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
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
< >
page |< < of 291 > >|
    <archimedes>
      <text>
        <front>
          <section>
            <table>
              <pb xlink:href="015/01/013.jpg"/>
              <row>
                <cell>CXXIII.</cell>
                <cell>C
                  <emph type="italics"/>
                ognita ratione umbræ ad gnomonem ſinum, & arcum altitudinis ab horizon­te, quouis tempore dignoſcere.
                  <emph.end type="italics"/>
                </cell>
                <cell>121</cell>
              </row>
              <row>
                <cell>CXXIIII.</cell>
                <cell>P
                  <emph type="italics"/>
                roportionem umbræ uerſæ eſſe ad gnomonem, uelut gnomonis ad umbram uerſam.
                  <emph.end type="italics"/>
                </cell>
                <cell>122</cell>
              </row>
              <row>
                <cell>CXXV.</cell>
                <cell>P
                  <emph type="italics"/>
                roportionem dimetientis, & peripheriæ cuiuslibet circuli paralleli æquino­ctiali per cognitam partem magni circuli demonſtrare.
                  <emph.end type="italics"/>
                </cell>
                <cell>123</cell>
              </row>
              <row>
                <cell>CXXVI.</cell>
                <cell>C
                  <emph type="italics"/>
                irculi horarij naturam declarare.
                  <emph.end type="italics"/>
                </cell>
                <cell>123</cell>
              </row>
              <row>
                <cell>CXXVII.</cell>
                <cell>D
                  <emph type="italics"/>
                ata poli altitudine ortus amplitudinem demonftrare.
                  <emph.end type="italics"/>
                </cell>
                <cell>124</cell>
              </row>
              <row>
                <cell>CXXVIII.</cell>
                <cell>N
                  <emph type="italics"/>
                ota amplitudine ortus, cuiuſque puncti arcum ſemidiurnum inuenire.
                  <emph.end type="italics"/>
                </cell>
                <cell>124</cell>
              </row>
              <row>
                <cell>CXXIX.</cell>
                <cell>D
                  <emph type="italics"/>
                ata altitudine
                  <emph.end type="italics"/>
                S
                  <emph type="italics"/>
                olis in quacunque regione, quacunque die diſtantiam
                  <emph.end type="italics"/>
                S
                  <emph type="italics"/>
                olis à meri­diano cognoſcere.
                  <emph.end type="italics"/>
                </cell>
                <cell>124</cell>
              </row>
              <row>
                <cell>CXXX.</cell>
                <cell>D
                  <emph type="italics"/>
                ata regionis altitudine, & loco
                  <emph.end type="italics"/>
                S
                  <emph type="italics"/>
                olis proportionem gnomonis, tam ad um­bram rectam quàm uerſam, uel etiam in cylindro determinare.
                  <emph.end type="italics"/>
                </cell>
                <cell>125</cell>
              </row>
              <row>
                <cell>CXXXI.</cell>
                <cell>S
                  <emph type="italics"/>
                i lineæ alicui duplum alterius adiungatur, erit proportio duarum ad primam maior quàm dupli cum prima ad primam cum una adiecta.
                  <emph.end type="italics"/>
                </cell>
                <cell>126</cell>
              </row>
              <row>
                <cell>CXXXII.</cell>
                <cell>S
                  <emph type="italics"/>
                i ad duas lineas quarum una alteri dupla ſit eadem linea addatur, erit aggrega­ti ex minore, & adiecta ad ipſam minorem, minor proportio quàm aggre­gati ex maiore, & adiecta ad ipſam maiorem duplicata.
                  <emph.end type="italics"/>
                </cell>
                <cell>126</cell>
              </row>
              <row>
                <cell>CXXXIII.</cell>
                <cell>S
                  <emph type="italics"/>
                i fuerint duæ quantitates,
                  <expan abbr="quarũ">quarum</expan>
                una alteri dupla ſit: minuatur à minore quæ­dam quantitas,
                  <expan abbr="eadẽque">eadenque</expan>
                maiori addatur, erit minoris ad reſiduum maior pro­portio, quàm aggregati ad maiorem duplicata.
                  <emph.end type="italics"/>
                S
                  <emph type="italics"/>
                i uerò minori addatur, & à maiore detrabatur, erit aggregati ad minorem minor proportio quàm maioris ad reſiduum duplicata.
                  <emph.end type="italics"/>
                </cell>
                <cell>127</cell>
              </row>
              <row>
                <cell>CXXXIIII.</cell>
                <cell>S
                  <emph type="italics"/>
                i rectangula ſuperficies ſit, cuius pars tertia quadrata ſit corpus, quod ex la­tere quadratæ in reſiduum ſuperficiei conſtat, maius eſt quouis corpore ex eadem ſuperficies, aliter diuiſa conſtituto.
