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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[3.13.] Quòd Ariſtotelisratio in 6. quæſtione poſit a non ſit admittenda. CAP. XIII.
Page: 167 (155)
[3.14.] Quòdrationes ab Ariſtotele de octaua quæstione confictæ ſufficient es non ſint. CAP. XIIII.
Page: 167 (155)
[3.15.] Quod Aristotelis ratio none queſtionis admittendanon ſit. CAP. XV.
Page: 171 (159)
[3.16.] Quod Aristotelis rationes de decima queſtione ſint reijciende. CAP. XVI.
Page: 171 (159)
[3.17.] De uer a cauſa .12. questionis mechanice. CAP. XVII.
Page: 172 (160)
[3.18.] De decimatertia questione. CAP. XVIII.
Page: 173 (161)
[3.19.] De decimaquart a queſtione. CAP. XIX.
Page: 173 (161)
[3.20.] De uer a r atione .17. queſtionis. CAP. XX.
Page: 174 (162)
[3.21.] De uera & intrinſeca cauſa trocble arum. CAP. XXI.
Page: 175 (163)
[3.22.] Depropria cauſa .24. quæſtionis. CAP. XXII.
Page: 177 (165)
[3.23.] De uer a cauſa .30. quæstionis. CAP. XXIIII.
Page: 179 (167)
[3.24.] Deratione .35. & ultimæ quæstionis. CAP. XXV.
Page: 179 (167)
[4.] DISPVTATIONES DE QVIBVSDAM PLACITIS ARISTOTELIS.
Page: 180 (168)
[4.1.] Qualiter & ubi Ariſtoteles de uelocitate motuum natura-lium localium aliter tractauerit quam nos ſentiamus. CAP.I.
Page: 180 (168)
[4.2.] Quædam ſupponenda ut conſtet cur circa uelocit atem motuum natur alium localium ab Ariſtotelis placitis recedamus. CAP. II.
Page: 181 (169)
[4.3.] Poſſe uelocitatem alicuius corporis proportionem contrariam in diuerſis medijs habere cum denſitate eorum. CAP. III.
Page: 182 (170)
[4.4.] Oſcitanter ab Ariſtotele nonnibil prolatum cap 8. lib. 4 Phyſicorum. CAP. IIII.
Page: 182 (170)
[4.5.] Exempla dictorum. CAP.V.
Page: 183 (171)
[4.6.] Quod proportiones ponderum eiuſdem corporis in diuerſis medijs pro portiones eorum mediorum denſit atum non ſeruant. Unde ne-ceßariò inæquales proportiones uelocitatum producuntur. CAP. VI.
Page: 184 (172)
[4.7.] Corpora grauia aut leuia eiuſdem figur æ et materiæ ſed inæqualis magnitudinis, in ſuis motibus natur alibus uelocit atis, in eo dem medio, proportionem longè diuerſam ſeruatura eße quam Aristoteliuiſum fuerit. CAP. VII.
Page: 184 (172)
[4.8.] Quod duo corpor a in æqualia eiuſdem materia in diuerſis medijs eandem uelocitatis proportionem retinebunt. CAP. VIII.
Page: 185 (173)
[4.9.] Anrectè Aristoteles diſeruerit de proportionibus mo-tuum in uacuo. CAP. IX.
Page: 186 (174)
[4.10.] Quòd in uacuo corpor a eiuſdem materiæ æquali uelocita-te mouerentur. CAP.X.
Page: 186 (174)
[4.11.] Corpora licet inæqualia eiuſdem materiæ & figuræ, ſireſiſten-tias habuerint ponderibus proportionales æqualiter mouebuntur. CAP. XI.
Page: 187 (175)
[4.12.] Maior hic demonſir atur eſſe proportio ponder is corpor is den ſioris ad pondus minus denſi in medijs dẽſioribus, quam ſit eorundem corporum in medio minus denſo, nec corporum ponder a ſeruare proportionem denſitatis mediorum. CAP. XII.
Page: 187 (175)
[4.13.] Longe aliter ueritatem ſe habere quam Aristoteles doceat in fine libri ſeptimi phyſicorum. CAP. XIII.
Page: 188 (176)
[4.14.] Quid ſequatur ex ſupradistis. CAP. XIIII.
Page: 189 (177)
[4.15.] Numrestè ſenſerit Philoſophus reſistentias proportionales eße cum corporibus mobilibus. CAP. XV.
Page: 189 (177)
[4.16.] Fdipſum aliter demonſtr atur. CAP. XVI.
Page: 190 (178)
[4.17.] De alio Aristo. lapſu. CAP. XVII.
Page: 190 (178)
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            <div xml:id="echoid-div89" type="math:theorem" level="3" n="41">
              <pb o="27" rhead="THEOREM. ARIT." n="39" file="0039" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0039"/>
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                <s xml:id="echoid-s364" xml:space="preserve">Quod vt ſpeculemus, conſideremus ſubſcriptam figuram, vigefiminoni theore-
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                matis figuræ ſimilem, in qua numeri quæſiti duabus
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                lineis directè coniunctis
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                et
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                fignificentur, ho
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                  <figure xlink:label="fig-0039-01" xlink:href="fig-0039-01a" number="54">
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                  <reg norm="summa" type="context">sũma</reg>
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                propo
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                nitur, quare etiam cognita. </s>
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                  <reg norm="Differentia" type="context">Differẽtia</reg>
                autem
                  <reg norm="duorum" type="context">duorũ</reg>
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                numerorum primo propofita fit
                  <var>.q.i.</var>
                eius verò qua-
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                dratum
                  <var>.m.e.</var>
                quod cognitum eſt ex ſua radice
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                .
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                </s>
                <s xml:id="echoid-s366" xml:space="preserve">quare gnomon
                  <var>.e.n.m.</var>
                ſimul cum quadrato minori
                  <var>.
                    <lb/>
                  g.s.</var>
                cognitus erit, quæ ſumma æqualis eſt duplo
                  <var>.g.r.</var>
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                producto datorum numerorum. </s>
                <s xml:id="echoid-s367" xml:space="preserve">Itaque & ipſa
                  <var>.g.
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                  r.</var>
                cognoſcetur, nunc ſi præcedentis theorematis ſpe-
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                culationem in reliquis conſuluerimus propoſitum
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                conſequemur.</s>
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            <div xml:id="echoid-div91" type="math:theorem" level="3" n="42">
              <head xml:id="echoid-head58" xml:space="preserve">THEOREMA
                <num value="42">XLII</num>
              .</head>
              <p>
                <s xml:id="echoid-s368" xml:space="preserve">ADhuc etiam & alia ratione idipſum conſequi poſſemus, non conſulto qua-
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                drageſimo theoremate. </s>
                <s xml:id="echoid-s369" xml:space="preserve">Nam ſubtracto quadrato differentiæ, numeri primi
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                (
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                ) propoſiti, ex
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                duorum quadratorum, nempe ex ſecundo numero pro-
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                poſito colligendum eſſet reſiduum in ſummam cum prædicto ſecundo numero, &
                  <lb/>
                ex ſumma hac deſumenda quadrata radix, quæ duorum numerorum ſumma erit,
                  <lb/>
                de qua detracto primo numero, remanebit duplum minoris numeri quæſiti, cuius
                  <lb/>
                dimidio addito primo numero propoſito, aut detracto minore inuento ex radice
                  <lb/>
                poſtremo inuenta, dabitur numerus maior, qui quæritur.</s>
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              <p>
                <s xml:id="echoid-s370" xml:space="preserve">Exempli gratia, cum ſuperfuerint .128. hæc ſi cum ſecundo numero
                  <reg norm="nempe" type="context">nẽpe</reg>
                .272.
                  <lb/>
                iunxerimus, dabunt .400. quorum radix erit .20. de quo numero detracto primo
                  <lb/>
                propoſito, nempe .12. ſupererunt .8. quorum
                  <reg norm="dimidium" type="context">dimidiũ</reg>
                erit .4. quo ex .20. detracto
                  <lb/>
                aut coniuncto .12. maior numerus orietur.</s>
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              <p>
                <s xml:id="echoid-s371" xml:space="preserve">Cuius rei contemplatio, præcedenti figura aperitur. </s>
                <s xml:id="echoid-s372" xml:space="preserve">Nam reſiduum detractionis
                  <lb/>
                quadrati
                  <var>.m.e.</var>
                ex ſumma
                  <reg norm="duorum" type="context">duorũ</reg>
                quadratorum
                  <var>.r.c.</var>
                et
                  <var>.g.s.</var>
                numerum præbet æqua-
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                lem duobus ſupplementis
                  <var>.q.n.</var>
                et
                  <var>.n.u.</var>
                ex .8. ſecundi Euclidis. qui coniunctus duo-
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                bus quadratis (quorum ſumma ſecundo propoſita fuit) cognitionem profert qua-
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                drati
                  <var>.q.u.</var>
                & eius radicis
                  <var>.q.p.</var>
                de qua, detracto primo dato numero, ſcilicet
                  <var>.q.i.</var>
                ſu-
                  <lb/>
                pereſt
                  <var>.i.p.</var>
                cuius dimidium nempe
                  <var>.g.p.</var>
                minor eſt numerus qui quęritur; </s>
                <s xml:id="echoid-s373" xml:space="preserve">reſiduum
                  <lb/>
                verò totius
                  <var>.g.q.</var>
                maior ſcilicet.</s>
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            <div xml:id="echoid-div92" type="math:theorem" level="3" n="43">
              <head xml:id="echoid-head59" xml:space="preserve">THEOREMA
                <num value="43">XLIII</num>
              .</head>
              <p>
                <s xml:id="echoid-s374" xml:space="preserve">CVR ij, qui volunt duos numeros inuenire, quorum ſumma æqualis propo-
                  <lb/>
                fito alicui numero futura ſit, & ſumma quadratorum maior eorum produ-
                  <lb/>
                cto per quantitatem alterius propoſiti numeri, rectè dimidium primi dati numeri in
                  <lb/>
                ſeipſum multiplicant, quod quadratum ex
                  <reg norm="ſecundo" type="context">ſecũdo</reg>
                dato numero detrahunt, ſumunt­
                  <lb/>
                q́ue tertię partis refidui quadratam radicem, quam dimidio primi numeri coniun-
                  <lb/>
                gunt, ex quo maior numerus
                  <reg norm="duorum" type="context">duorũ</reg>
                  <reg norm="quæſitorum" type="context">quæſitorũ</reg>
                datur, quo ex toto primo detracto, ſu-
                  <lb/>
                pererit minor.</s>
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              <p>
                <s xml:id="echoid-s375" xml:space="preserve">Exempli gratia, propoſito numero .20. cui æquanda eſt ſumma duorum nume-
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                rorum quæſitorum,
                  <reg norm="datoque" type="simple">datoq́;</reg>
                ſecundo numero .208. qui ſemper maior eſſe debet </s>
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