Cavalieri, Buonaventura, Geometria indivisibilibvs continvorvm : noua quadam ratione promota

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        <div xml:id="echoid-div1023" type="section" level="1" n="614">
          <head xml:id="echoid-head644" xml:space="preserve">III.</head>
          <p>
            <s xml:id="echoid-s11164" xml:space="preserve">SPatium Helicum voco, quod copræhenditur ſub ſpira-
              <lb/>
            li, vel eius quacumque portione, & </s>
            <s xml:id="echoid-s11165" xml:space="preserve">rectis, quæ à ter-
              <lb/>
            minis eiuſdem ſpiralis, ſeu illius portionis, ad initium re-
              <lb/>
            uolutionis ducuntur.</s>
            <s xml:id="echoid-s11166" xml:space="preserve"/>
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        <div xml:id="echoid-div1024" type="section" level="1" n="615">
          <head xml:id="echoid-head645" xml:space="preserve">IV.</head>
          <p>
            <s xml:id="echoid-s11167" xml:space="preserve">SPiralem verò intelligo iuxta diffinitionem Archimedis
              <lb/>
            lib. </s>
            <s xml:id="echoid-s11168" xml:space="preserve">de Spiralibus, nempè, ſi cuiuſcumque circuli ra-
              <lb/>
            dius æquali celeritate moueatur circa ipſius centrum (cu-
              <lb/>
            ius aliud extremum punctum periphæriam deſcribet) ini-
              <lb/>
            tio autem circulationis diſcedat à centro punctum æque-
              <lb/>
            uelociter motum ſuper radio, taliter vt eodem tempore
              <lb/>
            prædictum punctum percurrat circumferentiam, & </s>
            <s xml:id="echoid-s11169" xml:space="preserve">hoc ip-
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            ſum radium, quod ex compoſitione duorum motuum de-
              <lb/>
            ſcripta à puncto, quod radium percurrit, ipſa linea, ſit ea,
              <lb/>
            quam voco ſpiralem, cuius initium dicitur ipſum centrum,
              <lb/>
            terminus verò aliud extremum punctum ipſius radij; </s>
            <s xml:id="echoid-s11170" xml:space="preserve">& </s>
            <s xml:id="echoid-s11171" xml:space="preserve">ini-
              <lb/>
            tium circulationis, ſiue voluta ipſe radius: </s>
            <s xml:id="echoid-s11172" xml:space="preserve">Appellatur au-
              <lb/>
            tem hæc, ſpiralis in prima reuolutione genita, ſicuti aliæ
              <lb/>
            etiam ſunt in alijs reuolutionibus deſcriptibiles, produ-
              <lb/>
            cto radio, & </s>
            <s xml:id="echoid-s11173" xml:space="preserve">continuato motu, vt in ſecunda, in tertia, in
              <lb/>
            quarta reuolutione, & </s>
            <s xml:id="echoid-s11174" xml:space="preserve">ſic deinceps, vnde & </s>
            <s xml:id="echoid-s11175" xml:space="preserve">deſcripti cir-
              <lb/>
            culi dicuntur primi, ſecundi, tertij, &</s>
            <s xml:id="echoid-s11176" xml:space="preserve">c. </s>
            <s xml:id="echoid-s11177" xml:space="preserve">quæ Archimedem
              <lb/>
            lib. </s>
            <s xml:id="echoid-s11178" xml:space="preserve">de Spiralibus recolenti melius innoteſcent, eiuſdem
              <lb/>
            enim terminos in hoc Libro paſſim vſurpabimus</s>
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        <div xml:id="echoid-div1025" type="section" level="1" n="616">
          <head xml:id="echoid-head646" xml:space="preserve">SCHOLIVM.</head>
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            <s xml:id="echoid-s11179" xml:space="preserve">_A_Spice Schema Prop. </s>
            <s xml:id="echoid-s11180" xml:space="preserve">9. </s>
            <s xml:id="echoid-s11181" xml:space="preserve">huius, in quo eſt circuliradius, AE, qui
              <lb/>
            æqueuelociter motus circa, A, deſcribit circulum, SME, ipſum
              <lb/>
            verò, E, circumferentiam, MSE, initio autem reuolutionis diſcedat
              <lb/>
            ab, A, punctum motum æqueuelociter ſuper, AE, quam percurrat eo
              <lb/>
            tempore, quo punctum, E, pertranſit circumferentiam, MSE, deſi-
              <lb/>
            gnans curuam, AIE, hæc igitur dic itur ſpiralis in prima reuolutione
              <lb/>
            orta, cuius initium, A, terminus, E, &</s>
            <s xml:id="echoid-s11182" xml:space="preserve">, AE, vocatur circulationis
              <lb/>
            initium: </s>
            <s xml:id="echoid-s11183" xml:space="preserve">Exempla autem ſpir alm̃ in alijs reuolutionibus geni@ arum
              <lb/>
            babes in Schemate Cor. </s>
            <s xml:id="echoid-s11184" xml:space="preserve">Prop. </s>
            <s xml:id="echoid-s11185" xml:space="preserve">20. </s>
            <s xml:id="echoid-s11186" xml:space="preserve">huius, etenim, LSO, in ſecunda,
              <lb/>
            OTP, in tertia, PVG, autem in quarta reuolutione genitæ dicuntur.</s>
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