D B, angulo D A C. </s>
            <s xml:id="echoid-s4384" xml:space="preserve">Fiat angulus E D F,
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            æqualis angulo interno D A C; </s>
            <s xml:id="echoid-s4385" xml:space="preserve">cadetq́ue D F, recta ſupra rectam D B, æqui-
              <lb/>
            diſ
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            tabit q́ue rectæ A C. </s>
            <s xml:id="echoid-s4386" xml:space="preserve">Producatur D F, donec cum A B protracta conueniat
              <lb/>
              <note position="right" xlink:label="note-125-03" xlink:href="note-125-03a" xml:space="preserve">28. primi.</note>
            in F, du caturq́; </s>
            <s xml:id="echoid-s4387" xml:space="preserve">recta F C. </s>
            <s xml:id="echoid-s4388" xml:space="preserve">Quoniam igitur triangula A D C, A F C, æqualia
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            ſunt@tr i angulum autem A F C, maius eſt triangulo A B C; </s>
            <s xml:id="echoid-s4389" xml:space="preserve">maius quoque erit
              <lb/>
              <note position="right" xlink:label="note-125-04" xlink:href="note-125-04a" xml:space="preserve">37. primi.</note>
            trian gulum A D C, triangulo A B C. </s>
            <s xml:id="echoid-s4390" xml:space="preserve">Quam ob rem duorum triangulorũ Iſo-
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            perim etorum eandem habentium baſim, &</s>
            <s xml:id="echoid-s4391" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4392" xml:space="preserve">quod demonſtrandum erat.</s>
            <s xml:id="echoid-s4393" xml:space="preserve"/>
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        <div xml:id="echoid-div239" type="section" level="1" n="82">
          <head xml:id="echoid-head86" style="it" xml:space="preserve">THEOR. 8. PROPOS. 9.</head>
          <p style="it">
            <s xml:id="echoid-s4394" xml:space="preserve">IN ſimilibus triangulis rectangulis quadratum à lateribus, quæ an-
              <lb/>
              <note position="right" xlink:label="note-125-05" xlink:href="note-125-05a" xml:space="preserve">Proprieta
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              duorũ trian
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              gulorum re
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              ct angulorũ
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              ſimilium.</note>
            gulis rectis ſubtenduntur, tanquam ab una linea, deſcriptum æquale eſt
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            quadratis duobus ſimul, quæ à reliquis homologis lateribus, tanquam ex
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            duabus lineis, ita ut quælibet duo latera homologa conficiant unam lineam
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            rectam, deſcribitur.</s>
            <s xml:id="echoid-s4395" xml:space="preserve"/>
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            <s xml:id="echoid-s4396" xml:space="preserve">
              <emph style="sc">Sint</emph>
            triangula rectangula ſimilia A B C, D E F, ita ut anguli B, & </s>
            <s xml:id="echoid-s4397" xml:space="preserve">E,
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            ſint recti, anguli uero C, & </s>
            <s xml:id="echoid-s4398" xml:space="preserve">F, inter ſe æquales: </s>
            <s xml:id="echoid-s4399" xml:space="preserve">itemq́ue anguli A, & </s>
            <s xml:id="echoid-s4400" xml:space="preserve">D, inter ſe
              <lb/>
            æqua les: </s>
            <s xml:id="echoid-s4401" xml:space="preserve">homologaq́ue latera A B, D E; </s>
            <s xml:id="echoid-s4402" xml:space="preserve">Item
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            B C, E F, & </s>
            <s xml:id="echoid-s4403" xml:space="preserve">A C, D F. </s>
            <s xml:id="echoid-s4404" xml:space="preserve">Dico quadratum ex A C,
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              <figure xlink:label="fig-125-01" xlink:href="fig-125-01a" number="27">
                <image file="125-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/125-01"/>
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            D F, tan quam ex linea una, deſcriptum æqua-
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            le eſſe duobus quadratis, quorũ unum ex A B,
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            D E, tanquam ex una linea, alterum uero ex
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            BC, E F, tanquam ex vna quoque linea, deſcri-
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            bitur. </s>
            <s xml:id="echoid-s4405" xml:space="preserve">Producta namque D E, ad partes E, ſu-
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            matur E G, æqualis rectæ A B, & </s>
            <s xml:id="echoid-s4406" xml:space="preserve">ducatur G H,
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            recta æquidiſtans rectę E F, donec cum D F,
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            producta conueniat in puncto H; </s>
            <s xml:id="echoid-s4407" xml:space="preserve">Deinde per
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            F, ducatur recta F I, æquidiſtans rectæ E G.