                  <emph.end type="italics"/>
                </cell>
                <cell>127</cell>
              </row>
              <row>
                <cell>CXXXV.</cell>
                <cell>S
                  <emph type="italics"/>
                i linea in duas partes, quarum una fit alteri dupla diuidatur, erit quod fit ex tertia parte in quadratum reſidui parallelipedum maius omni pararalleli­pedo, quod ex diuiſione eiuſdem lineæ creari poßit.
                  <emph.end type="italics"/>
                </cell>
                <cell>128</cell>
              </row>
              <row>
                <cell>CXXXVI.</cell>
                <cell>D
                  <emph type="italics"/>
                enominationes in infinitum extendere.
                  <emph.end type="italics"/>
                </cell>
                <cell>129</cell>
              </row>
              <row>
                <cell>CXXXVII.</cell>
                <cell>R
                  <emph type="italics"/>
                ationem numerorum ex progreßione declarare.
                  <emph.end type="italics"/>
                </cell>
                <cell>131</cell>
              </row>
              <row>
                <cell>CXXXVIII.</cell>
                <cell>M
                  <emph type="italics"/>
                odos uſus horum numerorum declarare.
                  <emph.end type="italics"/>
                </cell>
                <cell>131</cell>
              </row>
              <row>
                <cell>CXXXIX.</cell>
                <cell>R
                  <emph type="italics"/>
                adices omnes à propoſitis numeris extrahere.
                  <emph.end type="italics"/>
                </cell>
                <cell>132</cell>
              </row>
              <row>
                <cell>CXL.</cell>
                <cell>R
                  <emph type="italics"/>
                adices per numeros fractos determinare.
                  <emph.end type="italics"/>
                </cell>
                <cell>133</cell>
              </row>
              <row>
                <cell>CXLI.</cell>
                <cell>N
                  <emph type="italics"/>
                umeros fractos ad minores in ea
                  <expan abbr="iẽ">iem</expan>
                proportione ualde propinqud deducere
                  <emph.end type="italics"/>
                </cell>
                <cell>136</cell>
              </row>
              <row>
                <cell>CXLII.</cell>
                <cell>D
                  <emph type="italics"/>
                  <expan abbr="enominationũ">enominationum</expan>
                in
                  <expan abbr="cremẽta">crementa</expan>
                ex extrema cognita inuenire.
                  <emph.end type="italics"/>
                E
                  <emph type="italics"/>
                t
                  <expan abbr="cõuerſo">conuerſo</expan>
                modo.
                  <emph.end type="italics"/>
                </cell>
                <cell>137</cell>
              </row>
              <row>
                <cell>CXLIII.</cell>
                <cell>S
                  <emph type="italics"/>
                i linea in duas partes diuidatur, corpora quæ fiunt ex una parte in alterius quadratum mutuo æqualia ſunt corpori, quod fit ex tota linea in ſuperfi­ciem unius partis in alteram.
                  <emph.end type="italics"/>
                </cell>
                <cell>138</cell>
              </row>
              <row>
                <cell>CXLIIII.</cell>
                <cell>D
                  <emph type="italics"/>
                uplum cubi medietatis maius eſt aggregato corporum mutuorum, cuiuslibet diuiſionis quantum eſt, quod fit ex tota in quadratum differentiæ.
                  <emph.end type="italics"/>
                </cell>
                <cell>139</cell>
              </row>
              <row>
                <cell>CXLV.</cell>
                <cell>S
                  <emph type="italics"/>
                i linea in duas partes diuidatur quadrata ambarum partium detracto eo, quod fit ex una parte in alteram, æqualia ſunt producto unius in alteram cum quadrato differentiæ.
                  <emph.end type="italics"/>
                </cell>
                <cell>139</cell>
              </row>
              <row>
                <cell>CXLVI.</cell>
                <cell>C
                  <emph type="italics"/>
                orpus quod fit ex linea diuiſa in ſuperficiem æqualem quadratis ambarum par tium detracta ſuperficie unius partis in alteram, eſt æquale aggregato cubo­rum ambarum partium.
                  <emph.end type="italics"/>
                </cell>
                <cell>139</cell>
              </row>
              <row>
                <cell>CXLVII.</cell>
                <cell>P
                  <emph type="italics"/>
                ropoſita linea diuiſa duas ei line as adijcere, ut proportio
                  <expan abbr="additarũ">additarum</expan>
                ſingularium
                  <emph.end type="italics"/>
                </cell>
                <cell/>
              </row>
            </table>
          </section>
        </front>
      </text>
    </archimedes>
Impressum