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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[2.9.] 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)
[3.22.] Depropria cauſa .24. quæſtionis. CAP. XXII.
Page: 177 (165)
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            <div xml:id="echoid-div413" type="section" level="3" n="17">
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              <p>
                <s xml:id="echoid-s2126" xml:space="preserve">Quod in vniuerſum nec etiam poteſt eſſe verum in pleno, quia cap .14. iam pro-
                  <lb/>
                baui, non eandem proportionem eſſe inter ſuperſicies corporum, & ipſa corpora.</s>
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            <div xml:id="echoid-div414" type="section" level="3" n="18">
              <head xml:id="echoid-head277" style="it" xml:space="preserve">Quomodo dignoſcatur proportio uelocitatis duorum ſimilium
                <lb/>
              corporum omogeniorum inaqualium.</head>
              <head xml:id="echoid-head278" xml:space="preserve">CAP. XVIII.</head>
              <p>
                <s xml:id="echoid-s2127" xml:space="preserve">ETiam ſi reperire in qua proportione motus naturaliter moueantur duo corpo-
                  <lb/>
                ra, figura & materia ſimilia, inęqualia tamen ad inuicem, non facile ſit, oſten-
                  <lb/>
                dam tamen qua ratione id conſequi poſſimus.</s>
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              <p>
                <s xml:id="echoid-s2128" xml:space="preserve">Proponantur nobis, exempli gratia, duo corpora
                  <var>.a.</var>
                et
                  <var>.o.</var>
                ſphęrica, inęqualia inui-
                  <lb/>
                cem, omogenea tamen materia, quorum
                  <var>.a.</var>
                maius ſit; </s>
                <s xml:id="echoid-s2129" xml:space="preserve">ſi voluerimus inuenire in qua
                  <lb/>
                nam velocitatis proportione naturaliter mouerentur. </s>
                <s xml:id="echoid-s2130" xml:space="preserve">Volo vt inquiratur corpus
                  <var>.i.</var>
                  <lb/>
                ſphęricum, alia tamen & diuerſa materia conſtans, ſed pondere ęquale corpori
                  <var>.o.</var>
                &
                  <lb/>
                ſuperſicie tam proportionata ſuperficiei corp oris
                  <var>.a.</var>
                quàm eſt ea, quæ eſt ſui ponde-
                  <lb/>
                ris ad pondus ipſius
                  <var>.a</var>
                . </s>
                <s xml:id="echoid-s2131" xml:space="preserve">Hoc facto, indagetur, quænam erit proportio inter ſu-
                  <lb/>
                perficies corporum
                  <var>.i.</var>
                et
                  <var>.o.</var>
                quę ſemper dupla eſt, vel ſubdupla ei quæ eſt diametro-
                  <lb/>
                rum; </s>
                <s xml:id="echoid-s2132" xml:space="preserve">ut iam cap .15. dixi, & hęc proportio ſuperficierum ſphęricarum
                  <reg norm="ipſius" type="simple">ipſiꝰ</reg>
                  <var>.o.</var>
                et
                  <var>.i.</var>
                ſub
                  <lb/>
                trahatur ab æqualitate, quod igitur remanebit, erit proportio
                  <reg norm="velocitatum" type="context">velocitatũ</reg>
                inter duo
                  <lb/>
                corpora
                  <var>.o.</var>
                et
                  <var>.i.</var>
                ideſt inter
                  <var>.o.</var>
                et
                  <var>.a.</var>
                vt exempli gratia, ſi proportio ſuperficiei
                  <var>.o.</var>
                ſuperfi
                  <lb/>
                ciei ipſius
                  <var>.i.</var>
                ſeſquitertiα
                  <unsure/>
                eſſet, ſub
                  <lb/>
                trahendo eam ab ęqualitate, rema-
                  <lb/>
                  <figure xlink:label="fig-0191-01" xlink:href="fig-0191-01a" number="256">
                    <image file="0191-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0191-01"/>
                  </figure>
                neret
                  <reg norm="proportio" type="simple">ꝓportio</reg>
                ſubſeſquitertia, vnde
                  <lb/>
                velocitas corporis maioris ( quod in
                  <lb/>
                pręſenti loco ſupponitur eſſe
                  <var>.o.</var>
                ) ei,
                  <lb/>
                quę eſt corporis minoris, quale eſt
                  <lb/>
                corpus
                  <var>.i.</var>
                ſubſeſquitertia eſſet; </s>
                <s xml:id="echoid-s2133" xml:space="preserve">aut
                  <lb/>
                dicamus quòd
                  <var>.i.</var>
                eſſet velocius ipſo
                  <lb/>
                o. in proportione ſeſquitertia ex ſe
                  <lb/>
                cundo ſuppoſito ſecundi capitis huius libri. </s>
                <s xml:id="echoid-s2134" xml:space="preserve">Sed
                  <var>.i.</var>
                tam velox eſt quam ipſum
                  <var>.a.</var>
                ex
                  <num value="11">.
                    <lb/>
                  11.</num>
                cap. ergo proportio velocitatis ipſius
                  <var>.a.</var>
                ſeſquitertia erit ei. quæ eſt ipſius
                  <var>.o</var>
                .</s>
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            <div xml:id="echoid-div416" type="section" level="3" n="19">
              <head xml:id="echoid-head279" style="it" xml:space="preserve">Quam ſit inanis ab Ariſtotele ſuſcepta demonſtratio quod
                <lb/>
              uacuum non detur.</head>
              <head xml:id="echoid-head280" xml:space="preserve">CAP. XIX.</head>
              <p>
                <s xml:id="echoid-s2135" xml:space="preserve">EX ijs, quæ ſuperius
                  <reg norm="demonſtrauimus" type="context">demõſtrauimus</reg>
                facilè cognoſci poteſt irritam eſſc eam ratio
                  <lb/>
                nem, quam Ariſtoteles .8. cap. lib. 4. phyſicorum ad deſtruendum vacuum,
                  <reg norm="con" type="context">cõ</reg>
                  <lb/>
                finxit. </s>
                <s xml:id="echoid-s2136" xml:space="preserve">Vtigitur idem facilius oſtendamus, compræhendamus imaginatione infini-
                  <lb/>
                ta media corporea, quorum vnum altero rarius ſit, in qua placuerit nobis ex propor
                  <lb/>
                tionibus, incipiendo ab uno, imaginemur etiam corpus
                  <var>.Q.</var>
                denſius primo medio, cu-
                  <lb/>
                ius corporis, totalis grauitas ſit
                  <var>.a.b.</var>
                & poſitum in ipſo medio, amittat partem
                  <var>.e.b.</var>
                ip-
                  <lb/>
                ſius grauitatis, & in ſecundo medio amittat
                  <var>.i.b.</var>
                & ſic per gradus vnde nobis patebie
                  <unsure/>
                </s>
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