Theodosius <Bithynius>; Clavius, Christoph, Theodosii Tripolitae Sphaericorum libri tres

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        <div xml:id="echoid-div522" type="section" level="1" n="253">
          <p>
            <s xml:id="echoid-s7120" xml:space="preserve">
              <pb o="184" file="196" n="196" rhead=""/>
            autem arcus AD, ad arcum AC, proportionem ſeſquialteram; </s>
            <s xml:id="echoid-s7121" xml:space="preserve">habebit chor
              <lb/>
            da AD, ad chordam BC, minorem proportionem, quam ſeſquialteram. </s>
            <s xml:id="echoid-s7122" xml:space="preserve">Cum
              <lb/>
            ergo chorda AD, arcus grad. </s>
            <s xml:id="echoid-s7123" xml:space="preserve">1. </s>
            <s xml:id="echoid-s7124" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s7125" xml:space="preserve">30. </s>
            <s xml:id="echoid-s7126" xml:space="preserve">ex præcedentibus inuẽta ſit partium
              <lb/>
            ferè 261792. </s>
            <s xml:id="echoid-s7127" xml:space="preserve">erit chorda AC, arcus grad. </s>
            <s xml:id="echoid-s7128" xml:space="preserve">1. </s>
            <s xml:id="echoid-s7129" xml:space="preserve">(ad quam nimirum chorda AD,
              <lb/>
            hoc eſt, numerus 261792. </s>
            <s xml:id="echoid-s7130" xml:space="preserve">minorem proportionem habet, quam ſeſquialterã.)
              <lb/>
            </s>
            <s xml:id="echoid-s7131" xml:space="preserve">maior, quam 174528. </s>
            <s xml:id="echoid-s7132" xml:space="preserve">cum ad hunc numerum numerus 261792. </s>
            <s xml:id="echoid-s7133" xml:space="preserve">proportio-
              <lb/>
              <note position="left" xlink:label="note-196-01" xlink:href="note-196-01a" xml:space="preserve">10.quinti.</note>
            nem ſeſquialteram habeat. </s>
            <s xml:id="echoid-s7134" xml:space="preserve">Conſtat igitur, chordam arcus grad. </s>
            <s xml:id="echoid-s7135" xml:space="preserve">1. </s>
            <s xml:id="echoid-s7136" xml:space="preserve">conſiſtere
              <lb/>
            inter duos hos numeros, 174532. </s>
            <s xml:id="echoid-s7137" xml:space="preserve">174528. </s>
            <s xml:id="echoid-s7138" xml:space="preserve">cum ille maior ſit, hic vero minor.
              <lb/>
            </s>
            <s xml:id="echoid-s7139" xml:space="preserve">Statuamus ergo eam eſſe 174530. </s>
            <s xml:id="echoid-s7140" xml:space="preserve">inter numeros illos omnino mediam. </s>
            <s xml:id="echoid-s7141" xml:space="preserve">Ita
              <lb/>
            enim ſenſibiliter non differet à vera chorda arcus grad. </s>
            <s xml:id="echoid-s7142" xml:space="preserve">1.</s>
            <s xml:id="echoid-s7143" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7144" xml:space="preserve">NON putes autem, eadem hac arte inueſtigari poſſe chordam arcus cu-
              <lb/>
            iuſuis plurium graduum ex duabus chordis notis duorum arcuum circunſtan
              <lb/>
            tium. </s>
            <s xml:id="echoid-s7145" xml:space="preserve">Nam cum in maioribus arcubus magna ſit differentia inter arcus, & </s>
            <s xml:id="echoid-s7146" xml:space="preserve">chor
              <lb/>
            das, ægre iudicari poterit, quinam numerus ex intermedijs inter duos inuẽtos
              <lb/>
            conſtitui debeat chorda arcus propoſiti. </s>
            <s xml:id="echoid-s7147" xml:space="preserve">Quod hoc exemplo faciemus perſpi-
              <lb/>
            cuum. </s>
            <s xml:id="echoid-s7148" xml:space="preserve">Sint cognitæ chordæ arcuum grad. </s>
            <s xml:id="echoid-s7149" xml:space="preserve">59. </s>
            <s xml:id="echoid-s7150" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s7151" xml:space="preserve">46. </s>
            <s xml:id="echoid-s7152" xml:space="preserve">& </s>
            <s xml:id="echoid-s7153" xml:space="preserve">grad. </s>
            <s xml:id="echoid-s7154" xml:space="preserve">60. </s>
            <s xml:id="echoid-s7155" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s7156" xml:space="preserve">30.
              <lb/>
            </s>
            <s xml:id="echoid-s7157" xml:space="preserve">partium 9964712. </s>
            <s xml:id="echoid-s7158" xml:space="preserve">& </s>
            <s xml:id="echoid-s7159" xml:space="preserve">10075480. </s>
            <s xml:id="echoid-s7160" xml:space="preserve">Si quis igitur ex his eruere vellet chordam ar-
              <lb/>
            cus grad. </s>
            <s xml:id="echoid-s7161" xml:space="preserve">60. </s>
            <s xml:id="echoid-s7162" xml:space="preserve">ita eſſet ei progrediendum. </s>
            <s xml:id="echoid-s7163" xml:space="preserve">Quoniam minor eſt proportio arcus
              <lb/>
              <note position="left" xlink:label="note-196-02" xlink:href="note-196-02a" xml:space="preserve">Coroll. 10.
                <lb/>
              huius.</note>
            grad. </s>
            <s xml:id="echoid-s7164" xml:space="preserve">59. </s>
            <s xml:id="echoid-s7165" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s7166" xml:space="preserve">46. </s>
            <s xml:id="echoid-s7167" xml:space="preserve">ad arcum grad. </s>
            <s xml:id="echoid-s7168" xml:space="preserve">60. </s>
            <s xml:id="echoid-s7169" xml:space="preserve">quam chordæ ad chordam: </s>
            <s xml:id="echoid-s7170" xml:space="preserve">Habet autem
              <lb/>
            9964712. </s>
            <s xml:id="echoid-s7171" xml:space="preserve">chorda arcus grad. </s>
            <s xml:id="echoid-s7172" xml:space="preserve">59. </s>
            <s xml:id="echoid-s7173" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s7174" xml:space="preserve">46. </s>
            <s xml:id="echoid-s7175" xml:space="preserve">ad 10003614 {1698/1793}. </s>
            <s xml:id="echoid-s7176" xml:space="preserve">proportio-
              <lb/>
            nem eandem, quam arcus grad. </s>
            <s xml:id="echoid-s7177" xml:space="preserve">59. </s>
            <s xml:id="echoid-s7178" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s7179" xml:space="preserve">46. </s>
            <s xml:id="echoid-s7180" xml:space="preserve">ad arcum grad. </s>
            <s xml:id="echoid-s7181" xml:space="preserve">60. </s>
            <s xml:id="echoid-s7182" xml:space="preserve">erit chorda ar-
              <lb/>
            cus grad. </s>
            <s xml:id="echoid-s7183" xml:space="preserve">60. </s>
            <s xml:id="echoid-s7184" xml:space="preserve">minor, quam 10003614 {1698/1793}. </s>
            <s xml:id="echoid-s7185" xml:space="preserve">vtpote ad quam chorda
              <lb/>
              <note position="left" xlink:label="note-196-03" xlink:href="note-196-03a" xml:space="preserve">10. quinti.</note>
            9964712. </s>
            <s xml:id="echoid-s7186" xml:space="preserve">maiorem proportionem habeat, quam ad 10003614 {1698/1793}. </s>
            <s xml:id="echoid-s7187" xml:space="preserve">Item
              <lb/>
            quia maior eſt proportio arcus grad. </s>
            <s xml:id="echoid-s7188" xml:space="preserve">60. </s>
            <s xml:id="echoid-s7189" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s7190" xml:space="preserve">30. </s>
            <s xml:id="echoid-s7191" xml:space="preserve">ad arcum grad. </s>
            <s xml:id="echoid-s7192" xml:space="preserve">60. </s>
            <s xml:id="echoid-s7193" xml:space="preserve">quam chor
              <lb/>
              <note position="left" xlink:label="note-196-04" xlink:href="note-196-04a" xml:space="preserve">10. huius.</note>
            dæ ad chordam: </s>
            <s xml:id="echoid-s7194" xml:space="preserve">Habet autem 10075480. </s>
            <s xml:id="echoid-s7195" xml:space="preserve">chorda arcus grad. </s>
            <s xml:id="echoid-s7196" xml:space="preserve">60. </s>
            <s xml:id="echoid-s7197" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s7198" xml:space="preserve">30. </s>
            <s xml:id="echoid-s7199" xml:space="preserve">ad
              <lb/>
            9992211 {69/121}. </s>
            <s xml:id="echoid-s7200" xml:space="preserve">eandem proportionem, quam arcus grad. </s>
            <s xml:id="echoid-s7201" xml:space="preserve">60. </s>
            <s xml:id="echoid-s7202" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s7203" xml:space="preserve">30. </s>
            <s xml:id="echoid-s7204" xml:space="preserve">ad
              <lb/>
            arcum grad. </s>
            <s xml:id="echoid-s7205" xml:space="preserve">60. </s>
            <s xml:id="echoid-s7206" xml:space="preserve">erit chorda arcus grad. </s>
            <s xml:id="echoid-s7207" xml:space="preserve">60. </s>
            <s xml:id="echoid-s7208" xml:space="preserve">maior, quam 9992211 {69/121}. </s>
            <s xml:id="echoid-s7209" xml:space="preserve">vt-
              <lb/>
              <note position="left" xlink:label="note-196-05" xlink:href="note-196-05a" xml:space="preserve">10. quinti.</note>
            pote ad quam chorda 10075480. </s>
            <s xml:id="echoid-s7210" xml:space="preserve">proportionem habeat minorem, quam ad
              <lb/>
            9992211 {69/121}. </s>
            <s xml:id="echoid-s7211" xml:space="preserve">Conſtituenda igitur eſſet chorda arcus grad. </s>
            <s xml:id="echoid-s7212" xml:space="preserve">60. </s>
            <s xml:id="echoid-s7213" xml:space="preserve">inter hos
              <lb/>
            duos numeros 10003614 {1698/1793}. </s>
            <s xml:id="echoid-s7214" xml:space="preserve">9992211 {69/121}. </s>
            <s xml:id="echoid-s7215" xml:space="preserve">qui cum valde inter ſe
              <lb/>
            differant (eſt enim eorum differentia ferme 11403.) </s>
            <s xml:id="echoid-s7216" xml:space="preserve">ambiguum erit, quanta ea
              <lb/>
            ſit aſſumenda. </s>
            <s xml:id="echoid-s7217" xml:space="preserve">Quæ ambiguitas in perueſtigatione chordæ arcus grad. </s>
            <s xml:id="echoid-s7218" xml:space="preserve">1. </s>
            <s xml:id="echoid-s7219" xml:space="preserve">lo-
              <lb/>
            cum non habet, cum in tam paruis arcubus chordę parũ ab arcubus differant.</s>
            <s xml:id="echoid-s7220" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7221" xml:space="preserve">IAM vero inuenta chorda arcus grad. </s>
            <s xml:id="echoid-s7222" xml:space="preserve">1. </s>
            <s xml:id="echoid-s7223" xml:space="preserve">reperiemus quoq;</s>
            <s xml:id="echoid-s7224" xml:space="preserve">, per propoſ.
              <lb/>
            </s>
            <s xml:id="echoid-s7225" xml:space="preserve">
              <note position="left" xlink:label="note-196-06" xlink:href="note-196-06a" xml:space="preserve">Supputatio
                <lb/>
              chordarũ
                <lb/>
              arcuum per
                <lb/>
              Min.15. ex-
                <lb/>
              tenſorum.</note>
            15. </s>
            <s xml:id="echoid-s7226" xml:space="preserve">eiusq́; </s>
            <s xml:id="echoid-s7227" xml:space="preserve">coroll. </s>
            <s xml:id="echoid-s7228" xml:space="preserve">chordam arcus Min. </s>
            <s xml:id="echoid-s7229" xml:space="preserve">30. </s>
            <s xml:id="echoid-s7230" xml:space="preserve">Et ex hac chordam arcus Min. </s>
            <s xml:id="echoid-s7231" xml:space="preserve">15.
              <lb/>
            </s>
            <s xml:id="echoid-s7232" xml:space="preserve">Sed hanc poſtremam etiam inueniemus per propoſ. </s>
            <s xml:id="echoid-s7233" xml:space="preserve">13. </s>
            <s xml:id="echoid-s7234" xml:space="preserve">eiusq́; </s>
            <s xml:id="echoid-s7235" xml:space="preserve">coroll. </s>
            <s xml:id="echoid-s7236" xml:space="preserve">cum ar-
              <lb/>
            cus Min. </s>
            <s xml:id="echoid-s7237" xml:space="preserve">15. </s>
            <s xml:id="echoid-s7238" xml:space="preserve">ſit differentia inter arcum grad. </s>
            <s xml:id="echoid-s7239" xml:space="preserve">1. </s>
            <s xml:id="echoid-s7240" xml:space="preserve">& </s>
            <s xml:id="echoid-s7241" xml:space="preserve">arcum Min. </s>
            <s xml:id="echoid-s7242" xml:space="preserve">45. </s>
            <s xml:id="echoid-s7243" xml:space="preserve">quorũ chordæ
              <lb/>
            iam ſunt cognitæ. </s>
            <s xml:id="echoid-s7244" xml:space="preserve">Per chordã autem arcus Min. </s>
            <s xml:id="echoid-s7245" xml:space="preserve">15. </s>
            <s xml:id="echoid-s7246" xml:space="preserve">cognoſcemus per propoſ. </s>
            <s xml:id="echoid-s7247" xml:space="preserve">
              <lb/>
            14. </s>
            <s xml:id="echoid-s7248" xml:space="preserve">eiusq́; </s>
            <s xml:id="echoid-s7249" xml:space="preserve">coroll. </s>
            <s xml:id="echoid-s7250" xml:space="preserve">chordã arcus Min. </s>
            <s xml:id="echoid-s7251" xml:space="preserve">30. </s>
            <s xml:id="echoid-s7252" xml:space="preserve">qui ex arcu Min. </s>
            <s xml:id="echoid-s7253" xml:space="preserve">15. </s>
            <s xml:id="echoid-s7254" xml:space="preserve">& </s>
            <s xml:id="echoid-s7255" xml:space="preserve">ex arcu Min. </s>
            <s xml:id="echoid-s7256" xml:space="preserve">15. </s>
            <s xml:id="echoid-s7257" xml:space="preserve">
              <lb/>
            componitur. </s>
            <s xml:id="echoid-s7258" xml:space="preserve">Item chordam arcus Min. </s>
            <s xml:id="echoid-s7259" xml:space="preserve">45. </s>
            <s xml:id="echoid-s7260" xml:space="preserve">ex arcubus Min. </s>
            <s xml:id="echoid-s7261" xml:space="preserve">30. </s>
            <s xml:id="echoid-s7262" xml:space="preserve">& </s>
            <s xml:id="echoid-s7263" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s7264" xml:space="preserve">15. </s>
            <s xml:id="echoid-s7265" xml:space="preserve">com
              <lb/>
            poſiti. </s>
            <s xml:id="echoid-s7266" xml:space="preserve">Item chordam arcus grad. </s>
            <s xml:id="echoid-s7267" xml:space="preserve">1. </s>
            <s xml:id="echoid-s7268" xml:space="preserve">ex arcubus Min. </s>
            <s xml:id="echoid-s7269" xml:space="preserve">45. </s>
            <s xml:id="echoid-s7270" xml:space="preserve">& </s>
            <s xml:id="echoid-s7271" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s7272" xml:space="preserve">15. </s>
            <s xml:id="echoid-s7273" xml:space="preserve">conflati. </s>
            <s xml:id="echoid-s7274" xml:space="preserve">
              <lb/>
            Et chordam arcus grad. </s>
            <s xml:id="echoid-s7275" xml:space="preserve">1. </s>
            <s xml:id="echoid-s7276" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s7277" xml:space="preserve">15. </s>
            <s xml:id="echoid-s7278" xml:space="preserve">Et chordam arcus grad. </s>
            <s xml:id="echoid-s7279" xml:space="preserve">1. </s>
            <s xml:id="echoid-s7280" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s7281" xml:space="preserve">30. </s>
            <s xml:id="echoid-s7282" xml:space="preserve">quam-
              <lb/>
            uis omnes hæ chordæ iam factæ ſint alia ratione notæ. </s>
            <s xml:id="echoid-s7283" xml:space="preserve">Deniq; </s>
            <s xml:id="echoid-s7284" xml:space="preserve">hac via reperie-
              <lb/>
            mus chordas omnium arcuum ſeſe ordine Minutis 15. </s>
            <s xml:id="echoid-s7285" xml:space="preserve">ſuperantium: </s>
            <s xml:id="echoid-s7286" xml:space="preserve">quamuis
              <lb/>
            multas illarum alijs rationibus inueſtigare poſsimus, vt ex propoſ. </s>
            <s xml:id="echoid-s7287" xml:space="preserve">13. </s>
            <s xml:id="echoid-s7288" xml:space="preserve">14. </s>
            <s xml:id="echoid-s7289" xml:space="preserve">15. </s>
            <s xml:id="echoid-s7290" xml:space="preserve">
              <lb/>
            earumq́; </s>
            <s xml:id="echoid-s7291" xml:space="preserve">corollarijs manifeſtum eſt.</s>
            <s xml:id="echoid-s7292" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7293" xml:space="preserve">QVOD ſi ſtatuantur ordine omnes arcus ſeſe Minutis 15. </s>
            <s xml:id="echoid-s7294" xml:space="preserve">ſuperantes,
              <lb/>
              <note position="left" xlink:label="note-196-07" xlink:href="note-196-07a" xml:space="preserve">Supputatio
                <lb/>
              chordarũ</note>
            vnà cum eorum chordis; </s>
            <s xml:id="echoid-s7295" xml:space="preserve">& </s>
            <s xml:id="echoid-s7296" xml:space="preserve">ad dexteram cuiuſuis chordæ aſcribatur </s>
          </p>
        </div>
      </text>
    </echo>
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