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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                    <pb o="8" rhead="IO. BAPT. BENED." n="20" file="0020" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0020"/>
                  n.c.</var>
                ad
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                ſint æquales inuicem quandoqui-
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                dem vnaquæque earum ex triangulorum ſimi
                  <lb/>
                litudine æqualis eſt proportioni
                  <var>.o.n.</var>
                ad
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                .
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                <s xml:id="echoid-s108" xml:space="preserve">itaque
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                  <var>.a.x.</var>
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                quanto
                  <var>.n.c.</var>
                maior eſt
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                vnde ficut
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                con-
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                ſtat octo nonis ipſius
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                ita pars
                  <var>.a.x.</var>
                ipſius
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                    <lb/>
                  a.e.</var>
                octo nonis conſtabit ipſius
                  <var>.a.i</var>
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              <p>
                <s xml:id="echoid-s109" xml:space="preserve">Hinc patet ratio cur partituri numerum mino
                  <lb/>
                rem per maiorem collocent minorem fupra
                  <lb/>
                virgulam & maiorem infra & zerum ad
                  <reg norm="læuam" type="context">læuã</reg>
                .</s>
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              <p>
                <s xml:id="echoid-s110" xml:space="preserve">Sciendum eſt præterea diuidere numerum
                  <lb/>
                per numerum: </s>
                <s xml:id="echoid-s111" xml:space="preserve">eſſe inuenire
                  <reg norm="alterum" type="context">alterũ</reg>
                latus à quo
                  <lb/>
                producitur, ſuppoſito ſemper quòd numerus
                  <lb/>
                diuifibilis ſuperſicialis ſit, & rectangulus.</s>
              </p>
              <p>
                <s xml:id="echoid-s112" xml:space="preserve">Exempli gratia, ſi proponantur triginta diuidenda per quinarium, nihil aliud erit
                  <lb/>
                hæc diuiſio, quam inuentio alterius numeri, qui multiplicatus per quinarium produ-
                  <lb/>
                cat triginta ſuperficies rectangulas, huiuſmodi verò eſt ſenarius, cuius ſingulæ vnita-
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                tes ſuperficiales erunt.</s>
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              <p>
                <s xml:id="echoid-s113" xml:space="preserve">Cuius rei gratia ſit ſubſcriptum rectangulum
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                triginta vnitatum
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                ,
                  <lb/>
                cuius latus
                  <var>.e.n.</var>
                ſit quinque vnitatum. </s>
                <s xml:id="echoid-s114" xml:space="preserve">hinc latus
                  <var>.a.n.</var>
                erit ſex vnitatum; </s>
                <s xml:id="echoid-s115" xml:space="preserve">ita diuiden-
                  <lb/>
                tes rectangulum
                  <var>.e.a.</var>
                nihil a iud faciemus, quam vt inue-
                  <lb/>
                  <figure xlink:label="fig-0020-02" xlink:href="fig-0020-02a" number="15">
                    <image file="0020-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0020-02"/>
                  </figure>
                nia mus quantum valeat latus
                  <var>.a.n.</var>
                quod erit ſex vnitatum.
