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
31 19
32 20
33 21
34 22
35 23
36 24
37 25
38 26
39 27
40 28
41 29
42 30
43 31
44 32
45 33
46 34
47 35
48 36
49 37
50 38
51 39
52 40
53 41
54 42
55 43
56 44
57 45
58 46
59 47
60 48
< >
page |< < (77) 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-s1023" xml:space="preserve">
                  <pb o="77" rhead="THEOREM. ARIT." n="89" file="0089" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0089"/>
                eo qui per
                  <var>.b.d.</var>
                ad tempus quo
                  <var>.q.p.</var>
                ſolum, qui per
                  <var>.q.p.</var>
                mouetur (mo-
                  <lb/>
                tus enim continui regulares & vniformes conſtituuntur) eadem ratione ita-
                  <lb/>
                que ea erit proportio
                  <var>.q.k.</var>
                ad
                  <var>.b.c.</var>
                quæ
                  <var>.q.g.</var>
                ad
                  <var>.q.p.</var>
                & cum probatum
                  <lb/>
                fuerit ita ſe habere
                  <var>.k.n.</var>
                ad
                  <var>.c.o.</var>
                vt
                  <var>.q.k.</var>
                ad
                  <var>.b.c.</var>
                itaque ſic ſe habebit
                  <var>.k.n.</var>
                ad
                  <var>.c.
                    <lb/>
                  o.</var>
                ut
                  <var>.q.g.</var>
                ad
                  <var>.q.p.</var>
                probatum etiam fuit ita ſe habere
                  <var>.q.k.</var>
                ad
                  <var>.k.n.</var>
                vt
                  <var>.b.c.</var>
                ad
                  <var>.c.o.</var>
                ex quo
                  <lb/>
                componendo ſic ſe habebit
                  <var>.q.n.</var>
                ad
                  <var>.n.k.</var>
                vt
                  <var>.b.o.</var>
                ad
                  <var>.o.c.</var>
                & permutando ita
                  <var>.q.n.</var>
                ad
                  <var>.b.
                    <lb/>
                  o.</var>
                vt
                  <var>.k.n.</var>
                ad
                  <var>.c.o.</var>
                hoc eſt
                  <var>.q.g.</var>
                ad
                  <var>.q.p.</var>
                nempe vt tempus lenti ad tempus velocis itine-
                  <lb/>
                rantis, & componendo ita
                  <var>.q.n.</var>
                cum
                  <var>.o.b.</var>
                hoc eſt
                  <var>.b.d.</var>
                ad
                  <var>.b.o.</var>
                vt ſumma
                  <reg norm="dierum" type="context">dierũ</reg>
                vnius &
                  <lb/>
                alterius viatoris ad
                  <reg norm="minorem" type="context">minorẽ</reg>
                  <reg norm="numerum" type="context">numerũ</reg>
                  <reg norm="dierum" type="context">dierũ</reg>
                velocioris. </s>
                <s xml:id="echoid-s1024" xml:space="preserve">Breuiter
                  <reg norm="itaque" type="simple">itaq;</reg>
                obtineremus in
                  <lb/>
                  <reg norm="tentum" type="context">tentũ</reg>
                  <reg norm="quando" type="wordlist">qñ</reg>
                diceremus ſi ſumma dierum, quibus iter agitur à viatoribus talis eſt (20) re-
                  <lb/>
                ſpectu numeri dierum velocioris(9) qualis & cui
                  <reg norm="reſpondebit" type="context">reſpõdebit</reg>
                totum ſpacium
                  <var>.b.d</var>
                ? </s>
                <s xml:id="echoid-s1025" xml:space="preserve">vn-
                  <lb/>
                de dabitur ſpacium
                  <var>.b.o.</var>
                vnde reliqua omnia nobis cognita emergent.</s>
              </p>
              <p>
                <s xml:id="echoid-s1026" xml:space="preserve">Cum autem antiquorum regula iubeat numerum dierum vnius, cum numero die-
                  <lb/>
                rum alterius multiplicari, ac poſtmodum diuidi productum per ſummam omnium
                  <lb/>
                dierum, rectèid quidem fit. </s>
                <s xml:id="echoid-s1027" xml:space="preserve">Nam cum ſic ſe habeat
                  <var>.b.d.</var>
                ad
                  <var>.b.o.</var>
                vt ſumma omnium
                  <lb/>
                dierum ad minorem quantitatem dierum velocioris ſcilicet. </s>
                <s xml:id="echoid-s1028" xml:space="preserve">Ideo temporis propor
                  <lb/>
                tio à mobili per
