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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[1.] IO. BAPTISTAE BENEDICTI PATRITII VENETI SERENISS. CAR. EM. ALLOBROGVM DVCIS PHILOSOPHI. Theoremata Arithmetica.
[2.] DE RATIONIBVS OPERATIONVM PERSPECTIVAE.
[2.1.] CAP.I.
[2.2.] CAP. II.
[2.3.] CAP. III.
[2.4.] CAP. IIII.
[2.5.] CAP.V.
[2.6.] CAP. VI.
[2.7.] CAP. VII.
[2.8.] CAP. VIII.
[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.
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              <head xml:id="echoid-head214" style="it" xml:space="preserve">Quod Aristo. in prima mechanicarum quæstionum eius quod
                <lb/>
              inquir it, uer am cauſam non attulerit.</head>
              <head xml:id="echoid-head215" xml:space="preserve">CAP. XI.</head>
              <p>
                <s xml:id="echoid-s1823" xml:space="preserve">QVærens Ariſtoteles vnde fiat, vt eæ libræ, quæ brachia habent alijs longiora,
                  <lb/>
                ſint exactiores cæteris, ait hoc euenire ratione maioris velocitatis extremo
                  <lb/>
                rum earundem. </s>
                <s xml:id="echoid-s1824" xml:space="preserve">Quod verum non eſt; </s>
                <s xml:id="echoid-s1825" xml:space="preserve">quia hîc effectus nil aliud eſt, quam clarius pro
                  <lb/>
                ponere ob omnium oculos obliquitatem brachiorum à linea orizontali, & oſtende-
                  <lb/>
                re etiam facilius à dicto orizontali ſitu exire brachia iam dicta. </s>
                <s xml:id="echoid-s1826" xml:space="preserve">Quæ quidem per ſe
                  <lb/>
                neque à velocitate, neque à tarditate motus, ſed à ratione vectis, & à ma-
                  <lb/>
                iori interuallo inter ſecundum ſitum extremorum à primo proficiſcuntur. </s>
                <s xml:id="echoid-s1827" xml:space="preserve">Vt exem-
                  <lb/>
                pli gratia, imaginemur magnam libram
                  <var>.A.B.</var>
                orizontalem, cuius centrum ſit
                  <var>.E.</var>
                et
                  <lb/>
                pondus
                  <var>.B.</var>
                maius ſit pondere ipſius
                  <var>.A.</var>
                vnde conceditur, quòd ob hanc rationem di-
                  <lb/>
                cta libra ſitum mutabit, qui ſecundus ſitus ſit in
                  <var>.H.F</var>
                . </s>
                <s xml:id="echoid-s1828" xml:space="preserve">Imaginemur etiam
                  <reg norm="paruam" type="context">paruã</reg>
                  <reg norm="quan- dam" type="context">quã-
                    <lb/>
                  dam</reg>
                libram
                  <var>.a.e.b.</var>
                orizontalem, quæ pondera habeat
                  <var>.a.</var>
                et
                  <var>.b.</var>
                æqualia duobus ponde
                  <lb/>
                ribus alterius libræ & ſecundus ſitus ſit in
                  <var>.h.f.</var>
                ita tamen vt anguli circa
                  <var>.e.</var>
                æquales
                  <lb/>
                ſint ijs, qui ſunt circa
                  <var>.E.</var>
                ideſt
                  <var>.b.e.f.</var>
                ſit ęqualis
                  <var>.B.E.F</var>
                . </s>
                <s xml:id="echoid-s1829" xml:space="preserve">Nunc dico ſitum
                  <var>.H.F.</var>
                  <reg norm="exa- ctiorem" type="context">exa-
                    <lb/>
                  ctiorẽ</reg>
                futurum & clariorem ſitu
                  <var>.h.e.f.</var>
                ratione interualli
                  <var>.B.F.</var>
                maioris, interuallo
                  <var>.
                    <lb/>
                  b.f.</var>
                quod
                  <var>.B.F.</var>
                in eadem proportione maior eſt ipſo
                  <var>.b.f.</var>
                in qua
                  <var>.B.E.</var>
                maius eſt
                  <var>.b.e.</var>
                  <lb/>
                quod autem interuallum
                  <var>.B.F.</var>
                breuiori, aut longiori temporis ſpacio quam
                  <var>.b.f.</var>
                ſit fa
                  <lb/>
                ctum, nil planè refert. </s>
                <s xml:id="echoid-s1830" xml:space="preserve">Ratione vectis deinde, dico
                  <reg norm="quod" type="simple">ꝙ</reg>
                ſi ſupponemus duas libras pa-
                  <lb/>
                res
                  <reg norm="æqualesque" type="simple">æqualesq́;</reg>
                in omni alio reſpectu, præter quàm in brachiorum longitudine, pon-
                  <lb/>
                dus
                  <var>.B.</var>
                maiorem vim habebit ad deprimendum brachium
                  <var>.E.B.</var>
                quàm pondus
                  <var>.b.</var>
                quia
                  <lb/>
                libræ materiales, cum ſuſtineantur ab
                  <var>.E.e.</var>
                & non à puncto mathematico, ſed
                  <lb/>
                à linea, aut ſuperficie naturali in materia exiſtente. </s>
                <s xml:id="echoid-s1831" xml:space="preserve">vnde aliqua reſiſtentia ipſi mo-
                  <lb/>
                tui brachiorum oritur, & hanc ob cauſam, ſupponendo hanc reſiſtentiam æqualem
                  <lb/>
                tam in
                  <var>.E.</var>
                quàm in
                  <var>.e.</var>
                clarum erit ob ea, quæ in cap .4. huius tractatus oſtendi
                  <var>.B.</var>
                cum
                  <lb/>
                minus dependeat ab
                  <var>.E.</var>
                aut minus quoque eidem
                  <var>.E.</var>
                annitatur, ponderoſum magis
                  <lb/>
                futurum, quam
                  <var>.b.</var>
                & hac de cauſa mouebit ad partem inferiorem, maiori cum agilita
                  <lb/>
                te, brachium
                  <var>.E.B.</var>
                multo magis etiam illud ipſum deprimet, ideſt maiorem etiam an
                  <lb/>
                gulum
                  <var>.B.E.F.</var>
                quàm erit angulus
                  <var>.b.e.f.</var>
                faciet.</s>
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