                  <lb/>
                </s>
                <s xml:id="echoid-s116" xml:space="preserve">Sin verò diuiſerimus per latus
                  <var>.a.n.</var>
                quæremus latus
                  <var>.e.n.</var>
                  <lb/>
                quinque vnitatum. </s>
                <s xml:id="echoid-s117" xml:space="preserve">ex quo, proportio totius numeri diuifi-
                  <lb/>
                bilis ad numerum qui oritur, erit ſicut diuidentis ad vnita-
                  <lb/>
                tem, ex prima ſexti, aut .18. vel .19. ſeptimi, & permutatim
                  <lb/>
                ita ſe habebit diuiſibile ad diuidentem, ſicut numerus qui
                  <lb/>
                oritur ad vnitatem.</s>
              </p>
              <p>
                <s xml:id="echoid-s118" xml:space="preserve">Partiri igitur nihil aliud eſt, quam inuenire latus rectanguli, quod productum in
                  <lb/>
                diuidente, numerum diuiſibilem compl at, ex quo numerus diuiſibilis ſuperficialis
                  <lb/>
                eſt, diuidens autem, & qui oritur, numeri lineares & latera producentia huiuſcemodi
                  <lb/>
                numerum diuiſibilem. </s>
                <s xml:id="echoid-s119" xml:space="preserve">nam multiplicare & diuidere opponuntur inuicem, cum au-
                  <lb/>
                tem ex multiplicatione laterum ſiue linearum generatur ſuperficies, ex diuiſione po-
                  <lb/>
                ſtea ipſius ſuperficiei inuenitur alterum latus. </s>
                <s xml:id="echoid-s120" xml:space="preserve">quare mirum non eſt, ſi proueniens ex
                  <lb/>
                vna diuiſione (via fractorum) ſit ſemper maius numero diuiſibili.</s>
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              <p>
                <s xml:id="echoid-s121" xml:space="preserve">Exempli gratia, diuidendo dimidium per tertiam partem, reſultat vnus integer nu
                  <lb/>
                merus cum dimidio pro numero qui oritur. </s>
                <s xml:id="echoid-s122" xml:space="preserve">Sit itaque dimidium ſuperſiciale diuiſi-
                  <lb/>
                bile
                  <var>.b.c.</var>
                cuius totum ſit
                  <var>.b.p.</var>
                quadratum. </s>
                <s xml:id="echoid-s123" xml:space="preserve">tertium verò lineare diuidens,
                  <var>b.n.</var>
                cuius to-
                  <lb/>
                tum lineare ſit
                  <var>.b.d.</var>
                quærendum nobis eſt latus
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                quod cum latere
                  <var>.b.n.</var>
                producat re
                  <lb/>
                ctangulum
                  <var>.n.s.</var>
                æquale dimidio ſuperſiciali propoſito
                  <var>.b.c.</var>
                quod ſi ſiat, ex .15. ſexti,
                  <lb/>
                aut .20. ſeptimi. erit eadem proportio
                  <var>.b.n.</var>
                ad
                  <var>.b.q.</var>
                quæ eſt
                  <var>.q.c.</var>
                ad
                  <var>.b.s.</var>
                dicemus itaque
                  <lb/>
                ſi
                  <var>.n.b.</var>
                dat
                  <var>.b.q.</var>
                quid dabit
                  <var>.q.c</var>
                ? </s>
                <s xml:id="echoid-s124" xml:space="preserve">certè
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                ſed
                  <var>.n.b.</var>
                eſt tertium lineare et
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                lineare
                  <reg norm="in- tegrum" type="context">in-
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                  tegrũ</reg>
                , &
                  <var>b.s.</var>
                proueniens lineare. </s>
                <s xml:id="echoid-s125" xml:space="preserve">& quia
                  <var>.b.c.</var>
                dimidium ſuperficiale, producitur à
                  <var>.q.c.</var>
                  <lb/>
                dimidio lineari in
                  <var>.q.b.</var>
                integro lineari. </s>
                <s xml:id="echoid-s126" xml:space="preserve">quare cum
                  <var>.n.s.</var>
                ſit ęqualis
                  <var>.b.c.</var>
                & productum ex
                  <var>.
                    <lb/>
                  b.n.</var>
                minori
                  <var>.q.c.</var>
                neceſſe eſt, vt producatur in
                  <var>.b.s.</var>
                maiore
                  <var>.q.b.</var>
                quod
                  <var>.q.b.</var>
                maius eſt
                  <var>.q.c.</var>
                  <lb/>
                quod quidem
                  <var>.q.c.</var>
                ita appellatur ſicut
                  <var>.b.c</var>
                . </s>
                <s xml:id="echoid-s127" xml:space="preserve">quare mirum non eſt ſi proueniens per fra-
                  <lb/>
                ctos numeros ex diuiſione, maior ſit numero diuiſibili.</s>
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