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

< >
[2.9.] CAP. IX.
[2.10.] CAP.X.
[2.11.] CAP. XI. ALITER IDEM.
[2.12.] JACOBO SOLDATO MEDIOLANENSI Serenißimi Ducis Sabaudiæ Architecto peritißimo. CAP. VII.
[2.13.] AD EVNDEM IACOBVM. CAP. XIII.
[2.14.] CAP. XIIII.
[2.15.] CAP. XV.
[3.] DE MECHANICIS.
[3.1.] De differentia ſitus brachiorum libra. CAP.I.
[3.2.] De proportione ponderis extremitatis brachij libr & in diuerſo ſitu ab orizontali. CAP. II.
[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.
[3.4.] Quemadmodum exſupradictis cauſis omnes staterarum & uectium cauſæ dependeant. CAP. IIII.
[3.5.] De quibuſdam rebus animaduerſione dignis. CAP.V.
[3.6.] De ratione cuiuſdam uis adauctæ. CAP. VI.
[3.7.] De quibuſdam erroribus Nicolai Tartaleæ circa pondera corporum & eorum motus, quorum aliqui deſumpti fuerunt à fordano ſcriptore quodam antiquo. CAP. VII.
[3.8.] CAP. VIII.
[3.9.] Quòdſummaratione ſtateræper æqualia interualla ſint diuiſæ. CAP. IX.
[3.10.] Quòd line a circularis non habe at concauum cum con-uexo coniunctum, & quod Aristo. cir caproportio nes motuum aberrauerit. CAP.X.
[3.11.] Quod Aristo. in prima mechanicarum quæstionum eius quod inquir it, uer am cauſam non attulerit. CAP. XI.
[3.12.] De uer a cauſa ſecundæ, & tertiæ quæstionis mechanicæ ab Ariſtotele nonperſpecta. CAP. XII.
[3.13.] Quòd Ariſtotelisratio in 6. quæſtione poſit a non ſit admittenda. CAP. XIII.
[3.14.] Quòdrationes ab Ariſtotele de octaua quæstione confictæ ſufficient es non ſint. CAP. XIIII.
[3.15.] Quod Aristotelis ratio none queſtionis admittendanon ſit. CAP. XV.
[3.16.] Quod Aristotelis rationes de decima queſtione ſint reijciende. CAP. XVI.
[3.17.] De uer a cauſa .12. questionis mechanice. CAP. XVII.
[3.18.] De decimatertia questione. CAP. XVIII.
[3.19.] De decimaquart a queſtione. CAP. XIX.
[3.20.] De uer a r atione .17. queſtionis. CAP. XX.
[3.21.] De uera & intrinſeca cauſa trocble arum. CAP. XXI.
[3.22.] Depropria cauſa .24. quæſtionis. CAP. XXII.
< >
page |< < (176) of 445 > >|
    <echo version="1.0">
      <text type="book" xml:lang="la">
        <div xml:id="echoid-div7" type="body" level="1" n="1">
          <div xml:id="echoid-div387" type="chapter" level="2" n="4">
            <div xml:id="echoid-div407" type="section" level="3" n="12">
              <p>
                <s xml:id="echoid-s2088" xml:space="preserve">
                  <pb o="176" rhead="IO. BAPT. BENED." n="188" file="0188" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0188"/>
                ſed proportio
                  <var>.p.f.</var>
                ad
                  <var>.q.i.</var>
                maior eſſet ea, quæ eſt
                  <var>.c.f.</var>
                ad
                  <var>.q.i.</var>
                ex. octaua lib. quinti, vn-
                  <lb/>
                de ex .12. eiuſdem lib. maior eſſet
                  <var>.p.f.</var>
                ad
                  <var>.q.i.</var>
                quàm.o.f. ad
                  <var>.n.i.</var>
                ex .33. igitur eiuſdem,
                  <lb/>
                maior erit proportio
                  <var>.p.o.</var>
                ad
                  <var>.q.n.</var>
                quàm.p.f. ad
                  <var>.q.i</var>
                . </s>
                <s xml:id="echoid-s2089" xml:space="preserve">Sic quoque ſe habebunt ad inui
                  <lb/>
                cem velocitates, quod eſt propoſitum. </s>
                <s xml:id="echoid-s2090" xml:space="preserve">Cum autem proportio
                  <var>.p.o.</var>
                ad
                  <var>.q.n.</var>
                maior ſit,
                  <lb/>
                quàm.p.f. ad
                  <var>.q.i.</var>
                permurando igitur maior erit proportio
                  <var>.p.o.</var>
                ad
                  <var>.p.f.</var>
                quam
                  <var>.q.n.</var>
                ad
                  <var>.
