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

Table of handwritten notes

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            <s xml:id="echoid-s7385" xml:space="preserve">
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            ad vnicum punctum D, aut G, vt in 2. </s>
            <s xml:id="echoid-s7386" xml:space="preserve">3. </s>
            <s xml:id="echoid-s7387" xml:space="preserve">4. </s>
            <s xml:id="echoid-s7388" xml:space="preserve">5. </s>
            <s xml:id="echoid-s7389" xml:space="preserve">7. </s>
            <s xml:id="echoid-s7390" xml:space="preserve">8. </s>
            <s xml:id="echoid-s7391" xml:space="preserve">9. </s>
            <s xml:id="echoid-s7392" xml:space="preserve">11. </s>
            <s xml:id="echoid-s7393" xml:space="preserve">12. </s>
            <s xml:id="echoid-s7394" xml:space="preserve">13. </s>
            <s xml:id="echoid-s7395" xml:space="preserve">14. </s>
            <s xml:id="echoid-s7396" xml:space="preserve">16.
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            </s>
            <s xml:id="echoid-s7397" xml:space="preserve">17. </s>
            <s xml:id="echoid-s7398" xml:space="preserve">ac 18. </s>
            <s xml:id="echoid-s7399" xml:space="preserve">figura, quoniam in his quoque vnicus eſt contactus inter circulũ,
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            & </s>
            <s xml:id="echoid-s7400" xml:space="preserve">Ellipſim; </s>
            <s xml:id="echoid-s7401" xml:space="preserve">vel ad duo tantùm puncta B, D, vt in prima, aut G, H, vt in
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            ſexta, in quot circulus Ellipſim contingit, & </s>
            <s xml:id="echoid-s7402" xml:space="preserve">quæ non ſunt extrema eiuſdem
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            applicatæ in vtraq; </s>
            <s xml:id="echoid-s7403" xml:space="preserve">ſectione ad communem axim; </s>
            <s xml:id="echoid-s7404" xml:space="preserve">vel tandem ad integram
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            circuli peripheriam à puncto A in decima figura, vel à puncto G in 15. </s>
            <s xml:id="echoid-s7405" xml:space="preserve">ex
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            figurarum reuolutione circa communem axim B D deſcriptam. </s>
            <s xml:id="echoid-s7406" xml:space="preserve">Cum ergo
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            Sphæra G H claudat Sphæroides A B C D, atque ipſum contingat tantùm,
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            vel in vno, vel in duobus punctis, vel ad integram circuli peripheriam, cũq; </s>
            <s xml:id="echoid-s7407" xml:space="preserve">
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            omnes rectæ, quæ à centro F ad punctum ſphæricæ ſuperficiei duci poſſunt
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            ſint æquales ijs, quæ ad prædicta contactuum pũcta, vel peripherias ducun-
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            tur, ideò quæ ab eodem centro ad incluſam Sphæroidis ſuperficiem, præter
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            ad prædicta puncta, vel peripherias ducentur minores erunt, ac propterea
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            ipſæ eductæ à centro F, ſiue à puncto dato ad prędicta puncta, vel periphe-
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            rias in Sphæroidis ſuperficie erunt _MAXIMAE_ quæſitæ. </s>
            <s xml:id="echoid-s7408" xml:space="preserve">Quod erat pri-
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            mò faciendum.</s>
            <s xml:id="echoid-s7409" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7410" xml:space="preserve">SIverò ad Sphæroidis ſuperficiem A B C D ducenda ſit _MINIMA_ linea à
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            puncto dato F. </s>
            <s xml:id="echoid-s7411" xml:space="preserve">Vel datum punctum eſt in ipſa ſuperficie, & </s>
            <s xml:id="echoid-s7412" xml:space="preserve">tunc _MI-_
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            _NIMA_ in punctum abit. </s>
            <s xml:id="echoid-s7413" xml:space="preserve">Vel cadit extra, & </s>
            <s xml:id="echoid-s7414" xml:space="preserve">tunc _MINIMA_ reperitur, vt in
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            58. </s>
            <s xml:id="echoid-s7415" xml:space="preserve">huius. </s>
            <s xml:id="echoid-s7416" xml:space="preserve">Vel tandem eſt intra Sphæroides, & </s>
            <s xml:id="echoid-s7417" xml:space="preserve">tunc ad _MINIMAM_ venan-
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            dam generalis conſtructio eſt huiuſmodi.</s>
            <s xml:id="echoid-s7418" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7419" xml:space="preserve">Secetur Sphæroides plano per axem B D, & </s>
            <s xml:id="echoid-s7420" xml:space="preserve">per datum punctum F, geni-
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            tricem Ellipſim efficiente A B C D, ductaque ex F ad Ellipſis peripheriam
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            _MINIMA_ recta linea, ipſa quoque erit _MINIMA_ ad Sphæroidis ſuperficiẽ.</s>
            <s xml:id="echoid-s7421" xml:space="preserve"/>
          </p>
          <note symbol="*" position="right" xml:space="preserve">23. h.</note>
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            <s xml:id="echoid-s7422" xml:space="preserve">Iam, vel datum Sphæroides eſt Oblongum, vel Prolatum. </s>
            <s xml:id="echoid-s7423" xml:space="preserve">Sit primò
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            Oblongum, vt in figuris 19. </s>
            <s xml:id="echoid-s7424" xml:space="preserve">20. </s>
            <s xml:id="echoid-s7425" xml:space="preserve">21. </s>
            <s xml:id="echoid-s7426" xml:space="preserve">22. </s>
            <s xml:id="echoid-s7427" xml:space="preserve">23. </s>
            <s xml:id="echoid-s7428" xml:space="preserve">Itaque datum punctum F, vel
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            eſt in centro, vt in 19. </s>
            <s xml:id="echoid-s7429" xml:space="preserve">& </s>
            <s xml:id="echoid-s7430" xml:space="preserve">tunc duæ F A, F C, ſunt _MINIMAE_, vel in ma-
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            iori axe A B diſtans à vertice B per interuallum maius dimidio recti, &</s>
            <s xml:id="echoid-s7431" xml:space="preserve">c.
