Viviani, Vincenzo, De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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            D M (cum latus rectum B F, vel duplum ſit, vel plus quàm duplum ad
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            B D) ergo M N ipſo aggregato B D cum D M adhuc maior erit, vnde
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            rectangulum ſub N M in M B, ſiue quadratum L M, maius erit
              <note symbol="a" position="right" xlink:label="note-0187-01" xlink:href="note-0187-01a" xml:space="preserve">Coroll.
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              primæ pri
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              mi huius.</note>
            gulo ſub aggregato B D cum D M, in eadem M B, quibus communi ad-
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            dito quadrato M D, erit quadratum L M cum M D, ſiue vnicum qua-
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            dratum D L, maius rectangulo ſub B D cum D M in M B, vna cum qua-
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            drato D M, ſiue maius vnico quadrato D B, quod prædicto
              <note symbol="b" position="right" xlink:label="note-0187-02" xlink:href="note-0187-02a" xml:space="preserve">1. huius.</note>
            æquale eſt, ſiue linea D L maior D B. </s>
            <s xml:id="echoid-s5262" xml:space="preserve">Quare ſegmentum axis D B, non
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            excedens dimidium recti lateris B F, eſt _MINIMA_ linearum ducibilium
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            ex D ad Hyperbolæ peripheriam. </s>
            <s xml:id="echoid-s5263" xml:space="preserve">Quod primò oſtendere oportebat.</s>
            <s xml:id="echoid-s5264" xml:space="preserve"/>
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            <s xml:id="echoid-s5265" xml:space="preserve">Præterea, quadratum A D ſuperat quadratum L M, eo exceſſu quo re-
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            ctangulum B D G ſuperat rectangulum B M N, (ſunt enim ſingula
              <note symbol="c" position="right" xlink:label="note-0187-03" xlink:href="note-0187-03a" xml:space="preserve">Coroll.
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              primæ pri
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              mi huius.</note>
            lis æqualia) ſed exceſſus rectanguli B D G ſupra rectangulum B M N ma-
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            ius eſt rectangulo M D G, ergo quadratum A D ſuperat
              <note symbol="d" position="right" xlink:label="note-0187-04" xlink:href="note-0187-04a" xml:space="preserve">4. huius.</note>
            L M maiori rectangulo quàm M D G; </s>
            <s xml:id="echoid-s5266" xml:space="preserve">ſed quadratum D L ſuperat idem
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            quadratum L M quadrato D M, quod minus eſt rectangulo MDG (nam
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            eſt D G maior D M, cum ſuperiùs demonſtrata ſit maior ipſa D B) ergo
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            quadratum D A maius eſt quadrato D L, ſiue linea D A maior quacun-
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            que D L, intercepta inter applicatam D A, & </s>
            <s xml:id="echoid-s5267" xml:space="preserve">axem D B.</s>
            <s xml:id="echoid-s5268" xml:space="preserve"/>
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            <s xml:id="echoid-s5269" xml:space="preserve">Ampliùs, ducatur alia quæpiam D O ſupra D A, ſed remotior à ſe-
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            gmento DB quàm D L, applicataque O P, producatur donec regulatrici
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            E F occurrat in Q. </s>
            <s xml:id="echoid-s5270" xml:space="preserve">Erit exceſſus quadrati O P ſupra quadratum L M,
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            idem ac exceſſus rectanguli B P Q ſupra B M N (nam ſunt
              <note symbol="e" position="right" xlink:label="note-0187-05" xlink:href="note-0187-05a" xml:space="preserve">Coroll.
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              primæ pri
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              mi huius.</note>
            quadratis æqualia, vtrumque vtrique) ſed exceſſus rectanguli B P Q ſu-
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            pra B M N maior eſt rectangulo M P Q, ergo exceſſus quadrati O P,
              <note symbol="f" position="right" xlink:label="note-0187-06" xlink:href="note-0187-06a" xml:space="preserve">4. huius.</note>
            pra quadratum L M, maior eſt rectangulo ſub M P, & </s>
            <s xml:id="echoid-s5271" xml:space="preserve">P Q; </s>
            <s xml:id="echoid-s5272" xml:space="preserve">at exceſſus
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            quadrati M D ſupra quadratum D P, minor eſt prædicto rectangulo (nam
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            quadratum M D ſuperat quadratum D P, rectangulo ſub M D cum
              <note symbol="g" position="right" xlink:label="note-0187-07" xlink:href="note-0187-07a" xml:space="preserve">1. huius.</note>
            in M P, quod eſt minus rectangulo ſub Q P in eadem M P, quoniam
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            M D cum D P minor eſt recto latere B F, & </s>
            <s xml:id="echoid-s5273" xml:space="preserve">eò minor ipſa QP,
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            quę maior eſt B F) quare exceſſus quadrati O P ſupra L M,
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            maior eſt exceſſu quadrati M D ſupra D P: </s>
            <s xml:id="echoid-s5274" xml:space="preserve">duo igi-
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              <handwritten xlink:label="hd-0187-1" xlink:href="hd-0187-1a" number="12"/>
            tur extrema ſimul quadrata O P, P D, ſiue vni-
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            cum quadratum D O, maius eſt duobus ſi-
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            mul quadratis medijs L M, M D, hoc
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            eſt vnico quadrato D L, ſiue li-
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            nea DO maior eſt linea DL.
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            </s>
            <s xml:id="echoid-s5275" xml:space="preserve">Vnde quæ minorem
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            efficit angulum
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            cum _MINI_-
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            _M A_
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            D B, minor eſt, &</s>
            <s xml:id="echoid-s5276" xml:space="preserve">c. </s>
            <s xml:id="echoid-s5277" xml:space="preserve">Quod
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            fuit vltimò demon-
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            ſtrandum. </s>
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            * * *
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            * *
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            *</s>
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