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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page |< < of 291 > >|
    <archimedes>
      <text>
        <front>
          <section>
            <table>
              <pb xlink:href="015/01/012.jpg"/>
              <row>
                <cell>XCIIII.</cell>
                <cell>S
                  <emph type="italics"/>
                i
                  <expan abbr="quãtitas">quantitas</expan>
                aliqua nota atque proportio erit producta,
                  <expan abbr="quãtitas">quantitas</expan>
                nota ſimiliter.
                  <emph.end type="italics"/>
                E
                  <emph type="italics"/>
                t ſi duæ proportiones notæ fuerint, erit producta ex his atque diuiſa coniunctaque atque detra­cta nota.
                  <emph.end type="italics"/>
                E
                  <emph type="italics"/>
                t ſi fuerit totius ad partem proportio nota, erit et ad aliam partem nota: & alterius partis ad
                  <expan abbr="alterã">alteram</expan>
                uno minor.
                  <emph.end type="italics"/>
                E
                  <emph type="italics"/>
                t ſi fuerit partis ad partem, erit ad totum monade minor atque nota.
                  <emph.end type="italics"/>
                E
                  <emph type="italics"/>
                t ſi fuerit unius
                  <expan abbr="quãtitatis">quantitatis</expan>
                ad duas
                  <expan abbr="quãtitates">quantitates</expan>
                proportio nota, erit &
                  <expan abbr="cõfuſa">confuſa</expan>
                ex eis nota.
                  <emph.end type="italics"/>
                E
                  <emph type="italics"/>
                t ſi fuerint trium quantitatum omiologarum, aut quatuor analogarum omnes præter unam cognitæ, erunt & illa alia cognita.
                  <emph.end type="italics"/>
                </cell>
                <cell>87</cell>
              </row>
              <row>
                <cell>XCV.</cell>
                <cell>C
                  <emph type="italics"/>
                uiuſuis trigoni rectanguli, aut cuius duo auguli ſint in dupla proportione, aut qui circulo inſcriptus ſit cognita quantitate unius lateris in comparatione ad dimetien
                  <expan abbr="tẽ">tem</expan>
                , ſi proportio duorum laterum cognita fuerit,
                  <expan abbr="erũt">erunt</expan>
                omnia eius latera cognita.
                  <emph.end type="italics"/>
                </cell>
                <cell>88</cell>
              </row>
              <row>
                <cell>XCVI.</cell>
                <cell>C
                  <emph type="italics"/>
                um in
                  <expan abbr="perſpicuũ">perſpicuum</expan>
                denſum radij luminoſi inciderint, quatuor fiunt luminis genera.
                  <emph.end type="italics"/>
                </cell>
                <cell>89</cell>
              </row>
              <row>
                <cell>XCVII.</cell>
                <cell>M
                  <emph type="italics"/>
                  <expan abbr="otũ">otum</expan>
                inuerſionis in figuris in
                  <expan abbr="cõparatione">comparatione</expan>
                ad
                  <expan abbr="motũ">motum</expan>
                ſphæræ in plano inueſtigare.
                  <emph.end type="italics"/>
                </cell>
                <cell>91</cell>
              </row>
              <row>
                <cell>XCVIII.</cell>
                <cell>P
                  <emph type="italics"/>
                roportionem ponderum æqualium per differentiam angulorum inuenire.
                  <emph.end type="italics"/>
                </cell>
                <cell>92</cell>
              </row>
              <row>
                <cell>XCIX.</cell>
                <cell>P
                  <emph type="italics"/>
                roportionem grauitatum per multitudinem ſuppoſitorum orbium oſtendere.
                  <emph.end type="italics"/>
                </cell>
                <cell>93</cell>
              </row>
              <row>
                <cell>C.</cell>
                <cell>P
                  <emph type="italics"/>
                  <expan abbr="roportionẽ">roportionem</expan>
                grauitatis
                  <expan abbr="ponderũ">ponderum</expan>
                attractorum per
                  <expan abbr="trochlearũ">trochlearum</expan>
                  <expan abbr="numerũ">numerum</expan>
                inueſtigare.
                  <emph.end type="italics"/>
                </cell>
                <cell>93</cell>
              </row>
              <row>
                <cell>CI.</cell>
                <cell>P
                  <emph type="italics"/>
                roportionem precij gemmarum ex tribus in eodem genere cognitis inuenire.
                  <emph.end type="italics"/>
                </cell>
                <cell>94</cell>
              </row>
              <row>
                <cell>CII.</cell>
                <cell>P
                  <emph type="italics"/>
                roportionem motuum inuerſionis, & attractionis in plano inuenire.
                  <emph.end type="italics"/>
                </cell>
                <cell>95</cell>
              </row>
              <row>
                <cell>CIII.</cell>
                <cell>P
                  <emph type="italics"/>
                roportionem eorundem in accliui demonſtrare.
                  <emph.end type="italics"/>
                </cell>
                <cell>95</cell>
              </row>
              <row>
                <cell>CIIII.</cell>
                <cell>P
                  <emph type="italics"/>
                roportionem motus attractionis in decliui ad motum in plano determinare.
                  <emph.end type="italics"/>
                </cell>
                <cell>95</cell>
              </row>
              <row>
                <cell>CV.</cell>
                <cell>P
                  <emph type="italics"/>
                roportionem ferentium pondus in pertica inuenire.
                  <emph.end type="italics"/>
                </cell>
                <cell>96</cell>
              </row>
              <row>
                <cell>CVI.</cell>
                <cell>Q
                  <emph type="italics"/>
                uales proportiones angulorum doceant laterum proportiones.
                  <emph.end type="italics"/>
                A
                  <emph type="italics"/>
                tque uicißim deter­minare.
                  <emph.end type="italics"/>
                </cell>
                <cell>97</cell>
              </row>
              <row>
                <cell>CVII.</cell>
                <cell>S
                  <emph type="italics"/>
                i in circulo duæ diametri ad rectum angulum ſe ſecauerint: aliæ uerò ad perpendicu­lum ex diametro exicrint ad circum ferentiam, ſingulæ ſupra diametrum erunt ma iores portionibus reliquis diametri ſuperioribus, infra autem minores.
                  <emph.end type="italics"/>
                D
                  <emph type="italics"/>
                imidium autem portionis ſuperioris reſiduum ad centrum maius ſagitta habebit.
                  <emph.end type="italics"/>
                I
                  <emph type="italics"/>
                n aliqua præterea portionis ſuperioris parte, quæ uerſus diametrum tranſuerſum poſita eſt, maior eſt differentia partis diametri ei
                  <expan abbr="correſpõdentis">correſpondentis</expan>
                ,
                  <expan abbr="q̃">quae</expan>
                line æ tranſuerſæ.
                  <emph.end type="italics"/>
                </cell>
                <cell>100</cell>
              </row>
              <row>
                <cell>CVIII.</cell>
                <cell>P
                  <emph type="italics"/>
                unctum æqualitatis differentiæ deſcenſus & remotionis à centro inuenire.
                  <emph.end type="italics"/>
                </cell>
                <cell>100</cell>
              </row>
              <row>
                <cell>CIX.</cell>
                <cell>R
                  <emph type="italics"/>
                ationem libræ expendere.
                  <emph.end type="italics"/>
                </cell>
                <cell>101</cell>
              </row>
              <row>
                <cell>CX.</cell>
                <cell>S
                  <emph type="italics"/>
                i duæ ſphæræ ex eadem materia deſcendant in aëre, eodem temporis momento ad planum ueniunt.
                  <emph.end type="italics"/>
                </cell>
                <cell>104</cell>
              </row>
              <row>
                <cell>CXI.</cell>
                <cell>C
                  <emph type="italics"/>
                ur ex medio tela ualidiorem ictum, & naues in ſcalmo à remo ac malo recipiant in­de ex puppi explorare.
                  <emph.end type="italics"/>
                </cell>
                <cell>105</cell>
              </row>
              <row>
                <cell>CXII.</cell>
                <cell>C
                  <emph type="italics"/>
                ur ex imo leuia longiùs ferantur declarare,
                  <emph.end type="italics"/>
                </cell>
                <cell>106</cell>
              </row>
              <row>
                <cell>CXIII.</cell>
                <cell>C
                  <emph type="italics"/>
                ur uirga longius mittatur à puero quam à uiro inueftigare.
                  <emph.end type="italics"/>
                </cell>
                <cell>107</cell>
              </row>
              <row>
                <cell>CXIIII.</cell>
                <cell>C
                  <emph type="italics"/>
                ircularis motus differentias quatuor eſſe, earumque rationem contemplari.
                  <emph.end type="italics"/>
                </cell>
                <cell>108</cell>
              </row>
              <row>
                <cell>CXV.</cell>
                <cell>P
                  <emph type="italics"/>
                roportionem motuum impulſionis, & attractionis inter ſe, ab eadem ui decla­rare.
                  <emph.end type="italics"/>
                </cell>
                <cell>110</cell>
              </row>
              <row>
                <cell>CXVI.</cell>
                <cell>C
                  <emph type="italics"/>
                ur machinæ oblongæ igneæ longius emittant ſphæram explorare.
                  <emph.end type="italics"/>
                </cell>
                <cell>111</cell>
              </row>
              <row>
                <cell>CXVII.</cell>
                <cell>I
                  <emph type="italics"/>
                n curriculis maior eſt uis pulueris copioſioris ampliore in ſpacio, quàm paucioris in minore iuxta proportionem eandem.
                  <emph.end type="italics"/>
                </cell>
                <cell>112</cell>
              </row>
              <row>
                <cell>CXVIII.</cell>
                <cell>Q
                  <emph type="italics"/>
                uanta proportione decedat ictus in obliquum parietem ab eo qui eſt ad perpendi­culum declarare.
                  <emph.end type="italics"/>
                </cell>
                <cell>114</cell>
              </row>
              <row>
                <cell>CXIX.</cell>
                <cell>Q
                  <emph type="italics"/>
                uantum ictus machinæ procliuis ad angulum minuatur explorare.
                  <emph.end type="italics"/>
                </cell>
                <cell>115</cell>
              </row>
              <row>
                <cell>CXX</cell>
                <cell>P
                  <emph type="italics"/>
                roportionem partium nauis ad eundem obliquum uentum explorare.
                  <emph.end type="italics"/>
                </cell>
                <cell>118</cell>
              </row>
              <row>
                <cell>CXXI.</cell>
                <cell>F
                  <emph type="italics"/>
                labelli uires atque naturam declarare.
                  <emph.end type="italics"/>
                </cell>
                <cell>219</cell>
              </row>
              <row>
                <cell>CXXII.</cell>
                <cell>C
                  <emph type="italics"/>
                ontemptus circa
                  <emph.end type="italics"/>
                S
                  <emph type="italics"/>
                olis rationem in umbris declarare.
                  <emph.end type="italics"/>
                </cell>
                <cell>120</cell>
              </row>
            </table>
          </section>
        </front>
      </text>
    </archimedes>
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