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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[3.3.] Quòd quantit as cuiuſlibet ponderis, aut uirtus mouens re-ſpectu alterius quantitatis cognoſcatur beneficio perpendicularium ductarum à centro libr & ad line am inclinationis. CAP. III.
Page: 155 (143)
[3.4.] Quemadmodum exſupradictis cauſis omnes staterarum & uectium cauſæ dependeant. CAP. IIII.
Page: 156 (144)
[3.5.] De quibuſdam rebus animaduerſione dignis. CAP.V.
Page: 157 (145)
[3.6.] De ratione cuiuſdam uis adauctæ. CAP. VI.
Page: 158 (146)
[3.7.] De quibuſdam erroribus Nicolai Tartaleæ circa pondera corporum & eorum motus, quorum aliqui deſumpti fuerunt à fordano ſcriptore quodam antiquo. CAP. VII.
Page: 160 (148)
[3.8.] CAP. VIII.
Page: 161 (149)
[3.9.] Quòdſummaratione ſtateræper æqualia interualla ſint diuiſæ. CAP. IX.
Page: 163 (151)
[3.10.] Quòd line a circularis non habe at concauum cum con-uexo coniunctum, & quod Aristo. cir caproportio nes motuum aberrauerit. CAP.X.
Page: 164 (152)
[3.11.] Quod Aristo. in prima mechanicarum quæstionum eius quod inquir it, uer am cauſam non attulerit. CAP. XI.
Page: 165 (153)
[3.12.] De uer a cauſa ſecundæ, & tertiæ quæstionis mechanicæ ab Ariſtotele nonperſpecta. CAP. XII.
Page: 166 (154)
[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)
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                <s xml:id="echoid-s1909" xml:space="preserve">Sit exempli gratia libra
                  <var>.a.i.e.</var>
                quæ in vtraque extremitate vnciam vnam ſolum
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                ponderis obtineat, & ſit libra
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                æqualis priori, quæ pro ſingula extremitate
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                <s xml:id="echoid-s1910" xml:space="preserve">Ariſtoteles admiratur, quòd addendo ipſi
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                mediam pon
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                deris vnciam, brachium
                  <var>.i.e.</var>
                velocius cadat, quàm
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                  <reg norm="ipsam" type="context">ipsã</reg>
                  <reg norm="mediam" type="context">mediã</reg>
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                ipſi
                  <var>.u.</var>
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                brachij
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                <s xml:id="echoid-s1911" xml:space="preserve">Quod à duabus cauſis proficiſcitur, quarum prior eſt, magna differentia
                  <lb/>
                proportionis vnius libræ ad medietatem vnius vnciæ, ad proportionem vnius vnciæ
                  <lb/>
                ad ipſam medietatem, quia ſi pondus adiectum extremo
                  <var>.u.</var>
                dimidiæ eſſet libræ , &
                  <lb/>
                cum eadem tarditate brachium moueret, optimo iure in admirationem poſſet Ari-
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                ſtoteles duci. </s>
                <s xml:id="echoid-s1912" xml:space="preserve">Sed hoc fieri non poſſet, quia ipſum deprimeret cum eadem quaſi ve
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                locitate, qua media vncia brachium
                  <var>.i.e</var>
                . </s>
                <s xml:id="echoid-s1913" xml:space="preserve">Dixi autem quaſi, quia nonnihil diſcrimi-
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                nis intercederet, quod proficiſcitur à ſecunda ratione. </s>
                <s xml:id="echoid-s1914" xml:space="preserve">Et hæc, reſiſtentia eſt , quæ
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                oritur à ſparto, quia quantò maius pondus continet libra, tantò magis præmit ſpar
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                tum in loco, in quo ſuſtinetur; </s>
                <s xml:id="echoid-s1915" xml:space="preserve">vnde maior reſiſtentia in circunuolutione
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                ſpar
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                ti, in loco, in quo quieſcit, exoritur, quia ipſum eſt corpus materiale. </s>
                <s xml:id="echoid-s1916" xml:space="preserve">Si quis autem
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                eadem agilitate, qua
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                deſcenderet, oporteret, vt propor-
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                tio dimidiæ librę adiectæ ponderi ipſius
                  <var>.u.</var>
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                quod eſt vnius libræ, vim ſuam haberet,
                  <lb/>
                quæ excederet reſiſtentiam ſui ſparti (me-
                  <lb/>
                dio brachiorum maiorum ijs qui ſunt
                  <var>.a.i.
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                  e.</var>
                ) ita proportionatam, vt proportionata
                  <lb/>
                eſt vis dimidiæ vnciæ ipſi e. iunctæ, reſiſten
                  <lb/>
                tiæ ſui ſparti. </s>
                <s xml:id="echoid-s1917" xml:space="preserve">Huiuſmodi rationes cum ro-
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                tis grauioribus
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                , & ijs, quę à cor
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                lectum confirmabunt.</s>
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              <head xml:id="echoid-head226" style="it" xml:space="preserve">De uer a cauſa .12. questionis mechanice.</head>
              <head xml:id="echoid-head227" xml:space="preserve">CAP. XVII.</head>
              <p>
                <s xml:id="echoid-s1918" xml:space="preserve">VEra ratio, cur multò longius corpus aliquod graue impellatur funda, quam
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                manu, inde oritur, quòd circunuoluendo fundam, maior impræſſio impetus
                  <lb/>
                motus fit in corpore graui, quàm fieret manu, quod corpus liberatum deinde cum
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                fuerit à funda, natura duce, iter
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                à puncto, à quo proſilijt, per lineam contiguam
                  <lb/>
                giro, quem poſtremò faciebat, ſuſcipit. </s>
                <s xml:id="echoid-s1919" xml:space="preserve">
                  <reg norm="Dubitandumque" type="simple">Dubitandumq́</reg>
                non eſt, quin dicta funda
                  <lb/>
                maior impetus motus dicto corpori imprimi poſſit,
                  <reg norm="cum" type="context">cũ</reg>
                ex multis circumactibus, ma-
                  <lb/>
                ior ſemper impetus dicto corpori accedat. </s>
                <s xml:id="echoid-s1920" xml:space="preserve">Manus autem eiuſdem corporis motus,
                  <lb/>
                dum illud ipſum circunuoluitur (pace Ariſtotelis dixerim) centrum non eſt, neque
                  <lb/>
                funis eſt ſemidiameter. </s>
                <s xml:id="echoid-s1921" xml:space="preserve">Immo manus quam maximè fieri poteſt in orbem cietur;
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                <s xml:id="echoid-s1922" xml:space="preserve">qui quidem motus in orbem, vt circumagatur etiam ipſum corpus, cogit, quod qui-
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                dem corpus, naturali quadam inclinatione, exiguo quodam impetu iam incępto,
                  <lb/>
                vellet recta iter peragere, vt in ſubſcripta figura patet, in qua
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                ſignificat manum
                  <var>.a.</var>
                  <lb/>
                corpus
                  <var>.a.b.</var>
                lineam rectam tangentem girum
                  <var>.a.a.a.a.</var>
                quando corpus liberum rema-
                  <lb/>
                net. </s>
                <s xml:id="echoid-s1923" xml:space="preserve">Verum quidem eſt, impręſſum illum impetum, continuò paulatim decreſcere
                  <lb/>
                vnde ſtatim inclinatio grauitatis eiuſdem corporis ſubingreditur, quæ ſeſe miſcens
                  <lb/>
                cum impręſſione facta per vim, non permittit, vt linea
                  <var>.a.b.</var>
                longo tempore recta per </s>
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