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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IO. BAPT. BENED.
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              <p>
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                  <reg norm="primum" type="context">primũ</reg>
                  <reg norm="reſiduum" type="context">reſiduũ</reg>
                . </s>
                <s xml:id="echoid-s963" xml:space="preserve">Ad hæc
                  <reg norm="numerum" type="context">numerũ</reg>
                  <reg norm="milliariorum" type="context">milliariorũ</reg>
                , quæ
                  <reg norm="ſecundus" type="context">ſecũdus</reg>
                viator die
                  <reg norm="ſeqennti" type="context">ſeqẽnti</reg>
                  <var>.s.f.</var>
                confi
                  <lb/>
                ciet
                  <reg norm="ſumatur" type="simple">ſumat̃</reg>
                , ex quo numerus
                  <reg norm="milliarium" type="context">milliariũ</reg>
                  <reg norm="diurnorum" type="context">diurnorũ</reg>
                primi detrahatur,
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                pariter re
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                ſeruetur,
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                ſecundum reſiduum, poſtmodum numerum milliarium primi
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                vnius diei multiplicetur per primum reſiduum ſeruatum,
                  <reg norm="productumque" type="simple">productumq́;</reg>
                per
                  <reg norm="ſecundum" type="context">ſecundũ</reg>
                  <lb/>
                reſiduum diuidatur
                  <var>.a.c.</var>
                  <reg norm="proueniens" type="context">proueniẽs</reg>
                (
                  <reg norm="quod" type="simple">ꝙ</reg>
                erit iter primi in ſequenti die) iungatur reſi-
                  <lb/>
                ſiduo primo, tot enim erunt milliaria conficienda a ſecundo ſequenti die, vt
                  <lb/>
                ſeſe conſequantur.</s>
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                <figure xlink:label="fig-0083-02" xlink:href="fig-0083-02a">
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              <p>
                <s xml:id="echoid-s964" xml:space="preserve">Vtautem ſciamus quantam partem diei
                  <reg norm="ſeqenntis" type="context">ſeqẽntis</reg>
                , ſingulos itinere agere oporteat,
                  <lb/>
                  <reg norm="proueniens" type="context">proueniẽs</reg>
                per .24. horas multiplicetur (ſuppoſito quod
                  <reg norm="ambulantes" type="context">ambulãtes</reg>
                  <reg norm="nullam" type="context">nullã</reg>
                  <reg norm="requiem" type="context">requiẽ</reg>
                nec
                  <lb/>
                die nec nocte
                  <reg norm="capiant" type="context">capiãt</reg>
                ),
                  <reg norm="productumque" type="simple context simple">ꝓductũq́;</reg>
                  <reg norm="per" type="simple">ꝑ</reg>
                  <reg norm="numerum" type="context">numerũ</reg>
                milliariorum vuius diei primi viatoris di
                  <lb/>
                uidatur, ex quo dabitur
                  <reg norm="quantitas" type="context">quãtitas</reg>
                  <reg norm="horarum" type="context">horarũ</reg>
                , & pars horæ, qua
                  <reg norm="cuique" type="simple">cuiq;</reg>
                illa die
                  <reg norm="ambulandum" type="context">ambulandũ</reg>
                  <lb/>
                eſt. </s>
                <s xml:id="echoid-s965" xml:space="preserve">Idem accideret ſi primum reſiduum reſeruatum cum proueniente in ſummam
                  <lb/>
                colligeretur,
                  <reg norm="eaque" type="simple">eaq́;</reg>
                ſumma per .24. horas multiplicaretur,
                  <reg norm="productumque" type="simple">productumq́;</reg>
                per
                  <reg norm="nume- rum" type="context">nume-
                    <lb/>
                  rũ</reg>
                milliariorum ſequenti die à ſecundo conficiendorum diuideretur. </s>
                <s xml:id="echoid-s966" xml:space="preserve">I dipſum quo-
                  <lb/>
                que eueniret multiplicato primo reſiduo per .24. & producto per ſecundum reſi-
                  <lb/>
                duum diuiſo.</s>
              </p>
              <p>
                <s xml:id="echoid-s967" xml:space="preserve">Exempli gratia, primus viator diurna milliaria vndecim conficit, ſecundus, pri-
                  <lb/>
                ma die tria, ſecunda .6. tertia .9.
                  <reg norm="atque" type="simple">atq;</reg>
                ita deinceps, diuidatur ergo .11. per .3. vnde
                  <lb/>
                pro numero
                  <var>.o.n.</var>
                dabitur .3.
                  <reg norm="ſupereritque" type="simple">ſupereritq́;</reg>
                .2. </s>
                <s xml:id="echoid-s968" xml:space="preserve">quare:
                  <var>u.n.</var>
                ab
                  <var>.e.n.</var>
                duobus milliaribus ſu-
                  <lb/>
                perabitur, et
                  <var>.i.t.</var>
                dictum
                  <var>.e.n.</var>
                vno milliario, ex quo ante diem
                  <var>.e.u.n.</var>
                duobus diebus
                  <lb/>
                iter egerunt,
                  <reg norm="totque" type="simple">totq́;</reg>
                diebus ambulandum erit poſt
                  <var>.t.i.</var>
                hoceſt .6. in vniuerſum inte-
                  <lb/>
                gris. </s>
                <s xml:id="echoid-s969" xml:space="preserve">Ad hęc multiplicato
                  <var>.o.f.</var>
                hoc eſt .6. per
                  <var>.x.o.</var>
                hoc eſt .3. habebimus
                  <var>.s.f.</var>
                  <reg norm="milliariorum" type="context">milliariorũ</reg>
                  <lb/>
                18.
                  <reg norm="tum" type="context">tũ</reg>
                  <reg norm="coniuncto" type="context context">cõiũcto</reg>
                  <var>.x.o.</var>
                primo termino hoc eſt .3.
                  <reg norm="cum" type="context">cũ</reg>
                  <var>.s.f.</var>
                hoc eſt .18. vltimo termino, habe
                  <lb/>
                bimus .21. quo multiplicato
                  <reg norm="cum" type="context">cũ</reg>
                dimidio
                  <var>.o.f.</var>
                hoc eſt .3. habebimus totam ſummam
                  <lb/>
                progreſſionis .63. ſex dierum integrorum ex .94. theoremate, tum multiplicato .11.
                  <lb/>
                nempe numero
                  <reg norm="milliariorum" type="context">milliariorũ</reg>
                diurnorum primi cum .6. hoc eſt cum
                  <var>.o.f.</var>
                habebimus pa
                  <lb/>
                rallelogrammum à primo ſex diebus integris confectum milliariorum .66. ex quo
                  <lb/>
                detracta .63. ſumma inquam progreſſionis, ſupererit pro primo reſiduo .3. ſumptis
                  <lb/>
                poſtea milliaribus .21. pro itinere, quod ſecundus die ſequenti
                  <var>.s.f.</var>
                conficeret, & ex
                  <lb/>
                ijs detracto numero
                  <reg norm="milliariorum" type="context">milliariorũ</reg>
                diurnorum primi, nempe .11. ſecundum reſiduum
                  <lb/>
                erit 10. quod pro diuidenti ſeruabitur. </s>
                <s xml:id="echoid-s970" xml:space="preserve">Iam multiplicato .11. cum primo reſiduo
                  <num value="3">.
                    <lb/>
                  3.</num>
                dabitur .33. qui diuiſus per .10. ſecundum reſiduum profert .3. cum tribus decimis,
                  <lb/>
                  <reg norm="eritque" type="simple">eritq́</reg>
                iter à primo viatore ſequenti die conficiendum, hoc etiam ipſum proueniens
                  <lb/>
                cum primo reſiduo .3. coniunctum, dat .6. cum tribus decimis, quod eſt iter ſecundi
                  <lb/>
                viatoris illa ſequenti die. </s>
                <s xml:id="echoid-s971" xml:space="preserve">Ad inueniendam autem quantitatem diei, qua vtrique
                  <lb/>
                ambulandum eſt, perinde erit multiplicare proueniens .3. & tres decimas per .24. ho
                  <lb/>
                ras, & productum per .11. dimidium iter primi viatoris partiri, ac multiplicare ſum
                  <lb/>
                mam .6. & tres decimas cum .24. horis,
                  <reg norm="productumque" type="simple">productumq́</reg>
                diuidere per .21. hoc eſt periter
                  <lb/>
                ſecundi viatoris ſequentis diei, vtrinque enim ſemper ſeptem horæcum .12. minu
                  <lb/>
                tis prouenient. </s>
                <s xml:id="echoid-s972" xml:space="preserve">Idipſum accidet multiplicato per .24. horas primo reſiduo .3. pro-
                  <lb/>
                  <reg norm="ductoque" type="simple">ductoq́;</reg>
                diuiſo per ſecundum reſiduum .10.</s>
              </p>
              <p>
                <s xml:id="echoid-s973" xml:space="preserve">Quarum ſpeculationum gratia, totum iter parallelogrammi primi viatoris die-
                  <lb/>
                rum integrorum fignificetur linea
                  <var>.n.e.</var>
                ſumma verò progreſſionis ſecundi linea
                  <var>.f.m.</var>
                  <lb/>
                parallela
                  <var>.n.e.</var>
                  <reg norm="eritque" type="simple">eritq́;</reg>
                  <var>.f.m.</var>
                minor
                  <var>.n.e</var>
                . </s>
                <s xml:id="echoid-s974" xml:space="preserve">Conſtituamus deinde à termino
                  <var>.f.n.</var>
                (majoris
                  <lb/>
                  <reg norm="intelligentię" type="context">intelligẽtię</reg>
                gratia) vtranque
                  <reg norm="perpendiculariter" type="context">perpẽdiculariter</reg>
                duci,
                  <reg norm="producatur" type="simple">ꝓducatur</reg>
                deinde
                  <var>.n.e.</var>
                donec
                  <var>.e.
                    <lb/>
                  d.</var>
                æqualis ſit itineri diurno primi viatoris, item etiam producatur
                  <var>.f.m.</var>
                donec
                  <var>.m.K.</var>
                  <lb/>
                æqualis ſit itineri à ſecundo confecto ſequenti die vltimum integrum progreſſio- </s>
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