                    <lb/>
                  q.i.</var>
                aut euerſim maior erit proportio
                  <var>.q.i.</var>
                ad
                  <var>.q.n.</var>
                quàm.p.f. ad
                  <var>.p.o.</var>
                vnde ſi proportio
                  <lb/>
                  <var>p.f.</var>
                ad
                  <var>.p.o.</var>
                eſſet ac ea, quæ eſt
                  <var>.o.g.</var>
                ad
                  <var>.f.g.</var>
                non eſſet
                  <var>.q.i.</var>
                ad
                  <var>.q.n.</var>
                ut eſt
                  <var>.o.g.</var>
                ad
                  <var>.f.g.</var>
                aut
                  <lb/>
                vt
                  <var>.n.k.</var>
                ad
                  <var>.i.k.</var>
                quodidem
                  <lb/>
                eſt, de quibus quidem re-
                  <lb/>
                  <figure xlink:label="fig-0188-01" xlink:href="fig-0188-01a" number="254">
                    <image file="0188-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0188-01"/>
                  </figure>
                bus, exemplis propoſitis
                  <lb/>
                quinto capite
                  <reg norm="mentionem" type="context">mẽtionem</reg>
                  <lb/>
                feci.</s>
              </p>
              <p>
                <s xml:id="echoid-s2091" xml:space="preserve">Velocitatibus autem ſe-
                  <lb/>
                quentibus pondera, ſequi
                  <lb/>
                tur proportionem veloci-
                  <lb/>
                citatum duorum corporum hetereogeneorum eandem non eſſe per diuerſa media,
                  <lb/>
                contra id, quod ſequeretur ſi Ariſtotelis opinionem .8. cap. lib. 4. phyſicorum re-
                  <lb/>
                ciperemus.</s>
              </p>
            </div>
            <div xml:id="echoid-div409" type="section" level="3" n="13">
              <head xml:id="echoid-head267" style="it" xml:space="preserve">Longe aliter ueritatem ſe habere quam Aristoteles
                <lb/>
              doceat in fine libri ſeptimi phyſicorum.</head>
              <head xml:id="echoid-head268" xml:space="preserve">CAP. XIII.</head>
              <p>
                <s xml:id="echoid-s2092" xml:space="preserve">NOn tam facile eſt aſſignare proportionem velocitatum duorum corporum na
                  <lb/>
                turalium, quam Ariſtoteles vltimo cap. lib. 7. phyſicorum putauit.</s>
              </p>
              <p>
                <s xml:id="echoid-s2093" xml:space="preserve">Quamobrem ſint duo corpora
                  <var>.B.</var>
                et
                  <var>.D.</var>
                materia
                  <reg norm="magnitudineque" type="simple">magnitudineq́;</reg>
                diuerſa, pondere
                  <lb/>
                tamen, & figura ſimilia, & proportio reſiſtentiarum, quas recipiunt à medio
                  <reg norm="dum" type="context">dũ</reg>
                mo-
                  <lb/>
                uentur, ſit. ut
                  <var>.o.i.</var>
                ad
                  <var>.a.e.</var>
                denotentur deinde velocitates totales abſque vlla reſiſten-
                  <lb/>
                tia ab
                  <var>.a.u.</var>
                et
                  <var>.o.c.</var>
                quæ æquales erunt ad inuicem per communem ſcientiam ex ſup-
                  <lb/>
                poſito, ſint alia deinde duo corpora
                  <var>.V.</var>
                et
                  <var>.M.</var>
                eodem modo ſe habentia ut prima
                  <var>.B.</var>
                  <lb/>
                et
                  <var>.D.</var>
                in eodem medio, ſed ex diuerſa materia ab ea, quæ eſt illorum duorum corpo
                  <lb/>
                rum, magnitudine tamen & figura ijſdem ſimilia: </s>
                <s xml:id="echoid-s2094" xml:space="preserve">ſignificentur quoque eo-
                  <lb/>
                rundem reſiſtentiæ per
                  <var>.t.s.</var>
                et
                  <var>.n.r.</var>
                & eorundem velocitates à nulla ex reſiſtentijs di-
                  <lb/>
                minutæ, per
                  <var>.n.x.</var>
                et
                  <var>.t.g.</var>
                vnde
                  <var>.n.r.</var>
                æqualis erit
                  <var>.a.e.</var>
                et
                  <var>.t.s.</var>
                ipſi
                  <var>.o.i.</var>
                et
                  <var>.n.x.</var>
                ipſi
                  <var>.t.g</var>
                :
                  <var>n.x.</var>
                ta-
                  <lb/>
                men et
                  <var>.t.g.</var>
                non erunt ęqualia
                  <var>.a.u.</var>
                et
                  <var>.o.c</var>
                . </s>
                <s xml:id="echoid-s2095" xml:space="preserve">Sed exempli gratia, ponamus ea eſſe mi-
                  <lb/>
                nora. </s>
                <s xml:id="echoid-s2096" xml:space="preserve">Supponamus nunc
                  <var>.e.u.</var>
                velocitatem eſſe quæ remanet ipſi
                  <var>.B.</var>
                cum applicata
                  <lb/>
                erit reſiſtentia
                  <var>.a.e.</var>
                dicto corpori
                  <var>.B.</var>
                quæ diminutam facit totam
                  <var>.a.u.</var>
                per
                  <var>.a.e.</var>
                  <reg norm="ſitque" type="simple">ſitq́;</reg>
                  <var>.i.c.</var>
                  <lb/>
                ea, quę remanet ipſi
                  <var>.o.c.</var>
                corporis
                  <var>.D.</var>
                et
                  <var>.r.x.</var>
                ea, quæ remanet
                  <var>.n.x.</var>
                corporis
                  <var>.V.</var>
                et
                  <var>.s.g.</var>
                  <lb/>
                ea, quæ eſt ex
                  <var>.t.g.</var>
                corporis
                  <var>.M</var>
                . </s>
                <s xml:id="echoid-s2097" xml:space="preserve">Vnde communi omnium
                  <reg norm="conſenſu" type="context">cõſenſu</reg>
                aſſequemur
                  <var>.e.u.</var>
                ma
                  <lb/>
                iorem futuram
                  <var>.r.x.</var>
                et
                  <var>.i.c.</var>
                ipſa
                  <var>.s.g</var>
                . </s>
                <s xml:id="echoid-s2098" xml:space="preserve">Scindatur deinde
                  <var>.a.m.</var>
                ad ęqualitatem
                  <var>.n.x.</var>
                et
                  <var>.o.z.</var>
                  <lb/>
                ipſius
                  <var>.t.g.</var>
                vnde
                  <var>.a.m.</var>
                ad
                  <var>.o.z.</var>
                et
                  <var>.m.u.</var>
                ad
                  <var>.z.c.</var>
                æquales habebimus, ut quoque
                  <var>.e.m.</var>
                ad
                  <var>.r.
                    <lb/>
                  x.</var>
                et
                  <var>.i.z.</var>
                ad
                  <var>.s.g.</var>
                quamobrem
                  <var>.e.m.</var>
                maior erit ipſa
                  <var>.z.i.</var>
                maior igitur erit proportio
                  <var>.z.c.</var>
                  <lb/>
                ad
                  <var>.z.i.</var>
                quàm.m.u. ad
                  <var>.m.e.</var>
                (quia
                  <var>.z.c.</var>
                ad
                  <var>.z.i.</var>
                ita ſe habet vt
                  <var>.m.u.</var>
                ad
                  <var>.i.z.</var>
                ex .7. lib. quin-
                  <lb/>
                ti, ſed
                  <var>.m.u.</var>
                ad
                  <var>.i.z.</var>
                maior eſt quam ad
                  <var>.m.e.</var>
                ex .8. dicti lib. vnde ex .12. eiuſdem
                  <var>.z.c.</var>
                ad
                  <lb/>
                ad
                  <var>.z.i.</var>
                maior erit, quàm.m.u. ad
                  <var>.m.e</var>
                . </s>
                <s xml:id="echoid-s2099" xml:space="preserve">Ergo ex .28. maior proportio erit
                  <var>.c.i.</var>
                ad
                  <var>.z.i.</var>
                </s>
              </p>
            </div>
          </div>
        </div>
      </text>
    </echo>