Cavalieri, Buonaventura, Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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              <pb o="428" file="0450" n="450" rhead="GEOMETRIÆ"/>
              <figure xlink:label="fig-0450-01" xlink:href="fig-0450-01a" number="309">
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            cumferentiam, CD, eſt
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            autem circulus, ABCD,
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            æqualis triang. </s>
            <s xml:id="echoid-s11214" xml:space="preserve">HOM,
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            ergo triangulus, HOM,
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            ad ſectorem, ECD, eſt
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            vt circumferẽtia, ABCD,
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            ad circumferentiam, CD,
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            ideſt vt, OM, ad, MN, id-
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            eſt vt triangulus, HOM,
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            ad, HNM, igitur idem
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            triangulus, HOM, ad ſe-
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            ctorem, ECD, ad trian-
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            gulum, HNM, eandem
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            habet rationem, ergo ſector, ECD, eſt æqualis triangulo,
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            HNM, quod oſtendere opus erat.</s>
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        <div xml:id="echoid-div1030" type="section" level="1" n="620">
          <head xml:id="echoid-head650" xml:space="preserve">COROLLARIVM I.</head>
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            <s xml:id="echoid-s11216" xml:space="preserve">_H_Inc patet, ſi ſumpto vtcumque puncto in, ED, vt, X, centro,
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            E, ad diſtantiam, X, circuferentia, FZX, deſcripta fuerit in-
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            ſuper abſciſſa, HR, æquali ipſi, EX, per, R, ducta fuerit, SR, parllela
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            ipſi, OM, ſecans, HN, in, I, trape zium, OSRM, æquari reſiduo circu-
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            li, ABCD, ab eo dempto circulo, FZX, quod reſiduum dicatur faſcia
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            circulorum, BD, FX, nam circulus, BD, ad circulum, FX, eſt vt qua-
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            dratum, DE ad quadratum, EX, ideſt vt quadratum, MH, ad qua-
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            dratum, HR, ideſt vt triangulus, HOM, ad triangulum, HSR, vnde,
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              <note position="left" xlink:label="note-0450-01" xlink:href="note-0450-01a" xml:space="preserve">_Coroll. 1._
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              _11. l. 3._</note>
            quia circulus, BD, æquatur triangulo, HOM, etiam circulus, FZX,
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            æquatur triangulo, HSR, vnde faſcia, BF, æquatur trapezio, OSRM;
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            </s>
            <s xml:id="echoid-s11217" xml:space="preserve">eoden modo colligemns reſiduum ſectoris DEC, ab eo dempto ſectore,
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              <note position="left" xlink:label="note-0450-02" xlink:href="note-0450-02a" xml:space="preserve">_Coroll. 1._
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              _19. l. 2._</note>
            XEZ, quod dicatur eorundem ſectorum faſcia, ſcilicet ipſum, ZXDC,
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            æquart trapezio, IRMN.</s>
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        <div xml:id="echoid-div1032" type="section" level="1" n="621">
          <head xml:id="echoid-head651" xml:space="preserve">COROLLARIVM II.</head>
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            <s xml:id="echoid-s11219" xml:space="preserve">_P_Atet inſuper, quia circulus, CDB, æquatur triangulo, HOM, & </s>
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            circulus, FZX, triang. </s>
            <s xml:id="echoid-s11221" xml:space="preserve">HSR, item circumferentia, ABCD, ipſi
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            OM, &</s>
            <s xml:id="echoid-s11222" xml:space="preserve">, FZX, ipſi, SR, (nam, DE, æquatur ipſi, MH, &</s>
            <s xml:id="echoid-s11223" xml:space="preserve">, EX, ipſi, RH,)
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            quod veluti, OM, ad, SR, eſt vt, MH, ad, HR ita circumferentia, ABCD,
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            ad, FZX, erit vt, DE, ad, EX. </s>
            <s xml:id="echoid-s11224" xml:space="preserve">Sic etiam oſtendemus ſimilium ſectorum,
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            CED, ZEX, circumferentias, CD, ZX, eſſe vt ſemidiametri, DE EX, & </s>
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            ipſos ſimiles ſectores eſſe vt quadrata ſemidiametrorũ, DE, EX, </s>
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