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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                <s xml:id="echoid-s334" xml:space="preserve">Hoc ipſum & alia ratione perfici poteſt, nempe, iuncta ſumma
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                <s xml:id="echoid-s335" xml:space="preserve">Michael Stifelius, vndecimo cap. tertij libri, problema eiuſmodi proponit,
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                quod tamen ipſe via algebræ diſsoluit.</s>
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            <div xml:id="echoid-div83" type="math:theorem" level="3" n="38">
              <head xml:id="echoid-head54" xml:space="preserve">THEOREMA
                <num value="38">XXXVIII</num>
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                <s xml:id="echoid-s336" xml:space="preserve">CVR ij, qui duos numeros inuenire volunt, quorum productum alicui nu-
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                mero propoſito æquetur, & quadratorum eorundem differentia alteri nu-
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                mero propoſito æqualis ſir. </s>
                <s xml:id="echoid-s337" xml:space="preserve">Rectè dimidium ſecundi numeri propoſiti in ſeipſum
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                multiplicent, cui quidem numero differentia quadratorum æquari debet; </s>
                <s xml:id="echoid-s338" xml:space="preserve">porrò
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                huic quadrato primi propoſiti numeri, cui æquandum eſt productum numerorum
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                quæſitorum, quadratum adiungant; </s>
                <s xml:id="echoid-s339" xml:space="preserve">tum radicem quadratam huius ſummæ co-
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                pulet dimidio ſecundi numeri propoſiti, ei inquam, cui differentia quadratorum
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                æqualis eſſe debet, ex quo quadratum maius conſurgit, à quo, detracto ſecundo
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                numero, ſupereſt quadratum minus.</s>
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                <s xml:id="echoid-s340" xml:space="preserve">Exempli gratia, ſi proponeretur primo loco numerus .8. cui æquandum eſt
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                productum numerorum quæſitorum, tum proponeretur numerus .12. cui, detra-
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                cto minore à maiore, differentia quadratorum vtriuſque quæſiti numeri æqualis
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                eſſe debet, oportet huius vltimi numeri .12. dimidium in ſeipſum multiplicare,
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                numeri .8. quod eſſet .64. quæ cum .36. efficerent .100. cuius centenarij radice, nem
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                pe .10. collecta in ſummam cum dimidio ſecundi numeri, nempe .6. daretur qua-
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                dratum maius, nempe .16. ex quo, detracto ſecundo numero, nempe .12. rema-
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                neret quadratum minus .4.</s>
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              <p>
                <s xml:id="echoid-s341" xml:space="preserve">Cuius ſpeculationis cauſa, maius quadratum
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                incognitum ſignificetur linea
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                minus verò
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                pariter incognitum linea
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                lum
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                deſignatum, & ita etiam
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                gnomon
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                prout ſexta ſecundi Euclidis pro
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                ponitur, ex quo quadratum
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                nempe
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                co-
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                gnitum erit, ſed gnomon æqualis eſt rectangulo
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                ex prædicta, aut ex .8. poſt .16. </s>
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