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
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
< >
page |< < of 291 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s id="id000408">
                <pb pagenum="21" xlink:href="015/01/040.jpg"/>
              cum ſuis duplicatis ſequentibus, & in c, & in d, & in reliquis pa­
                <lb/>
              riter conduplicatis ſuis ſequentibus ex altera, quod fit ex h in b ſe­
                <lb/>
              mel, in c ter, in d quinquies, in e ſepties, in f nouies, in g undecies,
                <lb/>
              in h tredecies, detractis ergo rurſus quod fit ex h in b ſemel, & ex
                <lb/>
              h in c d e f g h bis relinquetur, quod fit ex h in c, & duplo ſequen­
                <lb/>
              tium, & d & duplo ſequentium, & e & aliarum pariter: & ex alia
                <lb/>
              parte, quod fit ex h in c ſemel, & in d ter, & in e quinquies, in f ſe­
                <lb/>
              pties, in g nouies, in h undecies. </s>
              <s id="id000409">Ab his rurſus detractis, quòd fit
                <lb/>
              ex h in c ſemel, & in ſequentes bis, relinquetur h in d ſemel cum ſuis
                <lb/>
              ſequentibus bis, & in e ſemel cum ſuis ſequentibus & in f, & in g &
                <lb/>
              in h pariter, & ex alia parte, quod fit ex h in d ſemel, in e ter, f quin­
                <lb/>
              quies, g ſepties, h nouies, ab his rurſus detraho, quod fit ex h in d
                <lb/>
              ſemel, & in ſequentes bis, relinquetur ex una parte, quod fit ex h
                <lb/>
              in e f g h cum duplo ſequentium ex alia, quod fit ex h in e ſe­
                <lb/>
              mel, f ter, g quinquies, h ſepties, & ſimiliter ab his detractis, quod
                <lb/>
              fit ex h in e ſemel, & bis in ſequentes, relinquetur ex una par­
                <lb/>
              te; quod fit ex h in f ſemel, & in g h bis, & in g ſemel, & in h bis,
                <lb/>
              & in h ſemel, & ex alia, quod fit ex h in f ſemel, in g ter, in h quin­
                <lb/>
              quies. </s>
              <s id="id000410">Iterum detractis, quod fit ex h in f ſemel, & in g h bis com­
                <lb/>
              muniter relinquetur, quod fit ex h in g ſemel, & in h bis, & in h ſe­
                <lb/>
              mel, & ex alia parte quod fit ex h in g ſemel, & ex h in h ter. </s>
              <s id="id000411">Sed
                <lb/>
              iſta, quæ relicta ſunt iam, ſunt manifeſtè æqualia, ergo etiam pri­
                <lb/>
              ma aggregata ab initio fuere æqualia, ergo & æqualia illis qua­
                <lb/>
              drata a b c d e f g h his, quæ fiunt, ex h in eaſdem quantita­
                <lb/>
              tes cum duplo producti b in i, cin k, d in l, e in m, f in n, g in o,
                <lb/>
              h in p, ſed iam his quadratis a b c d e f g h demonſtrata ſunt eſſe du­
                <lb/>
              pla quadrata h p, g o, f n, e m, d l, c k, b i, cum duplo quadra­
                <lb/>
              ti a, ergo quadrata omnium quantitatum ſecundi ordinis cum
                <lb/>
              quadrato a rurſus repetito, & producto h in aggregatum quanti­
                <lb/>
              tatum primi ordinis ſunt tripla quadratis quantitatum primi ordi­
                <lb/>
              nis pariter acceptis, quod fuit propoſitum, & fuit Archimedis in li
                <lb/>
              bro de lineis ſpiralibus, & ego adieci hic propter modum demon
                <lb/>
              ſtrandi, qui eſt elegantiſsimus, & procedit ex principijs arithmeti­
                <lb/>
              cis, & diuerſis à communibus, & ideo non reuoluitur, ut ſolent re­
                <lb/>
              liquæ quæſtiones.</s>
            </p>
            <p type="margin">
              <s id="id000412">
                <margin.target id="marg67"/>
              I
                <emph type="italics"/>
              n
                <emph.end type="italics"/>
              5. E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
                <lb/>
              P
                <emph type="italics"/>
              rop.
                <emph.end type="italics"/>
              12.</s>
            </p>
            <p type="margin">
              <s id="id000413">
                <margin.target id="marg68"/>
              L
                <emph type="italics"/>
              ib.
                <emph.end type="italics"/>
              6. E
                <emph type="italics"/>
              le.
                <emph.end type="italics"/>
                <lb/>
              P
                <emph type="italics"/>
              rop.
                <emph.end type="italics"/>
              17.</s>
            </p>
            <p type="main">
              <s id="id000414">Propoſitio uigeſima.</s>
            </p>
            <p type="main">
              <s id="id000415">Cùm fuerint quatuor quantitates, fueritque ſecunda æqualis ter­
                <lb/>
              tiæ, aut primæ æqualis quartæ, erit proportio primæ ad quartam,
                <lb/>
              aut tertiæ ad ſecundam producta ex proportionibus primæ ad ſe­
                <lb/>
              cundam, & tertiæ ad quartam.
                <lb/>
                <arrow.to.target n="marg69"/>
              </s>
            </p>
            <p type="margin">
              <s id="id000416">
                <margin.target id="marg69"/>
              C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id000417">Cùm enim quantitates hæ non fuerint ęquales,
                <expan abbr="cõſtat">conſtat</expan>
              per </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum