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]

Page concordance

< >
Scan Original
81 71
82 70
83 71
84 72
85 73
86 74
87 75
88 76
89 77
90 78
91 79
92 80
93 81
94 82
95 89
96 84
97 85
98 96
99 87
100 88
101 89
102 90
103 91
104 92
105 93
106 94
107 95
108 96
109 97
110 98
< >
page |< < (76) 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-div7" type="chapter" level="2" n="1">
            <div xml:id="echoid-div217" type="math:theorem" level="3" n="114">
              <p>
                <s xml:id="echoid-s1007" xml:space="preserve">
                  <pb o="76" rhead="IO. BAPT. BENED." n="88" file="0088" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0088"/>
                Taurino Patauium .220. quæ quiſque confecerit.</s>
              </p>
              <p>
                <s xml:id="echoid-s1008" xml:space="preserve">Dum autem hæc ſpecularer attentius, occurrit alius ſoluendi modus, quamuis pro
                  <lb/>
                lixior. </s>
                <s xml:id="echoid-s1009" xml:space="preserve">Is
                  <reg norm="autem" type="wordlist">aũt</reg>
                eſt eiuſmodi. </s>
                <s xml:id="echoid-s1010" xml:space="preserve">
                  <reg norm="Accipiatur" type="simple">Accipiat̃</reg>
                medietas minoris numeri
                  <reg norm="dierum" type="context">dierũ</reg>
                ,
                  <reg norm="nempe" type="context">nẽpe</reg>
                .4.
                  <reg norm="cum" type="context">cũ</reg>
                dimi
                  <lb/>
                dio, & per .400. multiplicetur,
                  <reg norm="productumque" type="context simple">productũq́;</reg>
                per
                  <reg norm="maiorem" type="context">maiorẽ</reg>
                numerum diuidemus ſcilicet
                  <lb/>
                11. ex quo dabuntur .163. cum .7. vndecimis, quo proueniente è dimidio
                  <reg norm="millia- riorum" type="context">millia-
                    <lb/>
                  riorũ</reg>
                itineris .200. detracto, &
                  <reg norm="preſiduum" type="context">preſiduũ</reg>
                  <reg norm="nempe" type="context">nẽpe</reg>
                .36.
                  <reg norm="cum" type="context">cũ</reg>
                .4. vndecimis multiplicato pro
                  <lb/>
                  <reg norm="ductoque" type="simple">ductoq́;</reg>
                diuiſo
                  <reg norm="per" type="simple">ꝑ</reg>
                  <reg norm="ſummam" type="context">ſummã</reg>
                dimidij itineris .200.
                  <reg norm="cum" type="context">cũ</reg>
                primo
                  <reg norm="prouentu" type="context">prouẽtu</reg>
                .163. et .7. vndecimis
                  <lb/>
                  <reg norm="nempe" type="context">nẽpe</reg>
                  <reg norm="per" type="simple">ꝑ</reg>
                .363. ct .7. vndecimas partes
                  <reg norm="proueniet" type="simple">ꝓueniet</reg>
                .16.
                  <reg norm="cum" type="context">cũ</reg>
                .4. vndecimis, quo
                  <reg norm="coniuncto" type="context">cõiuncto</reg>
                pri
                  <lb/>
                mo
                  <reg norm="prouenienti" type="simple context">ꝓueniẽti</reg>
                , primus .180. milliaria
                  <reg norm="confecerit" type="context">cõfecerit</reg>
                , quæ è .400. detracta ſupererunt .220.
                  <lb/>
                pro itinere ſecundi, qui .9. diebus iter abſoluit. </s>
                <s xml:id="echoid-s1011" xml:space="preserve">Ad hæc ſi tempus ſcire velimus
                  <lb/>
                eius, qui .11. diebus appellit, multiplicabimus .11. cum .180.
                  <reg norm="productumque" type="simple">productumq́;</reg>
                per .400.
                  <lb/>
                partiemur,
                  <reg norm="prouenientque" type="simple">prouenientq́;</reg>
                paulominus, quam quinque dies, nempe .4. cum .22. horis
                  <lb/>
                et .48. minutis, quod tempus vtrique viatori inſeruiet, quandoquidem idipſum pro
                  <lb/>
                uenit multiplicato .220. per .9.
