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="015/01/011.jpg"/>
              <row>
                <cell/>
                <cell>
                  <emph type="italics"/>
                uitatis centrum.
                  <emph.end type="italics"/>
                </cell>
                <cell>51</cell>
              </row>
              <row>
                <cell>LXI.</cell>
                <cell>P
                  <emph type="italics"/>
                roportionum ictus ad pondus rei & diſtantiam generaliter conſiderare.
                  <emph.end type="italics"/>
                </cell>
                <cell>52</cell>
              </row>
              <row>
                <cell>LXII.</cell>
                <cell>P
                  <emph type="italics"/>
                roportionem motoris in plano ad motorem, qui eleuat pondus iuxta id quod mouet, inuenire.
                  <emph.end type="italics"/>
                </cell>
                <cell>53</cell>
              </row>
              <row>
                <cell>LXIII.</cell>
                <cell>O
                  <emph type="italics"/>
                mne graue quanto proximius alligatum plano, tantò facilius trabitur.
                  <emph.end type="italics"/>
                </cell>
                <cell>53</cell>
              </row>
              <row>
                <cell>LXIIII.</cell>
                <cell>O
                  <emph type="italics"/>
                mne mobile quantò latius tanto tardius moustur in plano.
                  <emph.end type="italics"/>
                </cell>
                <cell>54</cell>
              </row>
              <row>
                <cell>LXV.</cell>
                <cell>P
                  <emph type="italics"/>
                roportionem duorum mobilium inter ſe cum auxilio medij inuenire.
                  <emph.end type="italics"/>
                </cell>
                <cell>54</cell>
              </row>
              <row>
                <cell>LXVI.</cell>
                <cell>P
                  <emph type="italics"/>
                roportionem laterum eptagoni, & ſubtenſarum conſiderare, & quæ à reflexa proportione pendent.
                  <emph.end type="italics"/>
                </cell>
                <cell>55</cell>
              </row>
              <row>
                <cell>LXVII.</cell>
                <cell>S
                  <emph type="italics"/>
                i fuerint aliquot quantitates ab una quantitate aliæque totidem ab eadem analo­gæ, erit proportio tertiæ unius ordinis ad tertiam alterius, ut ſecundæ ad ſe­cundum duplicata, & quartæ ad quartam triplicata, quintæ ad quintam quadruplicata, atque ſic de alijs.
                  <emph.end type="italics"/>
                </cell>
                <cell>57</cell>
              </row>
              <row>
                <cell>LXVIII.</cell>
                <cell>P
                  <emph type="italics"/>
                ropoſitio collectorum ab
                  <emph.end type="italics"/>
                E
                  <emph type="italics"/>
                uclide &
                  <emph.end type="italics"/>
                A
                  <emph type="italics"/>
                rchimede.
                  <emph.end type="italics"/>
                </cell>
                <cell>57</cell>
              </row>
              <row>
                <cell>LXIX.</cell>
                <cell>P
                  <emph type="italics"/>
                ropoſitio collectorum ex quatuor libris
                  <emph.end type="italics"/>
                A
                  <emph type="italics"/>
                pollonij
                  <emph.end type="italics"/>
                P
                  <emph type="italics"/>
                ergei &
                  <emph.end type="italics"/>
                  <expan abbr="q.">que</expan>
                S
                  <emph type="italics"/>
                ereni.
                  <emph.end type="italics"/>
                </cell>
                <cell>59</cell>
              </row>
              <row>
                <cell>LXX.</cell>
                <cell>S
                  <emph type="italics"/>
                i fuerint tres quantitates in continua proportione, aliæque totidem in continua proportione poterunt conſtituere tres quantitates in æquali differentia per­uerſim copulatæ.
                  <emph.end type="italics"/>
                </cell>
                <cell>62</cell>
              </row>
              <row>
                <cell>LXXI.</cell>
                <cell>P
                  <emph type="italics"/>
                roportionem leuitatis ponderis per uirgam torcularem attracti ad rectam ſu­ſpenſionem inuenire.
                  <emph.end type="italics"/>
                </cell>
                <cell>63</cell>
              </row>
              <row>
                <cell>LXXII.</cell>
                <cell>P
                  <emph type="italics"/>
                roportionem ponderis ſphæræ pendentis ad aſcendentem per accliue planum inuenire.
                  <emph.end type="italics"/>
                </cell>
                <cell>63</cell>
              </row>
              <row>
                <cell>LXXIII.</cell>
                <cell>P
                  <emph type="italics"/>
                roportionem ponderum attractorum penes figuram in plano inuenire.
                  <emph.end type="italics"/>
                </cell>
                <cell>64</cell>
              </row>
              <row>
                <cell>LXXIIII.</cell>
                <cell>P
                  <emph type="italics"/>
                roportionem concutientis ad concuſſum inſtabili inuenire.
                  <emph.end type="italics"/>
                </cell>
                <cell>64</cell>
              </row>
              <row>
                <cell>LXXV.</cell>
                <cell>P
                  <emph type="italics"/>
                  <expan abbr="roportionẽ">roportionem</expan>
                immoti in aqua, ad
                  <expan abbr="immotũ">immotum</expan>
                in terra in excipiendo
                  <expan abbr="ictũ">ictum</expan>
                inuenire.
                  <emph.end type="italics"/>
                </cell>
                <cell>65</cell>
              </row>
              <row>
                <cell>LXXVI.</cell>
                <cell>P
                  <emph type="italics"/>
                roportionem
                  <expan abbr="duorũ">duorum</expan>
                mobilium ſibi
                  <expan abbr="inuicẽ">inuicem</expan>
                  <expan abbr="concurrentiũ">concurrentium</expan>
                per
                  <expan abbr="rectã">rectam</expan>
                inuenire.
                  <emph.end type="italics"/>
                </cell>
                <cell>66</cell>
              </row>
              <row>
                <cell>LXXVII.</cell>
                <cell>P
                  <emph type="italics"/>
                roportionem motus obliqui ad motum rectum in nauibus inuenire.
                  <emph.end type="italics"/>
                </cell>
                <cell>66</cell>
              </row>
              <row>
                <cell>LXXVIII.</cell>
                <cell>P
                  <emph type="italics"/>
                roportionem nauis ad triremes quotuis concurrentes demonſtrare.
                  <emph.end type="italics"/>
                </cell>
                <cell>67</cell>
              </row>
              <row>
                <cell>LXXIX.</cell>
                <cell>P
                  <emph type="italics"/>
                roportionem medicamentorum purgantium inuicem declarare
                  <emph.end type="italics"/>
                </cell>
                <cell>68</cell>
              </row>
              <row>
                <cell>LXXX.</cell>
                <cell>P
                  <emph type="italics"/>
                roportionem motus ſecundum obliquum ad rectum in ſpacio declarare.
                  <emph.end type="italics"/>
                </cell>
                <cell>69</cell>
              </row>
              <row>
                <cell>LXXXI.</cell>
                <cell>Q
                  <emph type="italics"/>
                ualis ſit angulus, per quem poteſt moueri nauis ad rectum explorare.
                  <emph.end type="italics"/>
                </cell>
                <cell>70</cell>
              </row>
              <row>
                <cell>LXXXII.</cell>
                <cell>P
                  <emph type="italics"/>
                roportionem uelorum indagare.
                  <emph.end type="italics"/>
                </cell>
                <cell>70</cell>
              </row>
              <row>
                <cell>LXXXIII.</cell>
                <cell>P
                  <emph type="italics"/>
                roportionem receſſus à recta uia ad obliquitatem inueſtigare.
                  <emph.end type="italics"/>
                </cell>
                <cell>72</cell>
              </row>
              <row>
                <cell>LXXXIIII.</cell>
                <cell>D
                  <emph type="italics"/>
                  <expan abbr="iſtantiã">iſtantiam</expan>
                centri terræ à centro mundi per motum lapidis
                  <emph.end type="italics"/>
                H
                  <emph type="italics"/>
                erculei declarare.
