Cardano, Geronimo, Opvs novvm de proportionibvs nvmerorvm, motvvm, pondervm, sonorvm, aliarvmqv'e rervm mensurandarum, non solùm geometrico more stabilitum, sed etiam uarijs experimentis & observationibus rerum in natura, solerti demonstratione illustratum, ad multiplices usus accommodatum, & in V libros digestum. Praeterea Artis Magnae, sive de regvlis algebraicis, liber vnvs abstrvsissimvs & inexhaustus planetotius Ariothmeticae thesaurus ... Item De Aliza Regvla Liber, hoc est, algebraicae logisticae suae, numeros recondita numerandi subtilitate, secundum Geometricas quantitates inquirentis ...

Page concordance

< >
Scan Original
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
< >
page |< < of 291 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s id="id000758">
                <pb pagenum="40" xlink:href="015/01/059.jpg"/>
              per numerum reuolutionum d, & partem reuolutionis exibit tem­
                <lb/>
              pus unius reuolutionis.</s>
            </p>
            <p type="margin">
              <s id="id000759">
                <margin.target id="marg129"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              10. P
                <emph type="italics"/>
              et.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id000760">
                <margin.target id="marg130"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              11. P
                <emph type="italics"/>
              et.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="id000761">Exemplum primi in re paulò obſcuriore: ſit f 4 & b 2 1/2 & a c 4/5, du
                <lb/>
              cemus 4 in 2 1/2 fit 10, adde 4/5 6 quod eſt 2 fit 12, diuide per 4/5 ſeu mul­
                <lb/>
              tiplica per 5/4 quod idem eſt, fit 15 circuitus e, in quatuor ergo circui­
                <lb/>
              tibus, & 4/5 qui ſunt duodecim anni perueniet a ad c, & in duodecim
                <lb/>
              annis e perueniet ad c, nam 12 ſunt 4/5 ipſius 15. Similiter in ſecundo
                <lb/>
              caſu ſit f 4 ut prius b 2 1/3 a c 1/7, ducemus 4 in 2 1/3 fit 9 1/3, addemusque h
                <lb/>
              portionem b qualis a c eſt totius circuitus, id eſt 1/7, eſt autem 1/7 2 1/3, 1/3
                <lb/>
              fient 9 1/3, ſimiliter ponatur d 5, & quia a c eſt 1/7 erunt 36/7, diuide ergo
                <lb/>
              9 2/3 id eſt 29/3 per 36/7 exeunt 203/108 tempus reuolutionis e. </s>
              <s id="id000762">Quin que ergo
                <lb/>
              reuolutiones e erunt 1015/108 addita ſeptima parte, quæ eſt 29/108 fient 2044/108
                <lb/>
              ſeu 261/27, & ſunt anni 9 18/27 ſeu 9 2/3, ergo in tanto tempore a faciet qua­
                <lb/>
              tuor circuitus, & ſeptimam partem, & e quinque circuitus, & ſe­
                <lb/>
              ptimam.
                <lb/>
                <arrow.to.target n="marg131"/>
              </s>
            </p>
            <p type="margin">
              <s id="id000763">
                <margin.target id="marg131"/>
              C
                <emph type="italics"/>
              om./>
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id000764">Ex hoc patet, quod non coniungentur in alio loco, neque alio tem
                <lb/>
              pore ante prædictum tempus.</s>
            </p>
            <p type="main">
              <s id="id000765">Propoſitio quinquageſima.</s>
            </p>
            <p type="main">
              <s id="id000766">Omnes circuituum portiones in eiuſdem temporibus
                <expan abbr="repetunt̃">repetuntur</expan>
              .</s>
            </p>
            <p type="main">
              <s id="id000767">Sint in circulo a b c d e f g: a & b iuncta, & in primo congreſſu
                <lb/>
              iungantur in c, in ſecundo in d, in tertio in e, in quarto in f, in quinto
                <lb/>
              in g, in ſexto in h, in ſeptimo in k, in octauo in l. </s>
              <s id="id000768">Et ſic deinceps
                <expan abbr="cũquetempora">cuique
                  <lb/>
                tempora</expan>
              ſint æqualia, erunt & circuitus totidem numero, & exceſ­
                <lb/>
              ſus æquales etiam a c, c d, d e, e f, f g, g h, h k,
                <lb/>
                <figure id="id.015.01.059.1.jpg" xlink:href="015/01/059/1.jpg" number="55"/>
                <lb/>
              k l. </s>
              <s id="id000769">Et ſi aggregatum a ſcilicet circulorum,
                <lb/>
              & portionis fuerit commenſum circulo, &
                <lb/>
              ita de b erunt omnia
                <expan abbr="cõmenſa">commenſa</expan>
              ad circulum, </s>
            </p>
            <p type="main">
              <s id="id000770">
                <arrow.to.target n="marg132"/>
                <lb/>
              & etiam inter ſe. </s>
              <s id="id000771">Et ſi inter ſe aggregata, uel
                <lb/>
              portiones erunt, & eodem modo reliqua.
                <lb/>
              </s>
              <s id="id000772">Et quoniam circuli circulis commenſi ſunt:
                <lb/>
              ſi portiones erunt inuicem commenſæ
                <expan abbr="erũt">erunt</expan>
              ,
                <lb/>
              & toti circuitus cum partibus commenſi, &
                <lb/>
              ſi non commenſi, neque erunt inter ſe, neque ad circulum. </s>
              <s id="id000773">Et ſi totum
                <lb/>
              ſpatium cum circuitibus erit unius generis, erunt duplicata, & tri­
                <lb/>
              plicata, & quadruplicata eiuſdem generis: quare cum ſpatia ipſa
                <lb/>
              detractis circuitibus uelut rhete habeant naturam reciſi, & ſpatia
                <lb/>
              ipſa tota ſint eiuſdem generis, erunt ſpatia, quæ relinquuntur eiuſ­
                <lb/>
              dem generis. </s>
              <s id="id000774">Erunt tamen incommenſa neceſſariò, ſi partes fuerint
                <lb/>
              incommenſæ toti. </s>
              <s id="id000775">Ponatur a c incommenſa toti circulo dico, quod
                <lb/>
              a k
                <expan abbr="etiã">etiam</expan>
              eſt incommenſa toti circulo: &
                <expan abbr="etiã">etiam</expan>
              a k, & k c. </s>
              <s id="id000776">Quia enim a c
                <lb/>
              eſt incommenſa circulo, & k a cum toto circulo ſemel eſt </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum