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 ...

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    <archimedes>
      <text>
        <front>
          <section>
            <table>
              <pb xlink:href="015/01/014.jpg"/>
              <row>
                <cell/>
                <cell>
                  <emph type="italics"/>
                & partium ſimul iunctarum ad additas ſit mutua.
                  <emph.end type="italics"/>
                </cell>
                <cell>148</cell>
              </row>
              <row>
                <cell>CXLVIII.</cell>
                <cell>P
                  <emph type="italics"/>
                ropoſitis tribus lineis primam ſic diuidere, ut adiectis duabus alijs lineis, ſecun­dum
                  <expan abbr="rationẽ">rationem</expan>
                mutuam ſingularum ſingulis,
                  <expan abbr="aggregatũ">aggregatum</expan>
                ex una
                  <expan abbr="adiectarũ">adiectarum</expan>
                , & par te ad
                  <expan abbr="aggregatũ">aggregatum</expan>
                ex alia parte, & adiecta ſe habeat, ut ſecunda ad
                  <expan abbr="tertiã">tertiam</expan>
                .
                  <emph.end type="italics"/>
                </cell>
                <cell>140</cell>
              </row>
              <row>
                <cell>CXLIX.</cell>
                <cell>D
                  <emph type="italics"/>
                atam lineam ſic diuidere, ut proportio quadratorum ad dupium unius partis in alteram ſit, ut lineæ datæ ad lineam datam.
                  <emph.end type="italics"/>
                </cell>
                <cell>141</cell>
              </row>
              <row>
                <cell>CL.</cell>
                <cell>P
                  <emph type="italics"/>
                ropoſitis duabus lineis, lineam communem utrique adiungere, ut ſit maioris ad ad­ditam proportio, uelut quadratorum minoris, & adiectæ ad duplum unius in alteram.
                  <emph.end type="italics"/>
                </cell>
                <cell>141</cell>
              </row>
              <row>
                <cell>CLI.</cell>
                <cell>P
                  <emph type="italics"/>
                roportio differentiæ quadratorum partium cuiuſuis lineæ, ad quadratum diffe­rentiæ illarum eſt, uelut totius lineæ ad differentiam.
                  <emph.end type="italics"/>
                </cell>
                <cell>142</cell>
              </row>
              <row>
                <cell>CLII.</cell>
                <cell>S
                  <emph type="italics"/>
                i linea in duas partes æquales, duasque inæquales diuidatur, fueritque proportio ag­gregati ex maiore, & dimidio ad ipſam maiorem, uelut ex minore, & ali­qua linea ad ipſam minorem, & rurſus aggregati ex minore, & dimidio ad ipſam minorem, uelut aggregati ex maiore, & alia addita ad ipſam maiorem, erit proportio dimidij ad partem unam inæqualem, uelut alterius partis inæ­qualis ad ſuam additam mutuò, & etiam proportio additarum inuicem, uelut proportio
                  <expan abbr="partiũ">partium</expan>
                  <expan abbr="inæqualiũ">inæqualium</expan>
                duplicata, & rurſus ipſum
                  <expan abbr="dimidiũ">dimidium</expan>
                lineæ aſſum­ptæ
                  <expan abbr="mediũ">medium</expan>
                , erit proportione inter additas.
                  <emph.end type="italics"/>
                D
                  <emph type="italics"/>
                  <expan abbr="emũ">emum</expan>
                proportio dimidij
                  <expan abbr="cũ">cum</expan>
                addita maiore ad
                  <expan abbr="dimidiũ">dimidium</expan>
                , cum addita minore, uelut maioris partis ad
                  <expan abbr="minorẽ">minorem</expan>
                .
                  <emph.end type="italics"/>
                </cell>
                <cell>142</cell>
              </row>
              <row>
                <cell>CLIII.</cell>
                <cell>V
                  <emph type="italics"/>
                im quamcunque manus multiplicare.
                  <emph.end type="italics"/>
                </cell>
                <cell>144</cell>
              </row>
              <row>
                <cell>CLIIII.</cell>
                <cell>S
                  <emph type="italics"/>
                i lineæ datæ alia linea adiungatur, ab extremitatibus autem prioris lineæ duæ rectæ in unum punctum concurrant proportionem habentes, quam mediam inter tota m & adiectam, & adiectam erit punctus, concurſus à puncto extre­mo lineæ adiectæ diſtans per lineam mediam.
                  <emph.end type="italics"/>
                Q
                  <emph type="italics"/>
                uod ſi ab extremo alicuius li­neæ æqua'is mediæ, ſeu peripheria circuli, cuius ſemidiameter ſit media linea duæ lineæ ad prædicta puncta producantur, ipſæ erunt in proportione mediæ ad adiectam.
                  <emph.end type="italics"/>
                </cell>
                <cell>145</cell>
              </row>
              <row>
                <cell>CLV.</cell>
                <cell>Q
                  <emph type="italics"/>
                uadr atorum numerum proportionem & inuentionem conſiderare.
                  <emph.end type="italics"/>
                </cell>
                <cell>147</cell>
              </row>
              <row>
                <cell>CLVI.</cell>
                <cell>H
                  <emph type="italics"/>
                orologiorum tempus multiplicare.
                  <emph.end type="italics"/>
                </cell>
                <cell>152</cell>
              </row>
              <row>
                <cell>CLVII.</cell>
                <cell>H
                  <emph type="italics"/>
                orologiorum molarium rationem oſtendere.
                  <emph.end type="italics"/>
                </cell>
                <cell>154</cell>
              </row>
              <row>
                <cell>CLVIII.</cell>
                <cell>R
                  <emph type="italics"/>
                ationem indicis mobilis cum rota, qua horarum numerus per ictus indicatur ex­plicare.
                  <emph.end type="italics"/>
                </cell>
                <cell>156</cell>
              </row>
              <row>
                <cell>CLIX.</cell>
                <cell>N
                  <emph type="italics"/>
                ullus angulus rectilineus æqualis eſſe poteſt alicui angulo contento recta, & cir culi portione.
                  <emph.end type="italics"/>
                </cell>
                <cell>158</cell>
              </row>
              <row>
                <cell>CLX.</cell>
                <cell>P
                  <emph type="italics"/>
                ropoſita linea tribusque in ea ſignis punctum inuenire, ex quo ductæ tres lineæ ad ſigna ſint in proportionibus datis.
                  <emph.end type="italics"/>
                </cell>
                <cell>162</cell>
              </row>
              <row>
                <cell>CLXI.</cell>
                <cell>S
                  <emph type="italics"/>
                i fuerint duo trianguli, quorum baſes in eadem linea ſint conſtituti, & æquales ad unum punctum terminati, & latus unum commune inter reliqua quantita­te medium neceſſe eſt angulum à maioribus lineis
                  <expan abbr="contentũ">contentum</expan>
                minorem eſſe.
                  <emph.end type="italics"/>
                </cell>
                <cell>162</cell>
              </row>
              <row>
                <cell>CLXII.</cell>
                <cell>P
                  <emph type="italics"/>
                roportionem duorum orbium, quorum diametrorum conuexæ partis, & conca­uæ proportiones datæ ſint inueſtigare.
                  <emph.end type="italics"/>
                </cell>
                <cell>164</cell>
              </row>
              <row>
                <cell>CLXIII.</cell>
                <cell>P
                  <emph type="italics"/>
                roportionem uirium ſtellarum per motus ſuos indagare.
                  <emph.end type="italics"/>
                </cell>
                <cell>165</cell>
              </row>
              <row>
                <cell>CLXIIII.</cell>
                <cell>S
                  <emph type="italics"/>
                yderum proportionem in magnitudine oſtendere.
                  <emph.end type="italics"/>
                </cell>
                <cell>166</cell>
              </row>
              <row>
                <cell>CLXV.</cell>
                <cell>P
                  <emph type="italics"/>
                roportionem motuum omnium ſtellarum ad
                  <emph.end type="italics"/>
                S
                  <emph type="italics"/>
                olem conſiderare.
                  <emph.end type="italics"/>
                </cell>
                <cell>167</cell>
              </row>
              <row>
                <cell>CLXVI.</cell>
                <cell>P
                  <emph type="italics"/>
                roportiones muſicas ſuperpartientes in eas, quæ particulá una tantum abundant reducere.
                  <emph.end type="italics"/>
                </cell>
                <cell>168</cell>
              </row>
            </table>
          </section>
        </front>
      </text>
    </archimedes>
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