                  <var>.b.d.</var>
                abſumpti ad tempus mobilis per
                  <var>.b.o.</var>
                eadem erit, quæ ſummæ
                  <lb/>
                omnium dierum ad namerum dierum velocioris. </s>
                <s xml:id="echoid-s1029" xml:space="preserve">Quarerectè dicemus, ſi eiuſmodi
                  <lb/>
                ſumma talem reſpectum habet ad minorem numerum dierum, quem numerum re-
                  <lb/>
                ſpiciet dies ipſius
                  <var>.b.d</var>
                ? </s>
                <s xml:id="echoid-s1030" xml:space="preserve">ex quo proferentur dies reſpondentes ipſi
                  <var>.b.o.</var>
                cætera iam
                  <lb/>
                dicta fuerunt.</s>
              </p>
              <p>
                <s xml:id="echoid-s1031" xml:space="preserve">Huiuſmodi verò ſpeculationis am-
                  <lb/>
                  <figure xlink:label="fig-0089-01" xlink:href="fig-0089-01a" number="120">
                    <image file="0089-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0089-01"/>
                  </figure>
                plitudo ad pauciſſima verba reduci
                  <lb/>
                poteft, in cuius
                  <reg norm="gratiam" type="context">gratiã</reg>
                ſit ſubſcripta
                  <lb/>
                figura pars
                  <reg norm="inquam" type="context">inquã</reg>
                pręcedentis, in qua
                  <lb/>
                  <reg norm="conſtituamus" type="context simple">cõſtituamꝰ</reg>
                  <var>.o.n.</var>
                  <reg norm="locum" type="context">locũ</reg>
                  <reg norm="eum" type="context">eũ</reg>
                eſſe quo ſibi
                  <lb/>
                viatores obuient, ex quo ſpacium
                  <var>.q.
                    <lb/>
                  n.</var>
                à ſuo viatore conficietur, eo ipſo
                  <lb/>
                tempore, quo à ſuo ſpacium
                  <var>.b.o.</var>
                ita
                  <lb/>
                que eadem erit proportio
                  <var>.q.n.</var>
                ad
                  <var>.b.</var>
                  <lb/>
                  <figure xlink:label="fig-0089-02" xlink:href="fig-0089-02a" number="121">
                    <image file="0089-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0089-02"/>
                  </figure>
                o. quæ
                  <var>.q.g.</var>
                ad
                  <var>.b.d.</var>
                eadem erit
                  <reg norm="inquam" type="context">inquã</reg>
                  <lb/>
                proportio
                  <var>.d.o.</var>
                ad
                  <var>.o.b.</var>
                quæ numeri
                  <lb/>
                dierum eius, qui à
                  <var>.b.</var>
                pergit in
                  <var>.d.</var>
                ad
                  <lb/>
                numerum dierum alterius qui à
                  <var>.q.</var>
                in
                  <lb/>
                p. proficiſcitur, & componendo
                  <reg norm="eadem" type="context">eadẽ</reg>
                  <lb/>
                erit proportio
                  <var>.d.b.</var>
                ad
                  <var>.b.o.</var>
                quæ ſum-
                  <lb/>
                mæ dierum ad minorem numerum ipſorum, & eadem quæ dierum
                  <var>.b.d.</var>
                ad dies
                  <lb/>
                ipſius
                  <var>.b.o</var>
                .</s>
              </p>
            </div>
            <div xml:id="echoid-div219" type="math:theorem" level="3" n="115">
              <head xml:id="echoid-head133" xml:space="preserve">THEOREMA
                <num value="115">CXV</num>
              .</head>
              <p>
                <s xml:id="echoid-s1032" xml:space="preserve">CIRCA hæc ipſa itinera aliud quæritur peruenuſtè, in quo quæſito illud con­
                  <lb/>
                ſtituitur cognitum eſſe, nempe interuallum inter duo diuerſa loca, è quibus
                  <lb/>
                duo viatores eodem inſtanti vt ſibi occurrant proficiſcuntur,
                  <reg norm="certaque" type="simple">certaq́;</reg>
                milliaria ſin-
                  <lb/>
                gulis diebus conficiant, ita tamen, ut unus ordinatè plura altero ambulet, quæritur
                  <lb/>
                deinde quoto die ſibi occurrent. </s>
                <s xml:id="echoid-s1033" xml:space="preserve">Hoc autem fit diuiſo toto interuallo locorum per
                  <lb/>
                ſummam milliariorum quam vterque quotidie abſoluit.</s>
              </p>
            </div>
          </div>
        </div>
      </text>
    </echo>
Impressum