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            </s>
            <s xml:id="echoid-s7432" xml:space="preserve">itemque duæ F G, F H ſunt _MINIMAE_, vt in 20. </s>
            <s xml:id="echoid-s7433" xml:space="preserve">vel per interuallum non
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            maius prædicto dimidio, vt in 21. </s>
            <s xml:id="echoid-s7434" xml:space="preserve">& </s>
            <s xml:id="echoid-s7435" xml:space="preserve">tunc vnica F B, in qua non eſt centrũ,
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            eſt _MINIMA_; </s>
            <s xml:id="echoid-s7436" xml:space="preserve">vel eſt in minori axe, vt in 22. </s>
            <s xml:id="echoid-s7437" xml:space="preserve">in qua F C vbi centrum non
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            reperitur eſt _MINIMA_; </s>
            <s xml:id="echoid-s7438" xml:space="preserve">vel tandem eſt inter axes, vt in 23. </s>
            <s xml:id="echoid-s7439" xml:space="preserve">& </s>
            <s xml:id="echoid-s7440" xml:space="preserve">tunc vnica F
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            G eſt _MINIMA_, &</s>
            <s xml:id="echoid-s7441" xml:space="preserve">c.</s>
            <s xml:id="echoid-s7442" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7443" xml:space="preserve">Sit denique Sphæroides Prolatum, vt in poſtremis figuris huius quarti
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            Schematiſmi. </s>
            <s xml:id="echoid-s7444" xml:space="preserve">Si punctum F congruit cum centro E, vt in 24. </s>
            <s xml:id="echoid-s7445" xml:space="preserve">figura duæ F
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            D, F B ſunt _MINIMAE_; </s>
            <s xml:id="echoid-s7446" xml:space="preserve">ſi eſt in ſemi- axe maiori E C, diſtans à C per in-
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            teruallum maius recti dimidio, &</s>
            <s xml:id="echoid-s7447" xml:space="preserve">c. </s>
            <s xml:id="echoid-s7448" xml:space="preserve">vt in 25. </s>
            <s xml:id="echoid-s7449" xml:space="preserve">duo item F G, F H ſunt _MINI-_
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            _MAE_; </s>
            <s xml:id="echoid-s7450" xml:space="preserve">ſi per interuallum non maius prædicto dimidio, vt in 26. </s>
            <s xml:id="echoid-s7451" xml:space="preserve">vnica F C
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            eſt _MINIMA_; </s>
            <s xml:id="echoid-s7452" xml:space="preserve">ſi in ſemi- axe minori E B, vt in 27. </s>
            <s xml:id="echoid-s7453" xml:space="preserve">ipſa F B, in qua non eſt
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            centrum eſt _MINIMA_; </s>
            <s xml:id="echoid-s7454" xml:space="preserve">ſi tandem inter axes, vt in 28. </s>
            <s xml:id="echoid-s7455" xml:space="preserve">vnica F G eſt _MINI-_
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            _MA_, quæ omnia in prop. </s>
            <s xml:id="echoid-s7456" xml:space="preserve">23. </s>
            <s xml:id="echoid-s7457" xml:space="preserve">huius ſunt demonſtrata.</s>
            <s xml:id="echoid-s7458" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s7459" xml:space="preserve">Siergo in his omnibus figuris cum centro F, ad interuallum nuper inuen-
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            tæ _MINIMAE_ deſcribatur circulus G H, ipſe circumſcriptus erit Ellipſi,
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            hanc tantùm contingens in eo, vel in ijs punctis, ad quæ _MINIMA_, vel
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            _MINIMAE_ perueniunt; </s>
            <s xml:id="echoid-s7460" xml:space="preserve">nam ſi alibi cum Ellipſi conuenirent, _MINIMAE_
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            plures eſſent, quàm eſſe poſſint. </s>
            <s xml:id="echoid-s7461" xml:space="preserve">Itaque in circulis figurarum 22. </s>
            <s xml:id="echoid-s7462" xml:space="preserve">23. </s>
            <s xml:id="echoid-s7463" xml:space="preserve">25. </s>
            <s xml:id="echoid-s7464" xml:space="preserve">26.</s>
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