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
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
< >
page |< < of 291 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s id="id000062">
                <pb pagenum="2" xlink:href="015/01/021.jpg"/>
              pus. </s>
              <s id="id000063">Dicimus enim motum tardum, uel uelocem in comparatione
                <lb/>
              ad tempus.</s>
            </p>
            <p type="margin">
              <s id="id000064">
                <margin.target id="marg1"/>
              C
                <emph type="italics"/>
              ar
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id000065">Nona diffinitio.</s>
            </p>
            <p type="main">
              <s id="id000066">Proportionum aliæ dicuntur rhete, aliæ alogæ, rhetæ quæ ſunt
                <lb/>
              ut numeri ad numerum, alogæ quæ non ſunt numeri ad numerum.</s>
            </p>
            <p type="main">
              <s id="id000067">Decima diffinitio</s>
            </p>
            <p type="main">
              <s id="id000068">Proportio rhete alia æqualis, alia multiplex, uel ſubmultiplex:
                <lb/>
              alia unius partis exceſſus, aut defectus, alia plurium, quam ſuper­
                <lb/>
              partientem, aut ſupartientem uocant.</s>
            </p>
            <p type="main">
              <s id="id000069">Vndecima diffinitio.</s>
            </p>
            <p type="main">
              <s id="id000070">Cum diuiſo denominatore per numeratorem exit quantitas alo
                <lb/>
              ga, proportio dicitur aloga: ſi autem numerus integer, aut pars nu­
                <lb/>
              meri nota dicitur rhete.</s>
            </p>
            <p type="main">
              <s id="id000071">Duodecima diffinitio.</s>
            </p>
            <p type="main">
              <s id="id000072">Proportionem in proportionem duci eſt, quoties recto ordine
                <lb/>
              tres quantitates in eiſdem collo
                <expan abbr="cant̃">cantur</expan>
              : ut ſint tres quan
                <lb/>
                <figure id="id.015.01.021.1.jpg" xlink:href="015/01/021/1.jpg" number="2"/>
                <lb/>
              titates a b c dicetur proportio a ad c producta ex pro
                <lb/>
              portione a ad b & b ad c, & ſimiliter proportio c ad
                <lb/>
              a producitur ex proportione b ad a, & c ad b.</s>
            </p>
            <p type="main">
              <s id="id000073">Tertia decima diffinitio.</s>
            </p>
            <p type="main">
              <s id="id000074">Proportionem per proportionem diuidi eſt, quoties ad eandem
                <lb/>
              quantitatem duæ quantitates comparantur, tunc illarum propor­
                <lb/>
              tio eſt, quæ prodit una per alteram diuiſa.</s>
            </p>
            <p type="main">
              <s id="id000075">Sint proportiones a & b ad c & interponatur b inter a & c, dico
                <lb/>
              proportionem a ad c diuiſam per proportionem a ad b, & prodire
                <lb/>
              proportionem b ad c, conſtat ex conuerſa præcedentis.</s>
            </p>
            <p type="main">
              <s id="id000076">Quarta decima diffinitio.</s>
            </p>
            <p type="main">
              <s id="id000077">Additio proportionum intelligitur quotiens duarum quanti­
                <lb/>
              tatum ad unam tertiam, proportiones per aggregatum ipſarum
                <lb/>
              quantitatum ad eandem coniunguntur.</s>
            </p>
            <p type="main">
              <s id="id000078">Velut ſi comparentur a b & b c ad d, inde tota
                <lb/>
                <figure id="id.015.01.021.2.jpg" xlink:href="015/01/021/2.jpg" number="3"/>
                <lb/>
              a c ad d dicemus proportionem, ac ad d eſſe con
                <lb/>
                <expan abbr="iunctã">iunctam</expan>
              ex duabus proportionibus a b ad d & b c
                <lb/>
              ad
                <expan abbr="eandẽ">eandem</expan>
              d. </s>
              <s id="id000079">Hoc & duo ſequentes ſicut & duę
                <expan abbr="antecedẽtes">antecedentes</expan>
              demon­
                <lb/>
              ſtrabitur eſſe. </s>
              <s id="id000080">nunc ſolum quomodo
                <expan abbr="intelligendũ">intelligendum</expan>
              ſit proponimus.</s>
            </p>
            <p type="main">
              <s id="id000081">Quinta decima diffinitio.</s>
            </p>
            <p type="main">
              <s id="id000082">Detractionem proportionis à proportione intelligimus fieri
                <lb/>
              per
                <expan abbr="detractionẽ">detractionem</expan>
              minoris quantitatis à maiore, comparatam ad ean­
                <lb/>
              dem quantitatem.</s>
            </p>
            <p type="main">
              <s id="id000083">Velut in exemplo ſuperiore detracta proportione b c ad d ex </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum