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="id001921">
                <pb pagenum="106" xlink:href="015/01/125.jpg"/>
              cilius ſit in anteriore parte propinquius comprehenſum calci, & ſi
                <lb/>
              craſsius, uel grauius propius cuſpidi. </s>
              <s id="id001922">Semper igitur ob hanc cau­
                <lb/>
              ſam mota ex medio grauitatis, ſeu uelo, ſeu ramo, ſeu manu uelo­
                <lb/>
              cius mouentur, quàm ex alijs partibus. </s>
              <s id="id001923">In remo etiam poteſt acce­
                <lb/>
              dere illud commodum, cuius meminit Ariſtoteles. </s>
              <s id="id001924">Propter hoc igi
                <lb/>
              tur, qui malum in naui collo carunt tantùm unum, in medio fermè
                <lb/>
              eum collocarunt, ut antiqui: & qui duos aut tres, maiorem craſsio­
                <lb/>
                <arrow.to.target n="marg396"/>
                <lb/>
              rem ſcilicet, & altiorem in medio conſtituerunt.</s>
            </p>
            <p type="margin">
              <s id="id001925">
                <margin.target id="marg392"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="margin">
              <s id="id001926">
                <margin.target id="marg393"/>
              P
                <emph type="italics"/>
              ropoſ.
                <emph.end type="italics"/>
              86.</s>
            </p>
            <p type="margin">
              <s id="id001927">
                <margin.target id="marg394"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              10.
                <lb/>
                <emph type="italics"/>
              quinti
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id001928">
                <margin.target id="marg395"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              8.
                <emph type="italics"/>
              quin­
                <lb/>
              ti
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id001929">
                <margin.target id="marg396"/>
              P
                <emph type="italics"/>
              ropoſ.
                <emph.end type="italics"/>
              82.</s>
            </p>
            <p type="main">
              <s id="id001930">Propoſitio centeſimaduodecima.</s>
            </p>
            <p type="main">
              <s id="id001931">Cur ex imo leuia longius ferantur declarare.</s>
            </p>
            <p type="main">
              <s id="id001932">Iam uerò
                <expan abbr="cõſideremus">conſideremus</expan>
              , quòd propoſitum eſt, non ſolum in com­
                <lb/>
                <arrow.to.target n="marg397"/>
                <lb/>
              paratione ad medium, ſed extremorum inuicem, miſſa enim ab imo
                <lb/>
              uelo cius feruntur, quàm à medio non ſolum manu, ſed ſcorpioni­
                <lb/>
              bus, & arcubus. </s>
              <s id="id001933">Videmus & hoc obſeruare pueros uirgam lon­
                <lb/>
              gius iacentes non ex medio, ſed imo apprehenſam, quoniam pars
                <lb/>
              ipſa anterior, & quæ manu apprehenſa eſt, uehementi impetu emit­
                <lb/>
              titur: & ut recipit impetum magis æqualem, longius fertur, nam
                <lb/>
              quod emittitur proportionem habet ad ſpatium. </s>
              <s id="id001934">Cum ergo appre
                <lb/>
              henſa in medio uirga ſolum medietate anteriore impetum recipiat
                <lb/>
              per ſe, ob id minus fertur: at impetus ſequitur proportionem, ut ui­
                <lb/>
              ſum eſt, quæ eſt circa medium ob leuitatem ponderis. </s>
              <s id="id001935">In leuibus
                <lb/>
              ergo maius ſpatium ſuperabunt emiſſa ex imo, quoniam propor­
                <lb/>
              tio ſpatij eadem eſt ad duplum, & ad dimidium. </s>
              <s id="id001936">igitur ex imo fer­
                <lb/>
              me duplum etiam ſpatij ſuperabit: non tamen omnino quia maio­
                <lb/>
              rem, ut dixi proportionem habet ad id, quod ex medio comprehen
                <lb/>
              ſum eſt. </s>
              <s id="id001937">At in leuibus non eſt neceſſarium, ut ex medio apprehen­
                <lb/>
              dantur, quoniam etiam cum incremento illo ponderis iam leuia
                <lb/>
              ſunt: plus ergo facit longitudo eius, quod eiaculatur, quàm impe­
                <lb/>
                <figure id="id.015.01.125.1.jpg" xlink:href="015/01/125/1.jpg" number="120"/>
                <lb/>
              tus, cuius demonſtratio eſt hæc. </s>
              <s id="id001938">Sit uirga
                <lb/>
              a b apprehenſa in medio ponderis unciæ
                <lb/>
              mediæ, & in a d, ut ſit d a palmus, & uigeſi­
                <lb/>
              ma pars totius a b, erit ergo reſiduum ad duplum, a d nonuplum,
                <lb/>
                <arrow.to.target n="marg398"/>
                <lb/>
              & a b tota unciarum quin que cum dimidia, ſi igitur grauetur, quia in
                <lb/>
              ſitu recto eſt mediæ unciæ, in æquidiſtanti terræ, quin que unciarum
                <lb/>
              cum dimidio, erit in ſitu dimidij recti unciarum trium. </s>
              <s id="id001939">Eſt igitur
                <lb/>
              proportio ſexcupla, ſi apprehendatur in medio, & ad æquidiſtan­
                <lb/>
              tem, ad apprehenſam in imo, & ad angulum medium: at emiſſa ex
                <lb/>
                <arrow.to.target n="marg399"/>
                <lb/>
              a d habet totum aërem a b circumdantem impulſum ex c b ſolum
                <lb/>
              dimidium reliqua pars ui trahitur, ergo proportio ſpatij a b, erit
                <lb/>
              ſexdecupla fermè ſpatio b c, quoniam eſt triplicata corporis ad cor
                <lb/>
              pus eius, quæ eſt longitudinis ad longitudinem, & quadruplicata </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum