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

Table of handwritten notes

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            <s xml:id="echoid-s11388" xml:space="preserve">
              <pb o="441" file="0461" n="461" rhead="LIBER VI."/>
            eumſcriptæ ſuper inſcriptam ſunttrapezia, HL, LK, KI, cum tri-
              <lb/>
            angulo, IFQ, quę, quia ęquantur trapezijs, ΓV, VN, NQ, & </s>
            <s xml:id="echoid-s11389" xml:space="preserve">
              <lb/>
            triangulo, IFQ, (nam dicta trapezia ſunt reſidua triangulorum in
              <lb/>
            ęqualibus baſibus, & </s>
            <s xml:id="echoid-s11390" xml:space="preserve">altitudinibus conſtitutorum) ideſt triangulo,
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            FΓG, ſubinde ſunt minora ſpatio, Ω, & </s>
            <s xml:id="echoid-s11391" xml:space="preserve">ideo circumſcriptã ſuperat
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            inſcriptaminori ſpatio, quam ſit Ω, ergo trilineum, FLHG, excedit
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            inſcriptã multò minori ſpatio, excedit autem ſpatium reſiduum cir-
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            culi, ECDB, iam dictum ſpatio Ω, ergo ſigura inſcriptaerit maior
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            dicto ſpatio reſiduo; </s>
            <s xml:id="echoid-s11392" xml:space="preserve">quod ſerua.</s>
            <s xml:id="echoid-s11393" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11394" xml:space="preserve">Diuidatut nunc, AB, ſim liter, ac diuiditut, FG, in punctis, 3,
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            4, 7, centro autem communi, A, ad diſtantiam punctorum, 3, 4,
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            7, deſcribantur circumferentiæ, 35Δ, 4ΣRβ, 789M, ſecantes ſpi-
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            ralem in punctis, S, R, M, per quæ tranſeant eductæ à centro, A,
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            productæque vſque ad circumferentiam, ECDB, rectæ, AD, AC,
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            AE, vt igitur in præhabita demonſtratione oſtendemus circumfer.
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            </s>
            <s xml:id="echoid-s11395" xml:space="preserve">53, & </s>
            <s xml:id="echoid-s11396" xml:space="preserve">rectam, IQ, inter ſe æquales eſſe, & </s>
            <s xml:id="echoid-s11397" xml:space="preserve">ſimiliter circumferen-
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            tiam, RΣ4, æquari rectæ, KT, &</s>
            <s xml:id="echoid-s11398" xml:space="preserve">, M987, ipſi, LV, & </s>
            <s xml:id="echoid-s11399" xml:space="preserve">quia, 53,
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              <note position="right" xlink:label="note-0461-01" xlink:href="note-0461-01a" xml:space="preserve">Corol. 1.
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              3.huius.</note>
            circumferentia ad circumfer. </s>
            <s xml:id="echoid-s11400" xml:space="preserve">Σ4, eſt, vt, 3 A, ad, A4, ideſt vt, QF,
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            ad, FT, ideſt vt, IQ, ad, NT, eſt autem ęqualis, 53, ipſi, IQ, ergo,
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            Σ4, erit ęqualis ipſi, NT, & </s>
            <s xml:id="echoid-s11401" xml:space="preserve">eſt, 34, ęqualis ipſi, QT, ergo faſcia, 53
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            4Σ, erit ęqualis trapezio, IQTN; </s>
            <s xml:id="echoid-s11402" xml:space="preserve">eodem modo oſtendemus faſciã,
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            R9874, æquari trapezio, KV, & </s>
            <s xml:id="echoid-s11403" xml:space="preserve">faſciam, MECDB7, ęquari tra-
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            pexio, PLVG, & </s>
            <s xml:id="echoid-s11404" xml:space="preserve">ideo figura compoſita ex dictis faſcijs ęqualis
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            erit figurę compoſitę ex his trapezijs inſcriptę trilineo, FLHG, eſt
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            autem hæc figura inſcripta maior ſpatio reſiduo circuli, ECDB, ab
              <lb/>
            eo dempto ſpatio ſub ſpirali, & </s>
            <s xml:id="echoid-s11405" xml:space="preserve">voluta, AB, ergo figura compo-
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            ſita ex dictis ſpatijs erit maior ſpatio dicto reſiduo, cui tamen eſt
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            inſcripta, quod eſt abſurdum, non ergo trilineum, FLHG, maius
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            eſt dicto reſiduo.</s>
            <s xml:id="echoid-s11406" xml:space="preserve"/>
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            <s xml:id="echoid-s11407" xml:space="preserve">Dico neq; </s>
            <s xml:id="echoid-s11408" xml:space="preserve">eſſe minus. </s>
            <s xml:id="echoid-s11409" xml:space="preserve">Sit, ſi fieri poteſt, minus ſpatio eodem,
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            Ω, ſit autem vt ſupra trilineo, FLHG, circumſcripta figura, ex
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            trapezijs, KQ, LT, HV, & </s>
            <s xml:id="echoid-s11410" xml:space="preserve">triangulo, IFk, compoſita, & </s>
            <s xml:id="echoid-s11411" xml:space="preserve">alia ei-
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            dem in cripta ex trapezijs, PO, OT, NQ, ita vt earum differentia
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            ſit minor ſpatio, Ω, igitur circumſcripta excedet trilineum, FLH
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            G, multò minori ſpatio, ergo circumſcripta figura minor erit ſpa-
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            tio reſiduo jam dicto circuli, ECDB, quod excedit trilineum, FLH
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            G, ſpatio, Ω, quod tamem eſt abſurdum, nam ſectorem, AS3, pa-
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            ret ęqualem eſſe triangulo, FIQ, faſciamque, ΑRΣ43, æquari oſtẽ
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            dem us trapezio, kQ, modo ſupra adhibito, & </s>
            <s xml:id="echoid-s11412" xml:space="preserve">faſciam, βΜ874, ip-
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            ſi trapezio, LT, & </s>
            <s xml:id="echoid-s11413" xml:space="preserve">totam faſciam, 679C, trapezio, HV, vnde fi-
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            gura compoſita ex dictis faſcijs, & </s>
            <s xml:id="echoid-s11414" xml:space="preserve">ſectore, A53, erit ęqualis </s>
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