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
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
< >
page |< < of 291 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s id="id003669">
                <pb pagenum="218" xlink:href="015/01/237.jpg"/>
              b a igitur quod fit ex d h in d g eſt ęquale quadratis d b, b a quę ſunt
                <lb/>
              ęqualia quadrato a d, igitur quadratum a d eſt ęquale ei quod fit ex
                <lb/>
                <arrow.to.target n="marg689"/>
                <lb/>
              h d in d g, quare proportio h d ad d a ut d a ad a g. </s>
              <s id="id003670">Quia ergo pro­
                <lb/>
                <arrow.to.target n="marg690"/>
                <lb/>
              portio d e ad d a ut d a ad d f, & d h ad d a ut d a ad d g, erit d e ad d h
                <lb/>
              ut d g ad d f.</s>
            </p>
            <p type="margin">
              <s id="id003671">
                <margin.target id="marg678"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="margin">
              <s id="id003672">
                <margin.target id="marg679"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              36.
                <emph type="italics"/>
              ter­
                <lb/>
              tij
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id003673">
                <margin.target id="marg680"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              6.
                <emph type="italics"/>
              ſecun
                <lb/>
              di
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id003674">
                <margin.target id="marg681"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              47.
                <emph type="italics"/>
              pri­
                <lb/>
              mi
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id003675">
                <margin.target id="marg682"/>
              P
                <emph type="italics"/>
              er tandem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id003676">
                <margin.target id="marg683"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              2.
                <emph type="italics"/>
              ſecun
                <lb/>
              di
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id003677">
                <margin.target id="marg684"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              17.
                <emph type="italics"/>
              ſex­
                <lb/>
              ti
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id003678">
                <margin.target id="marg685"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              2.
                <emph type="italics"/>
              ſecun
                <lb/>
              di
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id003679">
                <margin.target id="marg686"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              35.
                <emph type="italics"/>
              ter
                <lb/>
              tij
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id003680">
                <margin.target id="marg687"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              47.
                <emph type="italics"/>
              pri
                <lb/>
              mi
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id003681">
                <margin.target id="marg688"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              5.
                <emph type="italics"/>
              ſecun
                <lb/>
              di
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id003682">
                <margin.target id="marg689"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              17.
                <emph type="italics"/>
              ſex
                <lb/>
              ti
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id003683">
                <margin.target id="marg690"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              16.
                <emph type="italics"/>
              &
                <emph.end type="italics"/>
                <lb/>
              17.
                <emph type="italics"/>
              ſexti
                <emph.end type="italics"/>
                <lb/>
              E
                <emph type="italics"/>
              lement.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="id003684">Vnde manifeſtum eſt omnes has lineas in ſuam interiorem par­
                <lb/>
                <arrow.to.target n="marg691"/>
                <lb/>
              tem ductas rectangulum conſtituere ęquale quadrato quod circu­
                <lb/>
              lo eidem inſcribitur.</s>
            </p>
            <p type="margin">
              <s id="id003685">
                <margin.target id="marg691"/>
              C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id003686">Propoſitio centeſima nonageſima tertia.</s>
            </p>
            <p type="main">
              <s id="id003687">Rationem ponderis triplicem explicare.
                <lb/>
                <arrow.to.target n="marg692"/>
              </s>
            </p>
            <p type="margin">
              <s id="id003688">
                <margin.target id="marg692"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id003689">Superius declaratum eſt quòd id quod quieſcit, habet motum </s>
            </p>
            <p type="main">
              <s id="id003690">
                <arrow.to.target n="marg693"/>
                <lb/>
              occultum. </s>
              <s id="id003691">Quærit autem Ariſtoteles cur ſecuris pondere preſſa
                <expan abbr="nõ">non</expan>
                <lb/>
              diuidit lignum, minore uerò ſed moto ſed modo diuidit? </s>
              <s id="id003692">Diximus
                <lb/>
                <arrow.to.target n="marg694"/>
                <lb/>
              motum ineſſe qui perpetuo augetur, indicium eſt, quod ſi ex a de­
                <lb/>
              ſcendat,
                <expan abbr="maiorẽ">maiorem</expan>
              facit ictum, quoniam plurimus aër coadiuuat, ex d
                <lb/>
              autem occultum
                <expan abbr="ſolũ">ſolum</expan>
              , et eum qui fit ratione grauitatis, me­
                <lb/>
                <figure id="id.015.01.237.1.jpg" xlink:href="015/01/237/1.jpg" number="230"/>
                <lb/>
              dium ex medijs locis. </s>
              <s id="id003693">Omitto modo de motu aucto per
                <lb/>
              uim humanam, de quo uidetur quærere Ariſtoteles, quili­
                <lb/>
              bet enim aër addit ſuper motum iam acquiſitum & fit hoc
                <lb/>
              argumentum centies ac millies maius, quoniam m eſt qui
                <lb/>
              diuidit, pondus autem non ponetrat. </s>
              <s id="id003694">Sicut ergo cuneus
                <lb/>
              magis diuidit lignum quam claua, ita quod mouetur ſine
                <lb/>
              proportione (ut ita dicam) non ſolum ob
                <expan abbr="impetũ">impetum</expan>
              neceſſe
                <lb/>
              eſt ut uehementer diuidat lignum aut lapidem ſubiectum,
                <lb/>
              & non in proportione diſtantię. </s>
              <s id="id003695">Sicut ſi pondus in forma
                <lb/>
              ſecuris, & ipſa ſecuris diuidit longe magis ligna quam cla­
                <lb/>
              uis maioris ponderis & maiore ui deſcendens: ita pondus motum
                <lb/>
              quam immotum. </s>
              <s id="id003696">Hoc adeò perſpicuam habet cauſſam, ut quanto
                <lb/>
              plura uerba adderentur, eo redderetur res difficilior. </s>
              <s id="id003697">Habet ergo
                <lb/>
              propriam ſolum grauitatem & motum occultum. </s>
              <s id="id003698">Cęterum eſt ter­
                <lb/>
              tium, genus
                <expan abbr="mediũ">medium</expan>
              , cum idem pondus appenſum eſt, ue­
                <lb/>
                <figure id="id.015.01.237.2.jpg" xlink:href="015/01/237/2.jpg" number="231"/>
                <lb/>
              lut f quod dico eſſe maius & minus occultum quam ſi ia­
                <lb/>
              ceret in plano, quoniam ſicut tuber & cauitas in qua iacet
                <lb/>
              ſimul tempore ſunt, natura tamen tuber eſt prius cauitate,
                <lb/>
              ita pondus appenſum prius eſt, contrà nixum uinculi na­
                <lb/>
              tura & quodammodo tempore, ſemper enim grauat, & illud ſem­
                <lb/>
              per reſiſtit ſupra illius grauitatem: Sed pondus quod eſt in plano
                <lb/>
              occultam omnino habet actionem bifariamque diſtinguitur a pon­
                <lb/>
              dere ſuſpenſo: Primum quòd pondus quod quieſcit & contra in­
                <lb/>
              tendi principium ſimul non ſolum ſunt tempore ſed etiam natu­
                <lb/>
              ra. </s>
              <s id="id003699">Sed in appenſo, ut dixi, pondus prius grauat quam </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum