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

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          <head xml:id="echoid-head714" xml:space="preserve">THEOREMA I. PROPOS. I.</head>
          <p>
            <s xml:id="echoid-s12389" xml:space="preserve">FIguræ planæ quæcunq; </s>
            <s xml:id="echoid-s12390" xml:space="preserve">in eiſdem parallelis conſtitutę,
              <lb/>
            in quibus, ductis quibuſcunq; </s>
            <s xml:id="echoid-s12391" xml:space="preserve">eiſdem parallelis ęqui-
              <lb/>
            diſtantibus rectis lineis, conceptæ cuiuſcumq; </s>
            <s xml:id="echoid-s12392" xml:space="preserve">rectæ lineæ
              <lb/>
            portiones ſunt æquales, etiam inter ſe æquales erunt: </s>
            <s xml:id="echoid-s12393" xml:space="preserve">Et
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            figuræ ſolidæ quæcumq; </s>
            <s xml:id="echoid-s12394" xml:space="preserve">in eiſdem planis parallelis conſti-
              <lb/>
            tutæ, in quibus, ductis quibuſcunq; </s>
            <s xml:id="echoid-s12395" xml:space="preserve">planis eiſdem planis
              <lb/>
            parallelis æquidiſtantibus, conceptæ cuiuſcunq; </s>
            <s xml:id="echoid-s12396" xml:space="preserve">ſic ducti
              <lb/>
            plani in ipſis ſolidis figuræ planæ ſunt æquales, pariter in-
              <lb/>
            terſe æquales erunt. </s>
            <s xml:id="echoid-s12397" xml:space="preserve">Dicantur autem figuræ æqualiter
              <lb/>
            analogæ, tum planæ, tum ipſæ ſolidæ interſe comparatæ,
              <lb/>
            ac etiam iuxta regulas lineas, ſeu plana parallela, in qui-
              <lb/>
            bus eſse ſupponuntur, cum hoc fuerit opus explicare.</s>
            <s xml:id="echoid-s12398" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12399" xml:space="preserve">Sint quæcunq; </s>
            <s xml:id="echoid-s12400" xml:space="preserve">planę figuræ, BZ&</s>
            <s xml:id="echoid-s12401" xml:space="preserve">, CβΛ, in eiſdem parallelis,
              <lb/>
            AD, Y4, conſtitutæ, ductis autem ipſis, AD, Y4, quibuſcunque
              <lb/>
            parallelis, E6, LΣ, portione ex. </s>
            <s xml:id="echoid-s12402" xml:space="preserve">g. </s>
            <s xml:id="echoid-s12403" xml:space="preserve">ipſius, E6, in figuris conceptę,
              <lb/>
            nempè, FG, HI, inter ſe ſint æquales, necnon ipſius, LΣ, portio-
              <lb/>
            nes, MN, OP, ſimul ſumptæ (ſit enim figura, BZ&</s>
            <s xml:id="echoid-s12404" xml:space="preserve">, ex. </s>
            <s xml:id="echoid-s12405" xml:space="preserve">g. </s>
            <s xml:id="echoid-s12406" xml:space="preserve">intus ca-
              <lb/>
            ua ſecundum ambitum, {12/ }, N, {13/ }, O,) ipſi, SV, ſint pariter ęqua-
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            les, & </s>
            <s xml:id="echoid-s12407" xml:space="preserve">hoc contingat in quibuſcunq; </s>
            <s xml:id="echoid-s12408" xml:space="preserve">alijs ipſi, AD, æquidiſtanti-
              <lb/>
            bus. </s>
            <s xml:id="echoid-s12409" xml:space="preserve">Dico figuras, BZ&</s>
            <s xml:id="echoid-s12410" xml:space="preserve">, CβΛ, inter ſe æquales eſſe. </s>
            <s xml:id="echoid-s12411" xml:space="preserve">Aſſumpta
              <lb/>
            ergo alterutra figurarum, BZ&</s>
            <s xml:id="echoid-s12412" xml:space="preserve">, CβΛ, vt ipſa, BZ&</s>
            <s xml:id="echoid-s12413" xml:space="preserve">, cum paralle-
              <lb/>
            larum, AD, Y4, portionibus ipſi conterminantibus, nempè cum,
              <lb/>
            AB, Y&</s>
            <s xml:id="echoid-s12414" xml:space="preserve">, ſuperponatur reliquæ figuræ, CβΛ, ita tamen vt ipſæ, A
              <lb/>
            B, Y&</s>
            <s xml:id="echoid-s12415" xml:space="preserve">, cadant ſuper, BD, &</s>
            <s xml:id="echoid-s12416" xml:space="preserve">4, vel ergo tota, BZ& </s>
            <s xml:id="echoid-s12417" xml:space="preserve">congruit toti,
              <lb/>
            CβΛ, & </s>
            <s xml:id="echoid-s12418" xml:space="preserve">ita cum ſibi congruant æquales erunt, vel non, aliqua
              <lb/>
            tamen pars eſto, quod congruerit alicui parti, vt, CΙγβ587, pars
              <lb/>
            figuræ, BZ&</s>
            <s xml:id="echoid-s12419" xml:space="preserve">, ipſi, CΙγβ587, parti figuræ, CβΛ. </s>
            <s xml:id="echoid-s12420" xml:space="preserve">Manifeſtum eſt
              <lb/>
            autem ſuperpoſitione figurarum taliter effecta, vt portiones pa-
              <lb/>
            rallelarum, AD, Y4, ipſius figuris conterminantes ſint inuicem
              <lb/>
            ſuperpoſitæ, quod quæcumq; </s>
            <s xml:id="echoid-s12421" xml:space="preserve">rectæ lineæ in figuris conceptæ erãt
              <lb/>
            ſibi in Birectum, manent etiam ſibi in directum, vt ex. </s>
            <s xml:id="echoid-s12422" xml:space="preserve">g. </s>
            <s xml:id="echoid-s12423" xml:space="preserve">cum, M
              <lb/>
            N, OP, eſſent in directum ipſi, SV, dicta ſuperpoſitione facta, ma-
              <lb/>
            nent etiam ſibi in directum, nempè, QR, ST, in directum ipſi, SV,
              <lb/>
            eſt enim diſtantia ipſarum, MN, OP, ab, AD, æqualis diſtantiæ,
              <lb/>
            SV, ab eadem, AD, vnde quotieſcunque, AB, extendatur ſuper, B
              <lb/>
            D, vbicunque hoc fiat, ſemper, MN, OP, manebunt in </s>
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