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            </s>
            <s xml:id="echoid-s4408" xml:space="preserve">Erit igitur triangulum F I H, æquiangulum
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            triangulo D E F, hoc eſt, triangulo ABC: </s>
            <s xml:id="echoid-s4409" xml:space="preserve">Nam
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            angulus F I H, æqualis eſt angulo G, & </s>
            <s xml:id="echoid-s4410" xml:space="preserve">hic æ-
              <lb/>
              <note position="right" xlink:label="note-125-06" xlink:href="note-125-06a" xml:space="preserve">29. primi.</note>
            qualis angulo D E F, hoc eſt, angulo B: </s>
            <s xml:id="echoid-s4411" xml:space="preserve">an-
              <lb/>
              <note position="right" xlink:label="note-125-07" xlink:href="note-125-07a" xml:space="preserve">29. primi.</note>
            gulus uero H, æqualis eſt angulo D E F, hoc
              <lb/>
              <note position="right" xlink:label="note-125-08" xlink:href="note-125-08a" xml:space="preserve">32. primi.</note>
            eſt, angulo C; </s>
            <s xml:id="echoid-s4412" xml:space="preserve">ac proinde & </s>
            <s xml:id="echoid-s4413" xml:space="preserve">angulus I F H, an
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            gulo A; </s>
            <s xml:id="echoid-s4414" xml:space="preserve">Sunt autem & </s>
            <s xml:id="echoid-s4415" xml:space="preserve">latera A B, F I, æqualia;
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            </s>
            <s xml:id="echoid-s4416" xml:space="preserve">Nã recta F I, eſt æqualis rectæ E G, hæc autẽ
              <lb/>
              <note position="right" xlink:label="note-125-09" xlink:href="note-125-09a" xml:space="preserve">34. primi.</note>
            rectæ A B, ſumpta fuit æqualis. </s>
            <s xml:id="echoid-s4417" xml:space="preserve">Igitur & </s>
            <s xml:id="echoid-s4418" xml:space="preserve">altera
              <lb/>
            B C, I H, item A C, F H, æqualia inter ſe e-
              <lb/>
              <note position="right" xlink:label="note-125-10" xlink:href="note-125-10a" xml:space="preserve">26. primi.</note>
            runt. </s>
            <s xml:id="echoid-s4419" xml:space="preserve">Quare recta D H, compoſita erit ex A C,
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            D F; </s>
            <s xml:id="echoid-s4420" xml:space="preserve">Recta uero D G, ex A B, D E; </s>
            <s xml:id="echoid-s4421" xml:space="preserve">Recta deniq; </s>
            <s xml:id="echoid-s4422" xml:space="preserve">G H, ex B C, E F; </s>
            <s xml:id="echoid-s4423" xml:space="preserve">quòd G I, re-
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            cta æqualis ſit rectæ EF. </s>
            <s xml:id="echoid-s4424" xml:space="preserve">Et quoniam quadratũ rectæ D H, æquale eſt quadratis
              <lb/>
              <note position="right" xlink:label="note-125-11" xlink:href="note-125-11a" xml:space="preserve">34. primi.</note>
            rectarum D G, G H, ſimul, conſtat verum eſſe, quod proponitur. </s>
            <s xml:id="echoid-s4425" xml:space="preserve">In ſimilibus
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            igitur triangulis rectangulis quadratum à
              <unsure/>
            lateribus, quæ angulis rectis ſubten-
              <lb/>
              <note position="right" xlink:label="note-125-12" xlink:href="note-125-12a" xml:space="preserve">47. primi.</note>
            duntur, &</s>
            <s xml:id="echoid-s4426" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4427" xml:space="preserve">quod erat demonſtrandum.</s>
            <s xml:id="echoid-s4428" xml:space="preserve"/>
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