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
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
141 129
142 130
143 131
144 132
145 133
146 134
147 135
148 136
149 137
150 138
< >
page |< < (79) 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-div221" type="math:theorem" level="3" n="116">
              <p>
                <s xml:id="echoid-s1047" xml:space="preserve">
                  <pb o="79" rhead="THEOR. ARITH." n="91" file="0091" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0091"/>
                quoque ſumma par nunquam exiſtet, cuius medietatem aliquod medium ſemper
                  <lb/>
                ingredietur, & hanc ob cauſam poſterior ſumma cum fracto ſemper erit, & nume-
                  <lb/>
                rum deſumptum maiorem eſſe multiplici ad quatuor per duo ſignificabit.</s>
              </p>
              <p>
                <s xml:id="echoid-s1048" xml:space="preserve">At verò ſi inter impares reponatur, aut eorum erit qui ſuperant multiplicem
                  <lb/>
                ipſius quatuor per vnum, ſeu per tria, quod hinc innoteſcet, nempe, quia ſi eorum
                  <lb/>
                erit qui dictum multiplicem per vnum tantum vincunt, ſua medietate ipſi numero
                  <lb/>
                addita, & præter hanc medietatem medio etiam integro adiuncto, tota hæc prior
                  <lb/>
                ſumma in numerum parem ſemper euadet, vnde in poſteriori ſumma nullus nume-
                  <lb/>
                rus fractus conſpicietur, & hanc ob
                  <reg norm="causam" type="context">causã</reg>
                multiplici ipſius .4. vnitas ſemper addetur.</s>
              </p>
              <p>
                <s xml:id="echoid-s1049" xml:space="preserve">Sed ſi numerus deſumptus, in ſerie eorum, qui multiplicem ipſius .4. pertria ſu-
                  <lb/>
                perant, collocabitur, hinc compræhendetur, quia primæ ſummæ numerus cum
                  <lb/>
                media vnitate ſemper impar erit, vnde ſecunda ſumma præter integras cum me-
                  <lb/>
                dia vnitate nobis ſemper occur ret.</s>
              </p>
              <p>
                <s xml:id="echoid-s1050" xml:space="preserve">Quod autem nobis prodere faciamus an in prima diuiſione, & ſecunda numerus
                  <lb/>
                aliquis fractus conſiſtat, eò tantum nobis inſeruit, quò deueniamus in cognitionem
                  <lb/>
                an numerus animo conceptus multiplicem ipſius .4. per vnum, per duo, aut tria ſupe
                  <lb/>
                ret. </s>
                <s xml:id="echoid-s1051" xml:space="preserve">Quòd etiam medias eas vnitates ad integros reducere faciamus, eò tantum re
                  <lb/>
                fertur, vt minori labore eum, qui numerum imaginatione compræhendit, onere-
                  <lb/>
                mus, quia reuera numerus impar nunquam mente concipi poteſt, quin aliquis fra-
                  <lb/>
                ctus in prima diuiſione, aut in ſecunda ſequatur: </s>
                <s xml:id="echoid-s1052" xml:space="preserve">vnde à numeris imparibus, qui mul
                  <lb/>
                tiplicem ipſius .4. unitatis tantum exceſſu
                  <reg norm="ſuperant" type="context">ſuperãt</reg>
                , poſterior ſumma
                  <reg norm="cum" type="context">cũ</reg>
                quarta parte
                  <lb/>
                vnitatis, præter integros numeros, & ab imparibus qui dictum multiplicem ipſius
                  <num value="4">.
                    <lb/>
                  4.</num>
                per tria vincunt, cum tribus quartis vnius integri præter integras vnitates ; </s>
                <s xml:id="echoid-s1053" xml:space="preserve">& à
                  <lb/>
                numeris paribus, qui multiplicem ipſius .4. per duo cum medietate vnitatis præter
                  <lb/>
                integros ſemper procedit. </s>
                <s xml:id="echoid-s1054" xml:space="preserve">Ita cum is qui numerum ſecum conſiderat, ſi in nume-
                  <lb/>
                  <figure xlink:label="fig-0091-01" xlink:href="fig-0091-01a" number="123">
                    <image file="0091-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0091-01"/>
                  </figure>
                ris fractis verſatus eſſet, qui eum in-
                  <lb/>
                terrogat prudenter ſe gereret, ſi ſibi
                  <lb/>
                declarari curaret, quis nam ex fractis
                  <lb/>
                ſu per integros
                  <reg norm="ſecundæ" type="context">ſecũdæ</reg>
                  <reg norm="summæ" type="context">sũmæ</reg>
                remane
                  <lb/>
                ret, quia
                  <reg norm="per" type="simple">ꝑ</reg>
                quot quarta integros
                  <reg norm="ſecun- dæ" type="context">ſecũ-
                    <lb/>
                  dæ</reg>
                ſummæ ſuperaret, per
                  <reg norm="totidem" type="context">totidẽ</reg>
                inte
                  <lb/>
                gros numerus mente conceptus multiplicem ipſius .4. ſuperaret.</s>
              </p>
            </div>
            <div xml:id="echoid-div223" type="math:theorem" level="3" n="117">
              <head xml:id="echoid-head135" xml:space="preserve">THEOREMA
                <num value="117">CXVII</num>
              .</head>
              <p>
                <s xml:id="echoid-s1055" xml:space="preserve">VNDE fiat, vt ſi ali quis quemuis numerum animo compræhendat, eique
                  <lb/>
                numero alium etiam quemlibet numerum propoſitum addat, & à tertia par
                  <lb/>
                te huius ſummæ tertiam partem numeri imaginati detrah et, reſiduum ſecundi nu-
                  <lb/>
                meri adiuncti, ideſt propoſiti, tertia pars erit.</s>
              </p>
              <p>
                <s xml:id="echoid-s1056" xml:space="preserve">Vt exempli gratia, ſi aliquis de numero denario cogitaſſet,
                  <reg norm="huicque" type="simple">huicq́;</reg>
                .24. adderet,
                  <lb/>
                vnde triginta quatuor efficerent, detra hendo nunc tertiam partem numeri de na-
                  <lb/>
                rij cogitatione concepti, ideſt .3. cum tertia parte vnius, à tertia parte huius ſum mæ
                  <lb/>
                ideſt ab vndecim & vna tertia parte remanerent .8. ideſt tertia pars numeri additi.
                  <lb/>
                </s>
                <s xml:id="echoid-s1057" xml:space="preserve">Id quod mihi inter iocos in honeſtorum hominum cætu in mentem venit.</s>
              </p>
              <p>
                <s xml:id="echoid-s1058" xml:space="preserve">Pro cuius ratione, prior numerus ima
                  <lb/>
                  <figure xlink:label="fig-0091-02" xlink:href="fig-0091-02a" number="124">
                    <image file="0091-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0091-02"/>
                  </figure>
                ginatus mediante linea
                  <var>.a.b.</var>
                et is, qui ad-
                  <lb/>
                ditus eſt
                  <reg norm="intercedente" type="context">intercedẽte</reg>
                linea
                  <var>.b.d.</var>
                è directo </s>
              </p>
            </div>
          </div>
        </div>
      </text>
    </echo>
Impressum