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]

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            <div xml:id="echoid-div214" type="math:theorem" level="3" n="113">
              <pb o="74" rhead="IO. BAPT. BENED." n="86" file="0086" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0086"/>
              <p>
                <s xml:id="echoid-s988" xml:space="preserve">Exempli gratia, ſi primus octo diebus antequam ſecundus iter arripuiſſet, con-
                  <lb/>
                  <reg norm="feciſſetque" type="simple">feciſſetq́;</reg>
                fingulis diebus .20. milliaria, tum ſecundus .25. quotidie perfeciſſet, mul
                  <lb/>
                tiplicandus eſſet numerus .8. cum .20. ex quo darentur .160. milliaria à primo ſolo
                  <lb/>
                  <reg norm="ambulante" type="context">ambulãte</reg>
                confecta, quibus diuiſis per .5. differentiam motuum diurnorum, daretur
                  <num value="32">.
                    <lb/>
                  32.</num>
                numerus quæſitus dierum.</s>
              </p>
              <p>
                <s xml:id="echoid-s989" xml:space="preserve">Cuius ratio apertiſſima eſt. </s>
                <s xml:id="echoid-s990" xml:space="preserve">Sint enim duo rectanguli
                  <var>.a.n.</var>
                et
                  <var>.u.i.</var>
                æquales inter
                  <lb/>
                ſe, quibus motus itinerarium ſignificentur, quorum
                  <var>.a.n.</var>
                ſit primi, et
                  <var>.u.i.</var>
                ſecundi, præ
                  <lb/>
                tereà.
                  <var>a.c.</var>
                numerum milliarium diurnorum primi .et
                  <var>.u.e.</var>
                ſecundi, ex quo
                  <var>.a.c.</var>
                minor
                  <lb/>
                erit
                  <var>.u.e.</var>
                per
                  <var>.o.e.</var>
                atque ita
                  <var>.o.e.</var>
                co-
                  <lb/>
                gnoſcetur. </s>
                <s xml:id="echoid-s991" xml:space="preserve">Tum
                  <var>.c.o.</var>
                numerum
                  <reg norm="dierum" type="context">dierũ</reg>
                  <lb/>
                  <figure xlink:label="fig-0086-01" xlink:href="fig-0086-01a" number="118">
                    <image file="0086-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0086-01"/>
                  </figure>
                primi ſoli iter agentis denotet,
                  <reg norm="cumque" type="context simple">cũq;</reg>
                  <lb/>
                conſtituamus
                  <var>.a.n.</var>
                æqualem eſſe
                  <var>.u.i.
                    <lb/>
                  o.i.</var>
                ęqualis erit
                  <var>.o.a.</var>
                atque
                  <var>.o.a.</var>
                cogni
                  <lb/>
                tus ex ſuis producentibus
                  <var>.a.c.</var>
                et
                  <var>.c.o.</var>
                  <lb/>
                itaque
                  <var>.o.i.</var>
                etiam cognitus, qui diui-
                  <lb/>
                ſus per latus cognitum
                  <var>.o.e.</var>
                dabit
                  <var>.e.
                    <lb/>
                  i.</var>
                cognitum numerum ſcilicet dierum, quibus ſecundo ambulandum eſt, vt primum
                  <lb/>
                conſequatur.</s>
              </p>
              <head xml:id="echoid-head131" xml:space="preserve">APPENDIX THEOREM. CXIII.</head>
              <p>
                <s xml:id="echoid-s992" xml:space="preserve">AB hoc theoremate ſumpſi ordinem illius operationis, numeris mediantibus, ad
                  <lb/>
                inueniendam exactam temporis quantitatem, ſeu interuallum,
                  <reg norm="quod" type="simple">ꝙ</reg>
                tranſit, vel in
                  <lb/>
                tercedit inter vnam mediocrem coniunctionem & aliam proximam
                  <reg norm="ſequentem" type="context">ſequentẽ</reg>
                duo
                  <lb/>
                rum planetarum, vt patet in epiſtola noſtra ad Illuſtrem Bernardum Trottum con-
                  <lb/>
                tra Benedictum Altauillam repræhenſorem Ephemeridum. </s>
                <s xml:id="echoid-s993" xml:space="preserve">Verum tamen eſt
                  <reg norm="quod" type="simple">ꝙ</reg>
                  <lb/>
                cum praxis huiuſmodi theorematis ſit multiplex, viſum fuit vnam proponere, quę
                  <lb/>
                non ita perſpicua ſit, ſed ſubobſcura, non quòd aliquid voluerim latere illum ami
                  <lb/>
                cum mihi dilectiſſimum, cui priuatim omnes modos prius oſtenderam, ſed vt cere-
                  <lb/>
                brum illius mei aduerſarij in laberintum conijcerem inextricabilem vt feci, quam-
                  <lb/>
                uis modus ille egregius etiam ſit, vt nunc oſtendam.</s>
              </p>
              <p>
                <s xml:id="echoid-s994" xml:space="preserve">In dicta epiſtola igitur mente cogitaui medium motum tardioris planetæ, pu-
                  <lb/>
                ta ſaturni, illius temporis quo velocior planeta, ſcilicet Iupiter, percurrit ſuo medio
                  <lb/>
                motu totum zodiacum, incipiendo ambo eodem temporis puncto, nec non ab vna
                  <lb/>
                eorum media coniunctione, hoc eſt ab eodem zodiaci puncto, in quo coniunctę fue
                  <lb/>
                runt eorum lineæ mediorum motuum, vbi inueni vi regulæ de tribus, quòd Satur
                  <lb/>
                nus ſpacio dierum vnius mediocris reuolutionis Iouis, qui ſunt .4328. progreditur
                  <lb/>
                medio motu gra .145. min .4. hoc eſt min .8704. pofito quòd ipſe Saturnus perficiat
                  <lb/>
                vnam mediam reuolutionem ſpacio dierum .10740. vt dixi. </s>
                <s xml:id="echoid-s995" xml:space="preserve">Incipiendo igitur ite
                  <lb/>
                rum Iupiter aliam reuolutionem percurrere, reperto Saturno per min .8704. ante
                  <lb/>
                ipſum ſpacio .4328. dierum, certus eram hos dies ſignificatos eſſe à linea
                  <var>.a.u.</var>
                vel
                  <var>.c.
                    <lb/>
                  o.</var>
                (æquales enim inuicem ſunt) in figura huiuſmodi theorematis, & quòd rectangu
                  <lb/>
                lum
                  <var>.a.o.</var>
                præbebat ſummam graduum .145. min .4. hoc eſt min .8704. et quòd
                  <var>.a.c.</var>
                  <lb/>
                vel
                  <var>.o.u.</var>
                ſignificabat iter vnius diei ipſius Saturni, et
                  <var>.u.e.</var>
                iter vnius diei Iouis. </s>
                <s xml:id="echoid-s996" xml:space="preserve">Cogi-
                  <lb/>
                temus nunc
                  <var>.u.x.</var>
                ſignificari dies .30. & à puncto
                  <var>.x.</var>
                productam eſſe
                  <var>.x.f.</var>
                parallelam ipſi
                  <lb/>
                  <var>u.o.e.</var>
                vnde certi erimus rectangulum
                  <var>.e.x.</var>
                ſignificare iter Ionis ſpacio temporis die-
                  <lb/>
                rum .30. rectangulum verò
                  <var>.o.x.</var>
                iter Saturni eodem temporis interuallo, vnde rectan­ </s>
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