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="015/01/015.jpg"/>
              <row>
                <cell>CLXVII.</cell>
                <cell>P
                  <emph type="italics"/>
                roportionem muſicam ad ſapores & odores coaptare.
                  <emph.end type="italics"/>
                </cell>
                <cell>176</cell>
              </row>
              <row>
                <cell>CLXVIII.</cell>
                <cell>P
                  <emph type="italics"/>
                icturarum proportiones explicare.
                  <emph.end type="italics"/>
                </cell>
                <cell>179</cell>
              </row>
              <row>
                <cell>CLXIX.</cell>
                <cell>P
                  <emph type="italics"/>
                roportionem muſicam in inſtrumentis declarare iuxta compoſitionis ra­tionem.
                  <emph.end type="italics"/>
                </cell>
                <cell>182</cell>
              </row>
              <row>
                <cell>CLXX.</cell>
                <cell>C
                  <emph type="italics"/>
                oniugationes cuiuſuis numeri breuiter inuenire.
                  <emph.end type="italics"/>
                </cell>
                <cell>185</cell>
              </row>
              <row>
                <cell>CLXXI.</cell>
                <cell>P
                  <emph type="italics"/>
                ropoſitis duobus quibuslibet numeris, quotuis alios ſeu in continuum ſeu medios in continua proportione arithmetica, geometrica & muſica in­uenire.
                  <emph.end type="italics"/>
                </cell>
                <cell>187</cell>
              </row>
              <row>
                <cell>CLXXII.</cell>
                <cell>P
                  <emph type="italics"/>
                roportiones
                  <emph.end type="italics"/>
                S
                  <emph type="italics"/>
                tiphelij deſcribere.
                  <emph.end type="italics"/>
                </cell>
                <cell>191</cell>
              </row>
              <row>
                <cell>CLXXIII.</cell>
                <cell>C
                  <emph type="italics"/>
                irculum ſuper centro ſuo mouere æqualiter, ita quod omnia illius puncta per rectam lineam moueantur ultro citroque.
                  <emph.end type="italics"/>
                </cell>
                <cell>192</cell>
              </row>
              <row>
                <cell>CLXXIIII.</cell>
                <cell>P
                  <emph type="italics"/>
                rogreſſus & regreſſus, tam ſine latitudine quàm cum latitudine in planetis per ſolos concentricos circulos æqualiter motos demonſtrare.
                  <emph.end type="italics"/>
                </cell>
                <cell>194</cell>
              </row>
              <row>
                <cell>CLXXV.</cell>
                <cell>C
                  <emph type="italics"/>
                auſam uarietatis diametrorum ex ſuppoſitis concentricis demonſtra­re.
                  <emph.end type="italics"/>
                </cell>
                <cell>195</cell>
              </row>
              <row>
                <cell>CLXXVI.</cell>
                <cell>R
                  <emph type="italics"/>
                ationem centri grauitatis declarare.
                  <emph.end type="italics"/>
                </cell>
                <cell>197</cell>
              </row>
              <row>
                <cell>CLXXVII.</cell>
                <cell>S
                  <emph type="italics"/>
                i proportio aliqua ex duabus proportionibus eiuſdem quantitatis ad alias duas componatur, erit proportio illarum duarum eadem proportioni producti ex proportione in primam duarum quantitatum, detracta prio­re illa quantitate, quæ ad duas comparatur, ad eandem priorem quanti­tatem.
                  <emph.end type="italics"/>
                </cell>
                <cell>198</cell>
              </row>
              <row>
                <cell>CLXXVIII.</cell>
                <cell>P
                  <emph type="italics"/>
                roportionem miſtionis metallorum, maximè auri & argenti declara­re.
                  <emph.end type="italics"/>
                </cell>
                <cell>199</cell>
              </row>
              <row>
                <cell>CLXXIX.</cell>
                <cell>S
                  <emph type="italics"/>
                i duobus totis duæ portiones ſimiles abſcindantur ab eiſdem denuò, & ab­ſcißis portionibus partes eædem auferantur, denuoque ac denuò quoties libuerit à portionibus, & ù reſiduis ipſarum quantitatum partes eædem auferantur, erit reſiduí ad reſiduum, ueluti totius ad totum.
                  <emph.end type="italics"/>
                </cell>
                <cell>200</cell>
              </row>
              <row>
                <cell>CLXXX.</cell>
                <cell>S
                  <emph type="italics"/>
                i aliqua quantitas in duas partes diuidatur, fueritque alicuius quantitatis ad partes illas compoſita proportio, non poterit eiuſdem quantitatis ad par­tes alias quantitatis diuiſa, aliter proportio eadem componi.
                  <emph.end type="italics"/>
                </cell>
                <cell>202</cell>
              </row>
              <row>
                <cell>CLXXXI.</cell>
                <cell>C
                  <emph type="italics"/>
                um fuerit aliqua proportio, compoſita ex proportionibus primæ ad ſecun­dam & tertiam, & rurſus quartæ ad quintam & ſextam: ita ſe habebit proportio ſecundæ ad tertiam, ad proportionem quintæ ad ſextam, uelut producti ex proportione in ſecundam detracta prima ad primam ad pro­ductum ex proportione in quintam, detracta quarta ad quartam.
                  <emph.end type="italics"/>
                </cell>
                <cell>203</cell>
              </row>
              <row>
                <cell>CLXXXII.</cell>
                <cell>P
                  <emph type="italics"/>
                ropoſita differentia proportionum partium ſimilium ad partes aſſumptas, propoſitaque proportione totius ad reſidua eadem, differentiam propor­tionum totius ad reliquum reſidui inuenire.
                  <emph.end type="italics"/>
                </cell>
                <cell>203</cell>
              </row>
              <row>
                <cell>CLXXXIII.</cell>
                <cell>S
                  <emph type="italics"/>
                pacium uitæ naturalis per ſpacium uitæ fortuitum declarare.
                  <emph.end type="italics"/>
                </cell>
                <cell>204</cell>
              </row>
              <row>
                <cell>CLXXXIIII.</cell>
                <cell>Q
                  <emph type="italics"/>
                uæcunque grauia in uorticibus aquarum, merguntur, in medio uorticis, pri­mum uerſa mergantur.
                  <emph.end type="italics"/>
                </cell>
                <cell>211</cell>
              </row>
              <row>
                <cell>CLXXXV.</cell>
                <cell>C
                  <emph type="italics"/>
                ur homo ſedens quanto altius ſedet, & quanto magis crura ad fœmora, & fœmora ad pectus reclinata habet, facilius conſurgat, cum tamen hæc op­poſito modo inuicem ſe habeant, declarare.
                  <emph.end type="italics"/>
                </cell>
                <cell>213</cell>
              </row>
              <row>
                <cell>CLXXXVI.</cell>
                <cell>S
                  <emph type="italics"/>
                i fuerit proportio primæ & ſecundæ quantitatis ad tertiam, ut primæ & quartæ ad quintam, fueritque quarta ſecunda maior, erit proportio quar­tæ ad quintam maior quàm ſecundæ ad tertiam.
                  <emph.end type="italics"/>
                Q
                  <emph type="italics"/>
                uod ſi fuerit maior
                  <emph.end type="italics"/>
                </cell>
                <cell/>
              </row>
            </table>
          </section>
        </front>
      </text>
    </archimedes>
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