                  <emph.end type="italics"/>
                </cell>
                <cell>73</cell>
              </row>
              <row>
                <cell>LXXXV.</cell>
                <cell>P
                  <emph type="italics"/>
                roportio ponderis unius grauis ad aliud ſub eadem menſura eſt ueluti eiuſdem ad differentiam ponderis uaſis repleti ex altero graui, & ex ambobus de­tracto priore.
                  <emph.end type="italics"/>
                </cell>
                <cell>74</cell>
              </row>
              <row>
                <cell>LXXXVI.</cell>
                <cell>S
                  <emph type="italics"/>
                i circuli in æ quales ſeu in ſphæra ſeu in plano ſe ſecuerint, nunquàm oppoſitos angulos æquales habent.
                  <emph.end type="italics"/>
                </cell>
                <cell>77</cell>
              </row>
              <row>
                <cell>LXXXVII.</cell>
                <cell>P
                  <emph type="italics"/>
                roportiones craßitiei aquæ ad
                  <expan abbr="aẽrẽ">aerrem</expan>
                in
                  <expan abbr="cõparatione">comparatione</expan>
                ad radios demonſtrare.
                  <emph.end type="italics"/>
                </cell>
                <cell>78</cell>
              </row>
              <row>
                <cell>LXXXVIII.</cell>
                <cell>I
                  <emph type="italics"/>
                  <expan abbr="nſtrumentũ">nſtrumentum</expan>
                  <emph.end type="italics"/>
                A
                  <emph type="italics"/>
                colingen, quo momenta temporum
                  <expan abbr="deprehendãtur">deprehendantur</expan>
                fabricare.
                  <emph.end type="italics"/>
                </cell>
                <cell>79</cell>
              </row>
              <row>
                <cell>LXXXIX.</cell>
                <cell>P
                  <emph type="italics"/>
                roportionem denſitatis aquæ ad aërem per pondera inuenire.
                  <emph.end type="italics"/>
                </cell>
                <cell>82</cell>
              </row>
              <row>
                <cell>XC.</cell>
                <cell>R
                  <emph type="italics"/>
                ationem impetus uiolenti extra mißi ponderis ad æqualitatem reducere.
                  <emph.end type="italics"/>
                </cell>
                <cell>82</cell>
              </row>
              <row>
                <cell>XCI.</cell>
                <cell>P
                  <emph type="italics"/>
                roportionem grauis cubi, & ſphærici æqualium in accliui, & deſcenſus eorum demonſtrare.
                  <emph.end type="italics"/>
                </cell>
                <cell>83</cell>
              </row>
              <row>
                <cell>XCII.</cell>
                <cell>P
                  <emph type="italics"/>
                  <expan abbr="roportionẽ">roportionem</expan>
                ponderis æqualis iuxta longitudinis
                  <expan abbr="cõparationẽ">comparationem</expan>
                demonſtrare.
                  <emph.end type="italics"/>
                </cell>
                <cell>85</cell>
              </row>
              <row>
                <cell>XCIII.</cell>
                <cell>P
                  <emph type="italics"/>
                ropter qd in
                  <expan abbr="cõcußione">concußione</expan>
                  <expan abbr="etiã">etiam</expan>
                leui nauis loco moueatar
                  <expan abbr="oſtẽdere">oſtendere</expan>
                .
                  <emph.end type="italics"/>
                V
                  <emph type="italics"/>
                nde manifi
                  <expan abbr="ſiũ">ſium</expan>
                eſt duas naues ſibi
                  <expan abbr="inuicẽ">inuicem</expan>
                occurſantes retrocedere, &
                  <expan abbr="quãtũ">quantum</expan>
                  <expan abbr="retrocedãt">retrocedant</expan>
                ambæ.
                  <emph.end type="italics"/>
                </cell>
                <cell>86</cell>
              </row>
            </table>
          </section>
        </front>
      </text>
    </archimedes>
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