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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      <text>
        <body>
          <chap>
            <p type="main">
              <s id="id002170">
                <pb pagenum="123 [=122]" xlink:href="015/01/141.jpg"/>
              per demonſtrata b a cognita in comparatione a d e a, e a autem per
                <lb/>
              octauum contemptum eſt dimetiens circuli, ergo a b ſinus notus,
                <lb/>
              & arcus f a, quod eſt primum cognitum. </s>
              <s id="id002171">Et hic quidem circulus
                <lb/>
              uerticalis dicitur, quia per illum tranſit, aliter non eſſet ad perpen­
                <lb/>
              diculum horizonti.
                <lb/>
                <arrow.to.target n="marg420"/>
              </s>
            </p>
            <p type="margin">
              <s id="id002172">
                <margin.target id="marg417"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              _{m}.</s>
            </p>
            <p type="margin">
              <s id="id002173">
                <margin.target id="marg418"/>
              P
                <emph type="italics"/>
              ræced.
                <emph.end type="italics"/>
              P
                <emph type="italics"/>
              ro
                <lb/>
              poſ.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id002174">
                <margin.target id="marg419"/>
              P
                <emph type="italics"/>
              rop.
                <emph.end type="italics"/>
              113.</s>
            </p>
            <p type="margin">
              <s id="id002175">
                <margin.target id="marg420"/>
              C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              ^{m}. 1.</s>
            </p>
            <p type="main">
              <s id="id002176">Ex hoc ſequitur, quod altitudines ſolis æquales omnes in uno
                <lb/>
              ſunt circulo horizonti parallelo. </s>
              <s id="id002177">Et ſi ſol fuerit in uno circulo ho­
                <lb/>
              rizonti parallelo, altitudines ſolis, & umbræ magnitudines æqua­
                <lb/>
              les erunt.</s>
            </p>
            <p type="main">
              <s id="id002178">
                <arrow.to.target n="marg421"/>
              </s>
            </p>
            <p type="margin">
              <s id="id002179">
                <margin.target id="marg421"/>
              C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              ^{m}. 2.</s>
            </p>
            <p type="main">
              <s id="id002180">Sol niſi bis in una die poteſt eſſe in circulo horizonti parallelo,
                <lb/>
              ſemel ante meridiem, & ſemel poſt, tantundem ab eodem diſtans.</s>
            </p>
            <p type="main">
              <s id="id002181">
                <arrow.to.target n="marg422"/>
              </s>
            </p>
            <p type="margin">
              <s id="id002182">
                <margin.target id="marg422"/>
              C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              ^{m}. 3.</s>
            </p>
            <p type="main">
              <s id="id002183">Cum ergo ita ſit, neceſſe eſt umbras æquales, & circulum hori­
                <lb/>
              zonti
                <expan abbr="parallelũ">parallelum</expan>
              fieri ſub in æqualibus horis in diuerſis ſemper die­
                <lb/>
              bus, præterquam cum in punctis fuerit æqualis ab ęquinoctiali, &
                <lb/>
              in eandem partem declinationis, & hoc bis
                <expan abbr="cõtingit">contingit</expan>
              ſolum in anno
                <lb/>
              pro quolibet circulo parallelo, ſicut in eodem die etiam bis
                <expan abbr="tãtum">tantum</expan>
              ,
                <lb/>
              ut dictum eſt.</s>
            </p>
            <p type="main">
              <s id="id002184">
                <arrow.to.target n="marg423"/>
              </s>
            </p>
            <p type="margin">
              <s id="id002185">
                <margin.target id="marg423"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id002186">Nam exempli gratia, cum ſol eſt in initio Capricorni, & in Cœli
                <lb/>
              medio, minima eſt umbra eius diei, & totius anni. </s>
              <s id="id002187">Cum ergo fuerit
                <lb/>
              ante meridiem, uel poſt, erit umbra maior ex ſuppoſito ſecudo um­
                <lb/>
              bra meridiei: at ei æqualis poterit eſſe umbra meridiei alterius diei
                <lb/>
              ex primo ſuppoſito, ergo umbræ æquales diuerſorum dierum fi­
                <lb/>
              unt ſub diuerſo ſitu ſolis, quo ad circulum meridiei, quod erat de­
                <lb/>
              monſtrandum.</s>
            </p>
            <p type="main">
              <s id="id002188">
                <arrow.to.target n="marg424"/>
              </s>
            </p>
            <p type="margin">
              <s id="id002189">
                <margin.target id="marg424"/>
              C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              ^{m}. 4.</s>
            </p>
            <p type="main">
              <s id="id002190">Ex hoc ſequitur, quod horarum determinatio fit ſecundum line­
                <lb/>
              am in æqualem obliquam, quæ toti anno ſeruiat, ut æqualium um­
                <lb/>
              brarum determinatio hararum & partium eius numerum.</s>
            </p>
            <p type="main">
              <s id="id002191">
                <arrow.to.target n="marg425"/>
              </s>
            </p>
            <p type="margin">
              <s id="id002192">
                <margin.target id="marg425"/>
              C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              ^{m}. 5.</s>
            </p>
            <p type="main">
              <s id="id002193">Ex quo colligitur modus faciendi gnomonem, ſeu per umbras
                <lb/>
              rectas, ſeu per uerſas, qui docebit toto anno non
                <expan abbr="ſolũ">ſolum</expan>
              horas, ſed mo
                <lb/>
              menta
                <expan abbr="pulſuũ">pulſuum</expan>
              , de quibus
                <expan abbr="dictũ">dictum</expan>
              eſt quod MMMDC horam
                <expan abbr="perficiũt">perficiunt</expan>
              .</s>
            </p>
            <p type="main">
              <s id="id002194">Propoſitio centeſima uigeſima quarta.</s>
            </p>
            <p type="main">
              <s id="id002195">Proportionem umbræ uerſæ eſſe ad gnomonem, uelut gnomo­
                <lb/>
              nis ad umbram uerſam.</s>
            </p>
            <p type="main">
              <s id="id002196">
                <arrow.to.target n="marg426"/>
              </s>
            </p>
            <p type="margin">
              <s id="id002197">
                <margin.target id="marg426"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id002198">Vmbra uerſa dicitur, quoties gnomo in pariete ad perpendicu­
                <lb/>
              lum figitur, ſic ut gnomo æquidiſtet circulo horizontis. </s>
              <s id="id002199">Sit ergo
                <lb/>
              paries c k ad perpendiculum f g, & h k a d gnomo ad perpendicu­
                <lb/>
              lum parietis & ſol, ut prius in a, & ſit primo k h tantæ longitudinis </s>
            </p>
            <p type="main">
              <s id="id002200">
                <arrow.to.target n="marg427"/>
                <lb/>
              ut umbræ locus ſit
                <expan abbr="pũctus">punctus</expan>
              d, ut ſit radius a h d e, eritque angulus d u­
                <lb/>
              trin que æqualis, & propterea triangulus k h d ſimilis d c e. </s>
              <s id="id002201">Sit modo
                <lb/>
                <arrow.to.target n="marg428"/>
                <lb/>
              gnomo maior m l ipſo h k & c l maior c k ſeu æqualis, & quam an­
                <lb/>
              guli k & l recti ſunt, & anguli l m n, & k h d æqualis, quia a n, & a c </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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