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

Table of contents

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[21.] COROLL.
[22.] MONITVM.
[23.] PROBL. I. PROP. II.
[24.] ALITER.
[25.] ALITER.
[26.] MONITVM.
[27.] LEMMAI. PROP. III.
[28.] PROBL. II. PROP. IV.
[29.] MONITVM.
[30.] PROBL. III. PROP. V.
[31.] PROBL. IV. PROP. VI.
[32.] PROBL. V. PROP. VII.
[33.] MONITVM.
[34.] THEOR. II. PROP. VIII.
[35.] MONITVM.
[36.] LEMMA II. PROP. IX.
[37.] THEOR. III. PROP. X.
[38.] COROLL. I.
[39.] COROLL. II.
[40.] MONITVM.
[41.] THEOR. IV. PROP. XI.
[42.] COROLL.
[43.] MONITVM.
[44.] LEMMA III. PROP. XII.
[45.] ALITER idem breuiùs.
[46.] ITER VM aliter breuiùs, ſed negatiuè.
[47.] COROLL.
[48.] THEOR. V. PROP. XIII.
[49.] COROLL. I.
[50.] COROLL. II.
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            omnes Ellipſis affectiones circulo communes eſſe, ſed ferè omnes etiam Hy-
              <lb/>
            perbolæ, magnaque pars Parabolæ, præmittendo tamen nouas quaſdam ani-
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            maduerſiones, cautioneſque perutiles, nemini, quod ſciam, adhuc cognitæs,
              <lb/>
            præcipuèque vtendo methodo ab ipſo Apollonio ſatis diuerſa, certàque indu-
              <lb/>
            ſtria propoſitionum figuris characteres diſponendo, ad hoc vt eadem demon-
              <lb/>
            ſtratio cuin
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            libet com-ſectioni ſimul inſeruiat, non abſimili modo ab eo, quo
              <lb/>
            in ſuperiori Theoremate vſi ſumus, ex quibus maximum doctrinæ conicæ
              <lb/>
            compendium oriretur; </s>
            <s xml:id="echoid-s462" xml:space="preserve">ſed quoniamid, plus laboris, ac temporis, quam in-
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            genij requireret, libenter opusrelinquo ijs, quibus multum ocij ſuppetit,& </s>
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            quos magis iuuat in alienas lucubrationes commentaria ſcribere, quàm vel
              <lb/>
            ipſas latiùs promouere, vel nouas meditari, ac geometricè demonſtrare.</s>
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            <s xml:id="echoid-s465" xml:space="preserve">Quod autem in Apollonij ſubcontraria ſectione tranſuerſum, rectumque
              <lb/>
            latus reperiatur eadem methodo, rationeque illorum rectangulorum qua vti-
              <lb/>
            mur in præcedenti, quodque hæc ipſa latera inter ſe ſint æqualia manifeſtum
              <lb/>
            fiet ex eo, quod mox demonſirabimus non tantum in prædicta ſectione ſub-
              <lb/>
            contraria, quæ recta eſt plano trianguli per axem recto plano baſis coni ſcale-
              <lb/>
            ni, ſed etiam ei quæ ſecat planum baſis com ſecundum rectam lineam perpen-
              <lb/>
            dicularem baſi cuiuſcunq; </s>
            <s xml:id="echoid-s466" xml:space="preserve">trianguli per axem non iſoſcelis, vel ei, quæ ipſi baſi
              <lb/>
            indirectum producitur, dummodò talis ſectio ex ipſomet triangulo, triangu-
              <lb/>
            lum auferat ſibi ſimile, ſed ſubcontr ariè poſitum.</s>
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            <s xml:id="echoid-s468" xml:space="preserve">REpetitis igitur duabus vltimis præcedentibus figuris, intelligatur conũ
              <lb/>
            ABC ſcalenum eſſe, ſectumque plano per axem, quodcunque trian-
              <lb/>
              <figure xlink:label="fig-0027-01" xlink:href="fig-0027-01a" number="4">
                <image file="0027-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0027-01"/>
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            gulum efficiente ABC, dummodo non ſit æquicrure, (quod per doctrinam
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            lib. </s>
            <s xml:id="echoid-s469" xml:space="preserve">ſecundi Sereni, vnicum eſt) habent idcircò vnum latus altero </s>
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