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

Table of contents

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[311.] THEOR. XLII. PROP. LXVIII.
Page: 274 (88)
[312.] COROLL. I.
Page: 276 (90)
[313.] COROLL. II.
Page: 276 (90)
[314.] MONITVM.
Page: 276 (90)
[315.] DEFINITIONES. I.
Page: 278 (92)
[316.] II.
Page: 278 (92)
[317.] III.
Page: 279 (93)
[318.] IIII.
Page: 279 (93)
[319.] PROBL. XIV. PROP. LXIX.
Page: 280 (94)
[320.] SCHOLIVM I.
Page: 282 (96)
[321.] COROLL. I.
Page: 282 (96)
[322.] SCHOLIVM II.
Page: 282 (96)
[323.] COROLL. II.
Page: 282 (96)
[324.] SCHOLIVM III.
Page: 283 (97)
[325.] COROLL. III.
Page: 283 (97)
[326.] THEOR. XLIII. PROP. LXX.
Page: 284 (98)
[327.] COROLL.
Page: 286 (100)
[328.] THEOR. XLIV. PROP. LXXI.
Page: 286 (100)
[329.] COROLL.
Page: 287 (101)
[330.] THEOR. XLV. PROP. LXXII.
Page: 288 (102)
[331.] SCHOLIVM.
Page: 288 (102)
[332.] THEOR. XLVI. PROP. LXXIII.
Page: 288 (102)
[333.] THEOR. XLVII. PROP. LXXIV.
Page: 288 (102)
[334.] MONITVM.
Page: 290 (104)
[335.] LEMMA XIV. PROP. LXXV.
Page: 290 (104)
[336.] SCHOLIVM.
Page: 291 (105)
[337.] LEMMA XV. PROP. LXXVI.
Page: 292 (106)
[338.] THEOR. XLVIII. PROP. LXXVII.
Page: 292 (106)
[339.] MONITVM.
Page: 293 (107)
[340.] THEOR. IL. PROP. LXXVIII.
Page: 294 (108)
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            <s xml:id="echoid-s8184" xml:space="preserve">Iunctis enim rectis A I, G F, H C:
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            <s xml:id="echoid-s8185" xml:space="preserve">
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            patet has inter ſe æquidiſtare, ac
              <note symbol="a" position="right" xlink:label="note-0293-01" xlink:href="note-0293-01a" xml:space="preserve">ibidem.</note>
            ipſas proportionaliter diuidere rectas H
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            G M I, C F M A inter eas interceptas in
              <lb/>
            punctis G, F, M. </s>
            <s xml:id="echoid-s8186" xml:space="preserve">Erit ergo, in ſingulis
              <lb/>
            figuris, quadratum H G ad quadratum
              <lb/>
            G M, vt quadratum C F ad quadratum
              <lb/>
            F M, & </s>
            <s xml:id="echoid-s8187" xml:space="preserve">permutando quadratum H G
              <lb/>
            ad quadratum C F, vt quadratum G M
              <lb/>
            ad F M: </s>
            <s xml:id="echoid-s8188" xml:space="preserve">ſed, in præſenti figura, eſt qua-
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            dratum H G æquale rectangulo H M I
              <lb/>
            vnà cum quadrato G M, & </s>
            <s xml:id="echoid-s8189" xml:space="preserve">quadratum
              <lb/>
            C F æquatur rectangulo C M A vnà
              <lb/>
            cum quadrato F M, (cumrectæ H I, A C bifariam ſectæ ſint in G & </s>
            <s xml:id="echoid-s8190" xml:space="preserve">F, & </s>
            <s xml:id="echoid-s8191" xml:space="preserve">
              <lb/>
            non bifariam in M) atque eſt totum quadratum H G ad totum C F vt pars
              <lb/>
            ad partem, vel vt quadratum G M ad F M, ergo reliquum ad reliquum,
              <lb/>
            nempe rectangulum H M I ad C M A, vel rectangulum H G I ad T G
              <note symbol="b" position="right" xlink:label="note-0293-02" xlink:href="note-0293-02a" xml:space="preserve">76. h.</note>
            erit vt totum ad totum, ſiue vt quadratum H G ad quadratum C F, ſed an-
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            tecedentia ſunt æqualia, hoc eſt rectangulum H G I, & </s>
            <s xml:id="echoid-s8192" xml:space="preserve">quadratum H G,
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            cum ſit recta H G æqualis G I, ergo, & </s>
            <s xml:id="echoid-s8193" xml:space="preserve">conſequentia æqualia erunt, nem-
              <lb/>
            pe rectangulum T G S, & </s>
            <s xml:id="echoid-s8194" xml:space="preserve">quadratum C F. </s>
            <s xml:id="echoid-s8195" xml:space="preserve">Quod in anguli portionibus
              <lb/>
            demonſtrandum erat.</s>
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            <s xml:id="echoid-s8197" xml:space="preserve">In reliquis autem figuris iam dicti tertij Schematiſmi, eſt rectangulum H
              <lb/>
            G I ad rectangulum T G S, vt quadratum contingentis E N ipſi H I
              <note symbol="c" position="right" xlink:label="note-0293-03" xlink:href="note-0293-03a" xml:space="preserve">17. tertij
                <lb/>
              Conic.</note>
            rallelæ ad quadratum contingentis B N alteri A C æquidiſtantis, vel vt
              <lb/>
            quadratum G M ad M F (nam ibi primo loco oſtenſum fuit in ſingulis eſſe
              <lb/>
            E N ad N B, vt G M ad M F (vel ob parallelas A I, F G, C H, vt qua-
              <lb/>
            dratum H G ad quadratum C F, atque antecedentia ſunt æqualia, nempe
              <lb/>
            rectangulum H G I quadrato H G, cum recta H G ſit æqualis rectæ G I,
              <lb/>
            ergo, & </s>
            <s xml:id="echoid-s8198" xml:space="preserve">conſequentia, ſiue rectangulum T G S quadrato C F æquale erit.
              <lb/>
            </s>
            <s xml:id="echoid-s8199" xml:space="preserve">Quod omnino oſtendere propoſitum fuit.</s>
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        <div xml:id="echoid-div851" type="section" level="1" n="339">
          <head xml:id="echoid-head348" xml:space="preserve">MONITVM.</head>
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            <s xml:id="echoid-s8201" xml:space="preserve">CVM ad abſcindendas MAXIMAS, & </s>
            <s xml:id="echoid-s8202" xml:space="preserve">MINIMAS co-
              <lb/>
            ni - ſectionum portiones per punctum in ijs datum, animad-
              <lb/>
            uertiſsemus olim præmittendam eſſe inueſtigationem æqua-
              <lb/>
            lium portionum eiuſdem coni - ſectionis, quas deinde pro
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            quacunque coni - ſectione reperimus, atque vnica demonſtratione confir-
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            mauimus, (vt viſum eſt in 40. </s>
            <s xml:id="echoid-s8203" xml:space="preserve">huius, ac ſimul vt in 45. </s>
            <s xml:id="echoid-s8204" xml:space="preserve">eas om-
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            nes proprijs baſibus ſimilem, & </s>
            <s xml:id="echoid-s8205" xml:space="preserve">concentricam eiuſdem nominis ſectio-
              <lb/>
            nem contingere) ita dum MAXIMAS, ac MINIMAS Conorum, aut
              <lb/>
            Conoidalium, vel Sphæroidalium ſolidorum portiones nobis duximus in-
              <lb/>
            quirendum, neceſſe fuit prius contemplari, quæ nam eiuſdem Coni </s>
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