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
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
< >
page |< < of 291 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s id="id004096">
                <pb pagenum="240" xlink:href="015/01/259.jpg"/>
                <figure id="id.015.01.259.1.jpg" xlink:href="015/01/259/1.jpg" number="258"/>
                <lb/>
              ior eſt a d tanto facilius remouet ęquali ſpa
                <lb/>
                <arrow.to.target n="marg804"/>
                <lb/>
              tio d uerſus e. </s>
              <s id="id004097">Et licet remoueantur ab ipſo
                <lb/>
              d, ſemper eadem proportio manebit, ma­
                <lb/>
                <arrow.to.target n="marg805"/>
                <lb/>
              nente eadem longitudine b d & a d, nam
                <lb/>
                <arrow.to.target n="marg806"/>
                <lb/>
              proportio d f ad d c, eſt uelut f b d ad
                <lb/>
              c b d, & ut d f ad d e, ita f a d ad c a d, quare
                <lb/>
              fb d ad c b d, uelut f a d ad c a d, quare fb d
                <lb/>
              ad f a d, ut c b d ad c a d, quod fuit pro­
                <lb/>
              poſitum.</s>
            </p>
            <p type="margin">
              <s id="id004098">
                <margin.target id="marg802"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              _{m}.</s>
            </p>
            <p type="margin">
              <s id="id004099">
                <margin.target id="marg803"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              16.
                <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="id004100">
                <margin.target id="marg804"/>
              P
                <emph type="italics"/>
              er ult. >ſex­
                <lb/>
              ti
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id004101">
                <margin.target id="marg805"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              11.
                <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="id004102">
                <margin.target id="marg806"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              16.
                <emph type="italics"/>
              eiuſ
                <lb/>
              dem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="head">
              <s id="id004103">LEMMA TERTIVM.</s>
            </p>
            <p type="main">
              <s id="id004104">Grauitatem ponderis appenſi aut fluidi
                <lb/>
              in comparatione ad remotionem à centro
                <lb/>
              grauitatis inuenire.
                <lb/>
                <arrow.to.target n="marg807"/>
              </s>
            </p>
            <p type="margin">
              <s id="id004105">
                <margin.target id="marg807"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id004106">Nam cum d trahetur per planum ut ſuſpenſum, & non tractum </s>
            </p>
            <p type="main">
              <s id="id004107">
                <arrow.to.target n="marg808"/>
                <lb/>
              a d, erit dimidium ponderis appenſi, igitur ex lemmate ſecundo, pa
                <lb/>
              tebit proportio laboris in remouendo d à loco proprio in quan­
                <lb/>
              cunque partem & diſtantiam, & in quouis loco ſit appenſum.</s>
            </p>
            <p type="margin">
              <s id="id004108">
                <margin.target id="marg808"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              16.
                <emph type="italics"/>
              hu­
                <lb/>
              ius.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="id004109">Ex hoc ſequitur, quod poterit annulus tam altè appendi, ut iuxta
                <lb/>
                <arrow.to.target n="marg809"/>
                <lb/>
              proportionem angulí & leuitatem propriam cum filo tenuiſsimo,
                <lb/>
              & ut fuerit latus, & poſitus è regione oris, ut ex ſermone circum­
                <lb/>
              agatur quaqua uerſus, & percutiat labra uaſis aqua pleni fermè, ut
                <lb/>
              uideatur plane reſponſa dare.</s>
            </p>
            <p type="margin">
              <s id="id004110">
                <margin.target id="marg809"/>
              C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              ^{m}. 2.</s>
            </p>
            <p type="head">
              <s id="id004111">LEMMA QVARTVM.</s>
            </p>
            <p type="main">
              <s id="id004112">Quanto magis remotum fuerit pondus ex eodem centro à recta
                <lb/>
              linea, tanto maiore impetu agetur, ut ultra locum medium feratur
                <lb/>
              non æquali, ſed producta proportione.</s>
            </p>
            <p type="main">
              <s id="id004113">Sit a b, & ut dictum eſt, non eſt ei pondus, niſi quatenus remoue­
                <lb/>
                <arrow.to.target n="marg810"/>
                <lb/>
              tur a recta, & in c ſummam habeat grauitatem, & d ſit medium b c,
                <lb/>
                <figure id="id.015.01.259.2.jpg" xlink:href="015/01/259/2.jpg" number="259"/>
                <lb/>
              dico ergo quod multo maiore impetu feretur ex cin
                <lb/>
              b quam ex d, nam cum c ſit ſumma grauitas, erit ſal­
                <lb/>
              tem dupla grauitati d, ſed d grauitas eſt penè infinita,
                <lb/>
              ut demonſtratum eſt in comparatione ad b, ut iuxta
                <lb/>
              ſitum remotionis à linea b, cum ergo proportio ſin­
                <lb/>
                <arrow.to.target n="marg811"/>
                <lb/>
              gularum partium c d ad ſingulas d b medietate b c diſtantes ſit ma­
                <lb/>
                <figure id="id.015.01.259.3.jpg" xlink:href="015/01/259/3.jpg" number="260"/>
                <lb/>
              ior dupla augendo, erit proportio c d ad d b, uelut pro­
                <lb/>
              poſita h k dupla g f, & h e dupla e f, e k h ad e g f quadru­
                <lb/>
              pla, igitur & eo maior quo acquiſitus eſt impetus ex de­
                <lb/>
              monſtratis, quare proportio motus & impetus ex c in
                <lb/>
                <arrow.to.target n="marg812"/>
                <lb/>
              b, eſt multo maior impetu ex d in b quadrupla pro­
                <lb/>
              portione.</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum