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

Table of Notes

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            inrecta, Φ Λ, & </s>
            <s xml:id="echoid-s3210" xml:space="preserve">incidentem eiuſdem figuræ, nempè ipſam, 38, in
              <lb/>
            puncto, 4, igitur figuræ, BC, Π Ω, erunt duæ figurarum homolo-
              <lb/>
              <note position="right" xlink:label="note-0155-01" xlink:href="note-0155-01a" xml:space="preserve">Defin. 11.
                <lb/>
              huius.</note>
            garum ſolidorum, AP, V &</s>
            <s xml:id="echoid-s3211" xml:space="preserve">, &</s>
            <s xml:id="echoid-s3212" xml:space="preserve">, OX, Φ Λ, earum incidentes, &</s>
            <s xml:id="echoid-s3213" xml:space="preserve">,
              <lb/>
            LG, 38, erunt ſimiliter diuiſæ in punctis, E, 4, nam etiam altitu-
              <lb/>
              <note position="right" xlink:label="note-0155-02" xlink:href="note-0155-02a" xml:space="preserve">17. Vndec.
                <lb/>
              Elem.</note>
            dines propoſitorum ſimilium ſolidorum ſunt ſimiliter diuiſæ (ad ean-
              <lb/>
            dem partem ſub intellige) ſi igitur à punctis, O, Φ, duxerimus tan-
              <lb/>
            gentes figuras, BC, Π Ω, erunt iſtæ regulis homologarum earun-
              <lb/>
            dem figurarum parallelæ, vel pro regulis aliarum etiam aſſumi pote-
              <lb/>
            runt, & </s>
            <s xml:id="echoid-s3214" xml:space="preserve">quę à punctis, X, Λ, ducentur prędictis parallelę occurrent
              <lb/>
            eiſdem figuris, & </s>
            <s xml:id="echoid-s3215" xml:space="preserve">illas ex oppoſito prędictarum contingent, ita vt ha-
              <lb/>
            beamus (ſi & </s>
            <s xml:id="echoid-s3216" xml:space="preserve">iſtæ ductæ intelligantur, quæ ſint, XC, Λ Ω,) oppc-
              <lb/>
            fitas tangentes figuræ, BC, quæ erunt, BO, CX, & </s>
            <s xml:id="echoid-s3217" xml:space="preserve">figuræ, Π Ω,
              <lb/>
            quæ erunt, Π Φ, Ω Λ, necnon pro regulis homologarum earundem
              <lb/>
            haberi poterunt; </s>
            <s xml:id="echoid-s3218" xml:space="preserve">vel igitur figuræ, BC, Π Ω, adiacent ſuis inciden-
              <lb/>
            tibus, OX, Φ Λ, totę ad eandem partem, & </s>
            <s xml:id="echoid-s3219" xml:space="preserve">interius integrę exiſten-
              <lb/>
            tes, vel non, ſi ſic factum erit, quod volumus, ſi non transferantur
              <lb/>
            omnes lineæ figurarum, BC, Π Ω, regulis eiſdem tangentibus, in
              <lb/>
              <note position="right" xlink:label="note-0155-03" xlink:href="note-0155-03a" xml:space="preserve">Vide A.
                <lb/>
              15. huius
                <lb/>
              propèfin.</note>
            figuras ipſis, OX, Φ Λ, adiacentes, pro vt in Prop. </s>
            <s xml:id="echoid-s3220" xml:space="preserve">15. </s>
            <s xml:id="echoid-s3221" xml:space="preserve">effectum eſt,
              <lb/>
            hinc autem reſultantes figurę ſint, OZX, Φ Γ Λ, quę per talem con-
              <lb/>
            ſtructionem ad eandem partem incidentium, & </s>
            <s xml:id="echoid-s3222" xml:space="preserve">interius integrę nc-
              <lb/>
            bis proueniunt. </s>
            <s xml:id="echoid-s3223" xml:space="preserve">Similiter ſi intelligamus ducta alia duo plana prędi-
              <lb/>
            ctis ęquidiſtantia, quę ſolida propoſita ita ſecent, vt fiant in ipſis non
              <lb/>
            vnica in ſingulis figura, ſed plures, ex. </s>
            <s xml:id="echoid-s3224" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s3225" xml:space="preserve">in ſolido, AP, figurę, R,
              <lb/>
            I, & </s>
            <s xml:id="echoid-s3226" xml:space="preserve">in, V &</s>
            <s xml:id="echoid-s3227" xml:space="preserve">, figuræ, ℟, N, eadem autem ſecent figuras inciden-
              <lb/>
            tes in rectis, SY, Β Δ, & </s>
            <s xml:id="echoid-s3228" xml:space="preserve">rectas, LG, 38, in punctis, K, {10/ }, dum-
              <lb/>
            modo hæc plana pariter ſecent altitudines dictas propoſitorum ſoli-
              <lb/>
            dorum ſimiliter ad eandem partem, erunt figurę, R, I, binę ſimiles, & </s>
            <s xml:id="echoid-s3229" xml:space="preserve">
              <lb/>
              <note position="right" xlink:label="note-0155-04" xlink:href="note-0155-04a" xml:space="preserve">E. Def. 10.
                <lb/>
              lib. 1.</note>
            ſimiliter poſitę, ac figurę, ℟, N, .</s>
            <s xml:id="echoid-s3230" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s3231" xml:space="preserve">I, ſimilis ipſi, N, &</s>
            <s xml:id="echoid-s3232" xml:space="preserve">, R, ipſi, ℟, & </s>
            <s xml:id="echoid-s3233" xml:space="preserve">
              <lb/>
            linearum homologarum earundem regulæ ipſis, CX, Ω Λ, æquidi-
              <lb/>
            ſtabunt, ipſę autem rectę, S, Y; </s>
            <s xml:id="echoid-s3234" xml:space="preserve">β, Δ, erunt earundem incidentes,
              <lb/>
            vt, S, β, ipſarum, R, ℟, &</s>
            <s xml:id="echoid-s3235" xml:space="preserve">, Y, Δ, ipſarum, I, N, ſi igitur figurę,
              <lb/>
            R, I, ℟, N, non adiacent ſuis incidentibus, transferantur ſingula-
              <lb/>
            rum omnes lineę, regula ſemper, pro figuris, RI, ipſa, CX, & </s>
            <s xml:id="echoid-s3236" xml:space="preserve">pro
              <lb/>
              <note position="right" xlink:label="note-0155-05" xlink:href="note-0155-05a" xml:space="preserve">Videad
                <lb/>
              fig. A.</note>
            figuris, ℟, N, ipſa, Ω Λ, in figuras adiacentes lineis homologis figu-
              <lb/>
              <note position="right" xlink:label="note-0155-06" xlink:href="note-0155-06a" xml:space="preserve">Piop. 15.
                <lb/>
              huius.</note>
            rarum, H {00/ }, Σ 2, vt ſint nobis inuentæ figuræ, S, Y, β Δ, quæ
              <lb/>
            adiaceant homologis lineis figurarum incidentium, H, {00/ }, Σ 2: </s>
            <s xml:id="echoid-s3237" xml:space="preserve">Si
              <lb/>
            igitur eandem methodum ſeruemus in cæteris figuris, quæ ex lectio-
              <lb/>
            ne planorum tangentibus æquidiſtantium in dictis ſolidis producun-
              <lb/>
            tur, transferentes nempè omnes earum lineas homologas, regulis
              <lb/>
            ſemper ipſis, CX, Ω Λ, in figuras adiacentes lineis homologis figu-
              <lb/>
            rarum incidentium, H, {00/ }, Σ 2, quę reperientur totę ad eandem par-
              <lb/>
            tem, & </s>
            <s xml:id="echoid-s3238" xml:space="preserve">interius integrę, tandem nobis erunt comparata duo </s>
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