Benedetti, Giovanni Battista de, Io. Baptistae Benedicti ... Diversarvm specvlationvm mathematicarum, et physicarum liber : quarum seriem sequens pagina indicabit ; [annotated and critiqued by Guidobaldo Del Monte]

Table of contents

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[5.1.7.] SEPTIMVM. Euclidis uerò undecima propoſitio.
[5.1.8.] OCTAVVM. εuclidis uerò duodecima propoſitio.
[5.1.9.] NONVM. Euclidis uero tertiadecima propoſitio.
[5.1.10.] DECIMVM.
[5.1.11.] VNDECIMVM.
[5.1.12.] DVODECIMVM.
[Item 5.2.]
[5.2.1.] THEOR.I. II. ET III.
[5.2.2.] THEOREM. IIII.
[5.2.3.] THEOR.V. ET VI.
[5.2.4.] THEOR. VII. VIII. IX.X. XI. XII. XIII.
[5.2.5.] THEOREM. XIIII.
[5.2.6.] THEOR. XV.
[5.2.7.] THEOREM. XVI.
[5.2.8.] THEOR. XVII.
[5.2.9.] THEOREM. XVIII.
[5.2.10.] THEOREM. XIX.
[5.2.11.] THEOREM. XX.
[5.2.12.] THEOREM. XXI.
[5.2.13.] THEOREM. XXII. XXIII.
[6.] PHYSICA, ET MATHEMATICA RESPONSA. FO. BAPTISTAE BεNεDICTI PATRITII Veneti, Philoſophi Mathematici.
[Item 6.1.]
[Item 6.2.]
[Item 6.3.]
[Item 6.4.]
[Item 6.5.]
[Item 6.6.]
[Item 6.7.]
[Item 6.8.]
[Item 6.9.]
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                <s xml:id="echoid-s1758" xml:space="preserve">
                  <pb o="147" rhead="DE MECHAN." n="159" file="0159" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0159"/>
                lere verſus
                  <var>.u.</var>
                vnde linea eius inclinationis ſit ſemper
                  <var>.a.u.</var>
                ſupponamus etiam
                  <var>.a.o.b.</var>
                  <lb/>
                eſſe
                  <reg norm="libram" type="context">librã</reg>
                , aut ſtateram, aut vectem, &
                  <var>.o.</var>
                eius centrum, vnde vis, aut virtus ipſius
                  <var>.a.</var>
                  <lb/>
                proportionalis erit ipſi
                  <var>.o.t.</var>
                reſpectu virtutis, aut vis imaginatæ in
                  <var>.b.</var>
                inclinationis
                  <lb/>
                perpendicularis ipſi
                  <var>.b.a.</var>
                quæ quidem virtus, aut vis in
                  <var>.b.</var>
                proportionalis erit ipſi
                  <var>.b.
                    <lb/>
                  o.</var>
                ex tertio capite huius tractatus; </s>
                <s xml:id="echoid-s1759" xml:space="preserve">Si ergo fuiſſet poſita in
                  <var>.b.</var>
                virtus quædarn ad an-
                  <lb/>
                gulum rectum, trahens lineam
                  <var>.b.o.</var>
                tam proportionatam virtuti perpendiculari ip-
                  <lb/>
                ſius
                  <var>.a.</var>
                quam eſt
                  <var>.o.t.</var>
                proportionata ipſi
                  <var>.o.b.</var>
                ſtatera
                  <var>.b.o.a.</var>
                non moueretur, ſed quæuis
                  <lb/>
                portio maior in
                  <var>.b.</var>
                ſuperaret
                  <var>.a.</var>
                cum autem fuerit
                  <var>.o.x.</var>
                æqualis ipſi
                  <var>.o.b.</var>
                  <reg norm="idem" type="context">idẽ</reg>
                planè eue-
                  <lb/>
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                niet, communi quadam ſcientia, ponen-
                  <lb/>
                do virtutem
                  <var>.b.</var>
                in
                  <var>.x</var>
                . </s>
                <s xml:id="echoid-s1760" xml:space="preserve">Quantitas ergo virtu
                  <lb/>
                tis in
                  <var>.x.</var>
                quæ ſuperare debet reſiſtentiam
                  <lb/>
                in
                  <var>.a.</var>
                quæ ipſi
                  <var>.u.</var>
                contraponitur, debet ha-
                  <lb/>
                bere aliquantulum maioris proportionis
                  <lb/>
                ad reſiſtentiam, quæ in
                  <var>.a.</var>
                angulum re-
                  <lb/>
                ctum efficeret cum
                  <var>.a.o.</var>
                ea, quæ eſt
                  <var>.o.t.</var>
                  <lb/>
                ad
                  <var>.o.x</var>
                .</s>
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