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

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        <div xml:id="echoid-div1220" type="section" level="1" n="734">
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        <div xml:id="echoid-div1221" type="section" level="1" n="735">
          <head xml:id="echoid-head768" xml:space="preserve">ANNOTATIO.</head>
          <p>
            <s xml:id="echoid-s13627" xml:space="preserve">DDuertatur autem me in omnibus ſupra poſitis Corollarijs
              <lb/>
            ſupponere ſecantes lineas, parallelas ipſi, DF, in dictis figu-
              <lb/>
            ris, non niſi ſemel occurrere eidem rectæ lineæ, vt, BIE, ſemel, ac,
              <lb/>
            BNE, ſeorſim ſemel tantum; </s>
            <s xml:id="echoid-s13628" xml:space="preserve">ipſas verò parallelas ad ambitum fi-
              <lb/>
            guræ terminari, ac ſingulas integras eſſe, quódetiam ſuppono in
              <lb/>
            prop. </s>
            <s xml:id="echoid-s13629" xml:space="preserve">2 3. </s>
            <s xml:id="echoid-s13630" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s13631" xml:space="preserve">2. </s>
            <s xml:id="echoid-s13632" xml:space="preserve">integras autem eſſe ſubintelligo; </s>
            <s xml:id="echoid-s13633" xml:space="preserve">cum in plures re-
              <lb/>
            ctas lineas, aliquo interuallo ſeparatas, per ambitum figuræ, quæ
              <lb/>
            ab eadem regulæ parallela efficiuntur, diſiungi minimè comperien-
              <lb/>
            tur, in quo ſenſu ſciat lector (ne quis circa hoc hæſitaret) me ſem-
              <lb/>
            per in his libris hunc terminũ vſurpare, ſciat inſuper eaſdẽ regulas,
              <lb/>
            DF, FH, pro omnibus ſemperretineri. </s>
            <s xml:id="echoid-s13634" xml:space="preserve">Hæc autẽ ſegnius, quam for-
              <lb/>
            tè par erat, à me nunc explicata ſunt, ſed cum Propoſitiones Lib.
              <lb/>
            </s>
            <s xml:id="echoid-s13635" xml:space="preserve">Sec. </s>
            <s xml:id="echoid-s13636" xml:space="preserve">Elem. </s>
            <s xml:id="echoid-s13637" xml:space="preserve">hæc imitarentur, & </s>
            <s xml:id="echoid-s13638" xml:space="preserve">inſuper conſimilis doctrina, adhi-
              <lb/>
            bita tamen indiuiſibilium methodo, tradita iam fuiſſet Lib. </s>
            <s xml:id="echoid-s13639" xml:space="preserve">2. </s>
            <s xml:id="echoid-s13640" xml:space="preserve">Prop. </s>
            <s xml:id="echoid-s13641" xml:space="preserve">
              <lb/>
            23. </s>
            <s xml:id="echoid-s13642" xml:space="preserve">ideò ne rerum ſimilitudo faſtidium pareret, currenti, vtita di-
              <lb/>
            cam, calamo adnotata ſunt. </s>
            <s xml:id="echoid-s13643" xml:space="preserve">Ex ſupradictis autem facile eſt intel-
              <lb/>
            ligere nomen quadrati ſolidi alicuius figuræ planæ æquipollere
              <lb/>
            nomini omnium quadratorum eiuſdem figuræ, & </s>
            <s xml:id="echoid-s13644" xml:space="preserve">nomen rectan-
              <lb/>
            guli ſolidi ſub duabus figuris æquipollere nomini rectangulorum
              <lb/>
            ſub eiſdem figuris, quibus quidem in methodo indiuiſibilium vte-
              <lb/>
            bamur, ex quo patet, vt ſic nos indefinitum planorum numerum
              <lb/>
            euitare, cui ipſorum, quæ rectangula ſolida appellauimus, ſolidita-
              <lb/>
            tem ſatis concinne puto ſubſtituimus. </s>
            <s xml:id="echoid-s13645" xml:space="preserve">His autem paratis, ſequen-
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            tium propoſitionum demonſtrationes tum quæ ſuperſunt 1. </s>
            <s xml:id="echoid-s13646" xml:space="preserve">2. </s>
            <s xml:id="echoid-s13647" xml:space="preserve">tum
              <lb/>
            lib. </s>
            <s xml:id="echoid-s13648" xml:space="preserve">3. </s>
            <s xml:id="echoid-s13649" xml:space="preserve">4. </s>
            <s xml:id="echoid-s13650" xml:space="preserve">ac 5. </s>
            <s xml:id="echoid-s13651" xml:space="preserve">paucis mutatis compendioſiſſimè per hanc nouam
              <lb/>
            methodum, abſq; </s>
            <s xml:id="echoid-s13652" xml:space="preserve">ſolidarum figurarum circumſcriptione, & </s>
            <s xml:id="echoid-s13653" xml:space="preserve">inſcri-
              <lb/>
            ptione, vt alij conſueuerunt, necnon facile, oſtendemus, per hæc
              <lb/>
            verò Prop. </s>
            <s xml:id="echoid-s13654" xml:space="preserve">23. </s>
            <s xml:id="echoid-s13655" xml:space="preserve">Lib. </s>
            <s xml:id="echoid-s13656" xml:space="preserve">2. </s>
            <s xml:id="echoid-s13657" xml:space="preserve">iam ſatisfactum eſſe manifeſtò apparet.</s>
            <s xml:id="echoid-s13658" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div1222" type="section" level="1" n="736">
          <head xml:id="echoid-head769" xml:space="preserve">THEOREMA XVI. PROPOS. XVI.</head>
          <p>
            <s xml:id="echoid-s13659" xml:space="preserve">COnſpecta denuò figura Prop. </s>
            <s xml:id="echoid-s13660" xml:space="preserve">30. </s>
            <s xml:id="echoid-s13661" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s13662" xml:space="preserve">2. </s>
            <s xml:id="echoid-s13663" xml:space="preserve">& </s>
            <s xml:id="echoid-s13664" xml:space="preserve">aſſumpta
              <lb/>
            regula, FD, & </s>
            <s xml:id="echoid-s13665" xml:space="preserve">alia, quæ à puncto, F, quomodocunq;
              <lb/>
            </s>
            <s xml:id="echoid-s13666" xml:space="preserve">intelligatur eleuata ſuper planum, AF, perpendiculariter
              <lb/>
            ipſi, FD. </s>
            <s xml:id="echoid-s13667" xml:space="preserve">Rectangulum ſolidum ſub, AE, EC, ad rectan-
              <lb/>
            gulum ſolidum ſub, ADEC, trapezio, & </s>
            <s xml:id="echoid-s13668" xml:space="preserve">triangulo, CEF, re-
              <lb/>
            gulis iam dictis, contentum, erit vt, DE, ad compoſitam ex @. </s>
            <s xml:id="echoid-s13669" xml:space="preserve">
              <lb/>
            DE, & </s>
            <s xml:id="echoid-s13670" xml:space="preserve">{1/2}. </s>
            <s xml:id="echoid-s13671" xml:space="preserve">EF.</s>
            <s xml:id="echoid-s13672" xml:space="preserve"/>
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