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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[2.8.] CAP. VIII.
Page: 140 (128)
[2.9.] CAP. IX.
Page: 141 (129)
[2.10.] CAP.X.
Page: 142 (130)
[2.11.] CAP. XI. ALITER IDEM.
Page: 143 (131)
[2.12.] JACOBO SOLDATO MEDIOLANENSI Serenißimi Ducis Sabaudiæ Architecto peritißimo. CAP. VII.
Page: 145 (133)
[2.13.] AD EVNDEM IACOBVM. CAP. XIII.
Page: 149 (137)
[2.14.] CAP. XIIII.
Page: 150 (138)
[2.15.] CAP. XV.
Page: 152 (140)
[3.] DE MECHANICIS.
Page: 153 (141)
[3.1.] De differentia ſitus brachiorum libra. CAP.I.
Page: 153 (141)
[3.2.] De proportione ponderis extremitatis brachij libr & in diuerſo ſitu ab orizontali. CAP. II.
Page: 154 (142)
[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)
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                <s xml:id="echoid-s1325" xml:space="preserve">Quapropter non tacebo quod mihi in mentem venit circa hoc problema.</s>
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              <p>
                <s xml:id="echoid-s1326" xml:space="preserve">Sit ergo linea
                  <var>.a.b.</var>
                diuiſibilis in puncto
                  <var>.c.</var>
                ita vt cubum totius dictæ
                  <var>.a.b.</var>
                lineæ ad
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                ſummam cuborum
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                partium
                  <var>.a.c.</var>
                et
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                exempli gratia, vt .125. ad .65. vt vitemus fracta pro nunc, notantes talem propor-
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                tionem quadrupla nunquam maiorem eſſe poſſe, vt quilibet ex ſe contemplari po-
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                teſt, conſtituendo punctum
                  <var>.c.</var>
                in medio loco inter
                  <var>.a.</var>
                et
                  <var>.b.</var>
                vnde proportio totalis
                  <lb/>
                cubi ad ſummam partialium eſſet omnium maxima quæ poſſint eſſe, collocando
                  <var>.c.</var>
                  <lb/>
                vbi volueris in dicta linea
                  <var>.a.b.</var>
                & hæc eſſet quadrupla.</s>
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              <p>
                <s xml:id="echoid-s1327" xml:space="preserve">Sed vt ad propoſitum reuertamur, conſiderabimus cubum totalem ipſius
                  <var>.a.b.</var>
                  <lb/>
                eſſe vt .125. & ſummam partialium vt .65. quam detrahemus ex cubo totali & nobis
                  <lb/>
                remanebit .60. pro ſumma trium ſolidorum inuicem æqualium, quorum longitu-
                  <lb/>
                do vniuſcuiuſque erit tota linea
                  <var>.a.b.</var>
                nobis cognita vt radix dati cubi totalis, quæ erit
                  <lb/>
                in hoc exemplo quinque partium, latitudo verò vniuſcuiuſque dictorum
                  <reg norm="ſolidorum" type="context">ſolidorũ</reg>
                  <lb/>
                erit
                  <var>.a.c.</var>
                pars maior ipſius
                  <var>.a.b.</var>
                quæ quidem
                  <var>.a.c.</var>
                adhuc nobis ignota eſt, profunditas
                  <lb/>
                ſeu altitudo vniuſcuiuſque illorum ſolidorum, erit
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                pars reliqua ipſius
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                &
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                nobis incognita, ſed quia ſumma horum trium ſolidorum nobis manifeſta ſuperius
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                fuit, quæ erat .60. propterà nobis cognita erit quantitas vniuſcuiuſque illorum ſoli-
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                dorum, vt tertia pars totius ſummæ ipſorum quæ erit .20. in propoſito
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                , dein
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                de cum vnumquodque illorum ſolidorum producatur à ſuperficie contenta ſeu pro
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                ducta ab
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                in
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                in tota linea
                  <var>.a.b.</var>
                ſequitur quòd ſi diuiſerimus hoc ſolidum .20.
                  <lb/>
                per lineam
                  <var>.a.b.</var>
                quinque partium proueniet nobis cognita ſuperficies producta ab
                  <var>.
                    <lb/>
                  a.c.</var>
                in
                  <var>.c.b.</var>
                quatuor partium, ſed cum quadratum totius
                  <var>.a.b.</var>
                nobis cognitum ſit, eo
                  <lb/>
                quod
                  <var>.a.b.</var>
                vt eius latus etiam cognitum eſt. </s>
                <s xml:id="echoid-s1328" xml:space="preserve">Tunc dictum quadratum erit .25. quod
                  <lb/>
                quidem æquale eſt quadruplo illius quod fit ex
                  <var>.a.c.</var>
                in
                  <var>.c.b.</var>
                ſimul cum quadrato diffe
                  <lb/>
                rentiæ inter
                  <var>.a.c.</var>
                et
                  <var>.c.b.</var>
                per .8. ſecundi Eucli. </s>
                <s xml:id="echoid-s1329" xml:space="preserve">Vnde quia quadruplum illius quod fit
                  <lb/>
                ex
                  <var>.a.c.</var>
                in
                  <var>.c.b.</var>
                nobis cognitum eſt, vt
                  <lb/>
                16. eo quod ſimplum quod eſt .4.
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                inuentum fuit, ideo ſi hoc quadru-
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                plum .16. demptum fuerit ex totali
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                quadrato .25. reliquum erit .9. qua
                  <lb/>
                  <reg norm="dratum" type="context">dratũ</reg>
                ſcilicet vnius partis
                  <var>.a.c.</var>
                ipſius
                  <lb/>
                hoc eſt illius partis, quæ differentia
                  <lb/>
                eſt inter
                  <var>a.c.</var>
                et
                  <var>.c.b.</var>
                quæ quidem erit
                  <num value="3">.
                    <lb/>
                  3.</num>
                partium quæ differentia cum ſub-
                  <lb/>
                tracta fuerit ex
                  <var>.a.b.</var>
                reliquum erit du
                  <lb/>
                plum ipſius
                  <var>.c.b.</var>
                duo ſcilicet. </s>
                <s xml:id="echoid-s1330" xml:space="preserve">Quare
                  <var>.
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                  c.b.</var>
                erit vt
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                et
                  <var>.a.c.</var>
                vt .4. & productum
                  <var>.a.c.</var>
                in
                  <var>.c.b.</var>
                erit .4. vnitatum ſuperficialium.
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                <s xml:id="echoid-s1331" xml:space="preserve">& c.</s>
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