                  <reg norm="productoque" type="simple">productoq́;</reg>
                per .400. diuiſo.</s>
              </p>
              <p>
                <s xml:id="echoid-s1012" xml:space="preserve">Huius autem, qui à me pręſcribitur modi, ſpeculatio talis eſt. </s>
                <s xml:id="echoid-s1013" xml:space="preserve">Duo termini duabus
                  <lb/>
                rectis lineis æqualibus, & parallelis inter ſe
                  <var>.b.p.</var>
                et
                  <var>.d.q.</var>
                ſignificentur, quæ alijs dua-
                  <lb/>
                bus
                  <var>.b.d.</var>
                et
                  <var>.q.p.</var>
                  <reg norm="coniungantur" type="simple">coniungant̃</reg>
                , quę parallelæ & æquales erunt ex .33. primi, quibus ſigni
                  <lb/>
                ficentur duo itinera. </s>
                <s xml:id="echoid-s1014" xml:space="preserve">Viator primus quidem lentior à. b in
                  <var>.d.</var>
                velocior à
                  <var>.q.</var>
                in
                  <var>.p</var>
                . </s>
                <s xml:id="echoid-s1015" xml:space="preserve">Iam
                  <lb/>
                ſumatur
                  <reg norm="punctum" type="context">punctũ</reg>
                medium
                  <var>.q.p.</var>
                  <reg norm="ſitque" type="simple">ſitq́;</reg>
                  <var>.k.</var>
                & ab ipſo ad
                  <var>.b.d.</var>
                ducatur
                  <var>.k.i.</var>
                parallela
                  <var>.d.q.</var>
                aut
                  <lb/>
                  <var>b.p.</var>
                quod idem eſt, ex quo
                  <var>.b.i.</var>
                æqualis erit
                  <var>.p.k.</var>
                ex .34. primi, hoc eſt
                  <var>.q.k.</var>
                  <reg norm="certique" type="simple">certiq́;</reg>
                eri-
                  <lb/>
                mus primum viatorem
                  <var>.q.p.</var>
                in dimidio itineris
                  <var>.q.k.</var>
                occurrere non potuiſſe viatori ip
                  <lb/>
                ſius
                  <var>.b.i.</var>
                quandoquidem eo tempore, quo is, qui ipſius
                  <var>.q.p.</var>
                mouetur per
                  <var>.q.k.</var>
                (cum ſit
                  <lb/>
                altero velocior) qui per
                  <var>.b.d.</var>
                nondum peruenerit ad .i: Sit itaque punctum
                  <var>.c.</var>
                in quo
                  <lb/>
                lentior reperitur, dum velocior eſt in
                  <var>.k.</var>
                ex quo certi erimus eos inter
                  <var>.c.</var>
                et
                  <var>.i.</var>
                ſibi in-
                  <lb/>
                uicem obuiaturos eſſe. </s>
                <s xml:id="echoid-s1016" xml:space="preserve">Cogito deinde rectam lineam ductam
                  <var>.k.c.</var>
                & ut ſe habet
                  <var>.i.
                    <lb/>
                  c.</var>
                ad
                  <var>.c.b.</var>
                ita cogito ſe habere. u
                  <unsure/>
                  <var>.k.</var>
                ad
                  <var>.k.q.</var>
                & à puncto
                  <var>.u.</var>
                ad
                  <var>.i.</var>
                duco
                  <var>.u.i.</var>
                quæ, vt manife
                  <lb/>
                ſtum eſt, lineam
                  <var>.k.c.</var>
                in puncto
                  <var>.e.</var>
                interſecabit, à quo cum fuerit ducta
                  <var>.e.o.n.</var>
                parallela
                  <lb/>
                  <var>k.i.</var>
                habebimus
                  <var>.o.n.</var>
                ea ſcilicet puncta, quibus occurrunt ſibijpſis, nam cum ſic ſe ha
                  <lb/>
                beat
                  <var>.q.k.</var>
                ad
                  <var>.k.u.</var>
                vt
                  <var>.b.c.</var>
                ad
                  <var>.c.i.</var>
                et
                  <var>.k.u.</var>
                ad
                  <var>.k.n.</var>
                vt
                  <var>.c.i.</var>
                ad
                  <var>.c.o.</var>
                ex ſimilitudine manifeſta
                  <lb/>
                triangulorum, ex æqualitate proportionum ſic ſe habebit
                  <var>.q.k.</var>
                ad
                  <var>.k.n.</var>
                vt
                  <var>.b.c.</var>
                ad
                  <var>.c.o.</var>
