Viviani, Vincenzo, De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei

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          <head xml:id="echoid-head382" xml:space="preserve">THEOR. LXIII. PROP. XCVIII.</head>
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            <s xml:id="echoid-s8962" xml:space="preserve">Perpendicularium à vertice Coniſcaleni ſuper rectas baſis peri-
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            pheriam contingentes ducibilium, MAXIMA eſt, quæ ſuper con-
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            tingentẽ extermino MAXIMI lateris Coni ducitur, ſiue eſt ipſum
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            MAXIMVM Coni latus: </s>
            <s xml:id="echoid-s8963" xml:space="preserve">& </s>
            <s xml:id="echoid-s8964" xml:space="preserve">dum veſtigium verticis cadit intra ba-
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            ſim, vel in ipſius peripheriam, MINIMA eſt, quæ ſuper contin-
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            gentem ex termino MINIMI lateris, ſiue eſt idem latus MINI-
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            MVM: </s>
            <s xml:id="echoid-s8965" xml:space="preserve">dum autem cadit extra, MINIMA eſt, quæ cadit ſuper
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            contingentem ductam à puncto veſtigij verticis ad eandem baſis
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            peripheriam, ſiue MINIMA eſt ipſa Coni altitudo.</s>
            <s xml:id="echoid-s8966" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s8967" xml:space="preserve">ESto Conus ſcalenus A B C, cuius vertex B, baſis A C, centrum D, & </s>
            <s xml:id="echoid-s8968" xml:space="preserve">
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            altitudo B E baſi occurrens in puncto E (quod verticis veſtigium vo-
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            co,) quod vel cadat intra baſim, vt in prima figura, vel in ipſam peripheriã,
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            vt in ſecunda, vel extra, vt in tertia, per quàm B E, & </s>
            <s xml:id="echoid-s8969" xml:space="preserve">per centrum D con-
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            cipiatur ductum planum efficiens in Cono triangulum A B C, quod rectum
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            erit ad planum circuli A C, eritque triangulum ſcalenum, cuius maius
              <note symbol="a" position="left" xlink:label="note-0322-01" xlink:href="note-0322-01a" xml:space="preserve">14. ſe-
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              cundi Se-
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              reni.</note>
            tus, nempe B A erit _MAXIMVM_, minus verò B C _MINIMVM_
              <note symbol="b" position="left" xlink:label="note-0322-02" xlink:href="note-0322-02a" xml:space="preserve">15. ibid.</note>
            à vertice B ad baſis circumferentiam ducibilium.</s>
            <s xml:id="echoid-s8970" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s8971" xml:space="preserve">Præterea ex terminis diametri A, C, contingant peripheriam rectæ A
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            F, H C, & </s>
            <s xml:id="echoid-s8972" xml:space="preserve">ducto per axem quolibet alio plano efficiente triangulum I B L
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            obliquũ ad planum baſis A C, ex terminis I, L alterius diametri I D L, agan-
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            tur contingentes I M, L N, & </s>
            <s xml:id="echoid-s8973" xml:space="preserve">hoc fiat vt contingit, &</s>
            <s xml:id="echoid-s8974" xml:space="preserve">c. </s>
            <s xml:id="echoid-s8975" xml:space="preserve">Dico perpendicula-
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            rium, quæ à vertice B ad ipſas contingentes A F, C H, I M, L N, &</s>
            <s xml:id="echoid-s8976" xml:space="preserve">c. </s>
            <s xml:id="echoid-s8977" xml:space="preserve">du-
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            ci poſſunt, in ſigulis caſibus, _MAXIMAM_ eſſe, quæ ſuper A F, atque eam
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            eſſe ipſum _MAXIMVM_ latus B A: </s>
            <s xml:id="echoid-s8978" xml:space="preserve">in primò autem, & </s>
            <s xml:id="echoid-s8979" xml:space="preserve">ſecundò caſu _MINI-_
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            _MAM_ eſſe, quæ ſuper C H, atque hanc eſſe, ipſum _MINIMVM_ latus B C:
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            </s>
            <s xml:id="echoid-s8980" xml:space="preserve">in tertio denique ſi ex puncto veſtigij E ducatur E G peripheriam baſis
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            contingens. </s>
            <s xml:id="echoid-s8981" xml:space="preserve">Dico earundem perpendicularium _MINIMAM_ eſſe, quæ ſu-
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            per E G ducitur, & </s>
            <s xml:id="echoid-s8982" xml:space="preserve">hanc eſſe ipſam altitudinem B E.</s>
            <s xml:id="echoid-s8983" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8984" xml:space="preserve">Etenim, in ſingulis figuris, cum triangulum A B C ſit, ex hypotheſi re-
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            ctum ad planum baſis A C, & </s>
            <s xml:id="echoid-s8985" xml:space="preserve">ad communem eorum ſectionem A C ſit F A
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            perpendicularis (nam eſt A F contingens circulum, & </s>
            <s xml:id="echoid-s8986" xml:space="preserve">A D centrum iun-
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            gens) erit eadem F A recta ad planum A B C, ac propterea recta erit quo-
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            que ad A B, quæ eſt in eodem plano A B C, in quo eſt A C, hoc eſt B A
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            perpendicularis erit ſuper contingentem A F; </s>
            <s xml:id="echoid-s8987" xml:space="preserve">eadem ratione oſtendetur B
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            C perpendicularem eſſe ad contingentem C H.</s>
            <s xml:id="echoid-s8988" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s8989" xml:space="preserve">Præterea ducta ex E recta M E N parallela ad I L, cum anguli D I M, D
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            L N ſint recti, à contingentibus cum radijs conſtituti, erunt quoque reliqui
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            parallelarum interni I M E, L N E recti. </s>
            <s xml:id="echoid-s8990" xml:space="preserve">Iungantur denique B M, B N.
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            </s>
            <s xml:id="echoid-s8991" xml:space="preserve">Et cum B E ſit recta ad planum baſis A C, erit etiam planum trianguli
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            M B N, quod per eam ducitur, rectum ad ipſam baſim, ſiue baſis recta
              <note symbol="c" position="left" xlink:label="note-0322-03" xlink:href="note-0322-03a" xml:space="preserve">18. vnd.
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            triangulum M B N, eſtque I M perpendicularis ad eorum communem </s>
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