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
111 99
112 100
113 101
114 102
115 103
116 104
117 105
118 106
119 107
120 108
121 109
122 110
123 111
124 112
125 113
126 114
127 115
128 116
129 117
130 118
131 119
132 120
133 121
134 122
135 123
136 124
137 125
138 126
139 127
140 128
< >
page |< < (71) 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-div207" type="math:theorem" level="3" n="110">
              <p>
                <s xml:id="echoid-s952" xml:space="preserve">
                  <pb o="71" rhead="THEOREM. ARIT." n="83" file="0083" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0083"/>
                te verò à ſecundo milliario vno primus antecedatur, ex communi ſcientia neceſſe
                  <lb/>
                eſt ſecundum tot diebus
                  <reg norm="cum" type="context">cũ</reg>
                primo iter agere quot ſunt
                  <var>.o.n.</var>
                qui ſimul æquales erunt
                  <var>.
                    <lb/>
                  u.n.</var>
                ſed
                  <var>.u.n.</var>
                minor eft numero milliarium diurnorum primi vnitate
                  <var>.e</var>
                . </s>
                <s xml:id="echoid-s953" xml:space="preserve">Itaque rectè
                  <lb/>
                ſequemur regulam, quæ iubet ex numero milliarium vnitatem demere, quo nu
                  <lb/>
                merum dierum habere poſſimus.</s>
              </p>
            </div>
            <div xml:id="echoid-div209" type="math:theorem" level="3" n="111">
              <head xml:id="echoid-head128" xml:space="preserve">THEOREMA
                <num value="111">CXI</num>
              .</head>
              <p>
                <s xml:id="echoid-s954" xml:space="preserve">SI verò ſecundi viatoris progreſſio per ternarium aſcenderet, ſumpto initio ab
                  <lb/>
                ipſo ternario, animaduertendum eſt an numerus milliarium diurnorum primi,
                  <lb/>
                ternario menſuretur necne, etenim ſi menſuretur, tandem aliquando paria millia-
                  <lb/>
                ria conficient, quæ dies ſit
                  <var>.u.n.</var>
                </s>
                <s xml:id="echoid-s955" xml:space="preserve">quare ſub
                  <lb/>
                  <figure xlink:label="fig-0083-01" xlink:href="fig-0083-01a" number="114">
                    <image file="0083-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0083-01"/>
                  </figure>
                  <var>u.n.</var>
                totidem quot ſupra termini
                  <reg norm="erunt" type="context">erũt</reg>
                ,
                  <lb/>
                &
                  <reg norm="cum" type="context">cũ</reg>
                  <var>.o.n.</var>
                tertia ſit pars
                  <var>.u.n.</var>
                ex .95. theo-
                  <lb/>
                remate. </s>
                <s xml:id="echoid-s956" xml:space="preserve">Itaque tota
                  <var>.o.f.</var>
                minor erit
                  <lb/>
                duabus tertijs
                  <var>.u.n.</var>
                vnitate, vtiam re-
                  <lb/>
                ctè ſumendæ ſint duæ tertiæ partes
                  <var>.u.n.</var>
                  <lb/>
                ex quibus vnitas detrahatur ſuperſitq́ue
                  <lb/>
                numerus
                  <var>.o.f.</var>
                dierum quæſitorum.</s>
              </p>
            </div>
            <div xml:id="echoid-div211" type="math:theorem" level="3" n="112">
              <head xml:id="echoid-head129" xml:space="preserve">THEOREMA
                <num value="112">CXII</num>
              .</head>
              <p>
                <s xml:id="echoid-s957" xml:space="preserve">CVM verò milliarium numerus p rimi viatoris metirinon poterit à numero
                  <lb/>
                aſcendente ſecundi, patet nullam futuram diem qua pari milliaria conficient,
                  <lb/>
                </s>
                <s xml:id="echoid-s958" xml:space="preserve">quare illa vltima qua primus ſecundum antecedet, vno aut duobus milliaribus an-
                  <lb/>
                tecedet in præſenti caſu. </s>
                <s xml:id="echoid-s959" xml:space="preserve">Antecedat itaque duobus milliaribus,
                  <reg norm="ſitque" type="simple">ſitq́;</reg>
                dies
                  <var>.u.n.</var>
                & alte
                  <lb/>
                ra
                  <var>.t.i.</var>
                ſecundus primum vno milliari ſuperabit, ita quod ſub
                  <var>.t.i.</var>
                non poterunt plu-
                  <lb/>
                res integros dies iter agere, quam ambulauerunt ante diem
                  <var>.u.n.</var>
                hoc eſt vſquequo
                  <lb/>
                ſecundtis iunctus ſit primo, qui numerus dierum, tertia parte
                  <var>.o.n.</var>
                ipſius
                  <var>.u.n.</var>
                vnitate
                  <lb/>
                minor erit, cum ex .95. theoremate
                  <var>.o.n.</var>
                ſit tertia pars
                  <var>.u.n.</var>
                ex quo numerus
                  <var>.o.f.</var>
                ter-
                  <lb/>
                minorum aut dierum intergrorum cognitus erit, qui ſi cum numero alcendente
                  <lb/>
                cognoſcetur, ſtatim ex .99. theoremate deueniemus in cognitionem vltimi diei in
                  <lb/>
                tegri
                  <var>.s.f.</var>
                atque ita etiam totius ſummæ progreſſionis ex .95. theoremate. </s>
                <s xml:id="echoid-s960" xml:space="preserve">Iam verò
                  <lb/>
                cognito numero milliarium diurnorum primi, ſimul cum numero terminorum, aut
                  <lb/>
                dierum conſequenter nouerimus rectanguli ſummam, hoc eſt productum à primo
                  <lb/>
                viatore formatum, quarum duarum ſummarum in præſenti caſu ſemper ea, quæ
                  <lb/>
                huiuſmodi producti eſt, maior erit, cum conſtitutum fuerit ſecundum viatorem à
                  <lb/>
                primo ſuperari ipſa die
                  <var>.u.n.</var>
                vno milliari amplius quam ſequente die
                  <var>.t.i.</var>
                primus à ſe
                  <lb/>
                cundo ſuperatur, tum pari gradu iter egerunt ſub
                  <var>.t.i.</var>
                quo ſupra
                  <var>.u.n.</var>
                ambulauerant.
                  <lb/>
                </s>
                <s xml:id="echoid-s961" xml:space="preserve">Hoc animaduertendo, quòd ſi ſumma progreſſionis maior eſſet rectangulo, ex ea
                  <lb/>
                ſumma neceſſe eſſet
                  <reg norm="numerum" type="context">numerũ</reg>
                mil
                  <lb/>
                liarium vltimi termini in ſumma
                  <lb/>
                  <figure xlink:label="fig-0083-02" xlink:href="fig-0083-02a" number="115">
                    <image file="0083-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0083-02"/>
                  </figure>
                incluſi detrahere, & reſiduo ope-
                  <lb/>
                rari. </s>
                <s xml:id="echoid-s962" xml:space="preserve">Nunc verò ſummam pro-
                  <lb/>
                greſſionis exſumma rectanguli à
                  <lb/>
                primo viatore facti ſubtrahi de-
                  <lb/>
                bet,
                  <reg norm="reſiduumque" type="simple">reſiduumq́;</reg>
                ſeruari
                  <reg norm="voceturque" type="simple">voceturq́;</reg>
                </s>
              </p>
            </div>
          </div>
        </div>
      </text>
    </echo>
Impressum