                  <lb/>
                & permutando ita
                  <var>.k.q.</var>
                ad
                  <var>.b.c.</var>
                vt
                  <var>.k.n.</var>
                ad
                  <var>.c.o.</var>
                & cum
                  <var>.q.k.</var>
                et
                  <var>.b.c.</var>
                ſpatia ſint tempori-
                  <lb/>
                bus æqualibus confecta, itaque ſpatia
                  <var>.k.n.</var>
                et
                  <var>.c.o.</var>
                ex communi ſcientia temporibus
                  <lb/>
                æqualibus conficientur.</s>
              </p>
              <p>
                <s xml:id="echoid-s1017" xml:space="preserve">Quare rectè dicimus, ſi tot diebus à
                  <var>.b.</var>
                in
                  <var>.d.</var>
                aliquis peruenit, quot milliaria in di
                  <lb/>
                midio temporis alterius viatoris idem conficiet? </s>
                <s xml:id="echoid-s1018" xml:space="preserve">ex quo ex regula de tribus quam
                  <lb/>
                primum iter
                  <var>.b.c.</var>
                cognoſcitur, quo ex dimidio itineris detracto, remanet
                  <var>.c.i.</var>
                cogni
                  <lb/>
                tus, ſed cum probauerimus
                  <var>.q.k.</var>
                ad
                  <var>.k.n.</var>
                hoc eſt
                  <var>.i.o.</var>
                (cum ſint æquales inter ſe, ex .34
                  <lb/>
                primi) ita ſe habere. vt
                  <var>.b.c.</var>
                ad
                  <var>.c.o.</var>
                permutando ſic ſe habebit
                  <var>.q.k.</var>
                ad
                  <var>.b.c.</var>
                vt
                  <var>.i.o.</var>
                ad
                  <var>.
                    <lb/>
                  o.c.</var>
                &
                  <reg norm="componendo" type="context">cõponendo</reg>
                  <var>.q.k.</var>
                et
                  <var>.b.c.</var>
                ad
                  <var>.b.c.</var>
                vt
                  <var>.i.c.</var>
                ad
                  <var>.c.o.</var>
                </s>
                <s xml:id="echoid-s1019" xml:space="preserve">quare rectè dicimus ſi ſumma
                  <var>.q.
                    <lb/>
                  k.</var>
                cum
                  <var>.b.c.</var>
                dat
                  <var>.b.c.</var>
                quid dabit
                  <var>.i.c</var>
                ? </s>
                <s xml:id="echoid-s1020" xml:space="preserve">nempe dabit
                  <var>.c.o.</var>
                quo coniuncto cum
                  <var>.b.c.</var>
                cogno-
                  <lb/>
                ſcitur
                  <var>.b.o.</var>
                quo
                  <var>.b.o.</var>
                detracto ex
                  <var>.b.d.</var>
                remanet cognitus
                  <var>.o.d.</var>
                nempe
                  <var>.q.n.</var>
                illi æqualis
                  <lb/>
                ex .34. prædicta. </s>
                <s xml:id="echoid-s1021" xml:space="preserve">Gratia verò
                  <reg norm="temporis" type="context">tẽporis</reg>
                patet nos rectè dicere ſi
                  <var>.b.d.</var>
                tot diebus abſolui
                  <lb/>
                tur, aut etiam
                  <var>.q.p</var>
                : quo
                  <var>.b.o.</var>
                aut
                  <var>.q.n.</var>
                abſoluetur.</s>
              </p>
              <p>
                <s xml:id="echoid-s1022" xml:space="preserve">Vt autem ad ſpeculationem regulæ antiquorum deueniamus, cogitemus pri-
                  <lb/>
                mum viatorem ipſius
                  <var>.q.p.</var>
                velociorem eo, qui per
                  <var>.b.d.</var>
                iter agit, tanto tempore præ
                  <lb/>
                tergredi
                  <var>.p.</var>
                quanto alter
                  <var>.b.d.</var>
                abſoluit. </s>
                <s xml:id="echoid-s1023" xml:space="preserve">Is autem ad
                  <var>.g.</var>
                pertingat, ex quo eadem pro-
                  <lb/>
                portio ſpacij
                  <var>.q.g.</var>
                ad
                  <var>.q.p.</var>
                hoc eſt
                  <var>.b.d.</var>
                dabitur, quæ temporis quo
                  <var>.b.d.</var>
                abſoluitur ab </s>
              </p>
            </div>
          </div>
        </div>
      </text>
    </echo>
Impressum