Clavius, Christoph, In Sphaeram Ioannis de Sacro Bosco commentarius

Table of contents

< >
[71.] IIII.
Page: 119 (82)
[72.] V.
Page: 119 (82)
[73.] THEOR. 1. PROPOS. 1.
Page: 119 (82)
[74.] THEOR. 2. PROPOS. 2.
Page: 120 (83)
[75.] THEOR. 3. PROPOS. 3.
Page: 121 (84)
[76.] THEOR. 4. PROPOS. 4.
Page: 122 (85)
[77.] THEOR. 5. PROPOS. 5.
Page: 122 (85)
[78.] THEOR. 6. PROPOS. 6.
Page: 123 (86)
[79.] THEOR. 1. PROPOS. 7.
Page: 124 (87)
[80.] SCHOLIVM.
Page: 125 (88)
[81.] THEOR. 7. PROPOS. 8.
Page: 125 (88)
[82.] THEOR. 8. PROPOS. 9.
Page: 126 (89)
[83.] PROBL. 2. PROPOS. 10.
Page: 127 (90)
[84.] THEOR. 9. PROPOS. 11.
Page: 128 (91)
[85.] THEOR. 10. PROPOS. 52
Page: 130 (93)
[86.] SCHOLIVM.
Page: 132 (95)
[87.] THEOR. 11. PROPOS. 13.
Page: 134 (97)
[88.] COROLLARIVM.
Page: 135 (98)
[89.] THEOR. 12. PROPOS. 14.
Page: 135 (98)
[90.] THEOR. 13. PROPOS. 15.
Page: 136 (99)
[91.] THEOR. 14. PROPOS. 16.
Page: 137 (100)
[92.] THEOR. 15. PROPOS. 17.
Page: 139 (102)
[93.] THEOR. 16. PROPOS. 18.
Page: 139 (102)
[94.] COMMENTARIVS.
Page: 142 (105)
[95.] COMMENTARIVS.
Page: 143 (106)
[96.] COMMENTARIVS.
Page: 145 (108)
[97.] TERRAM, ET AQVAM ESSE ROTVNDAS.
Page: 147 (110)
[98.] COMMENTARIVS.
Page: 147 (110)
[99.] COMMENTARIVS.
Page: 150 (113)
[100.] COMMENTARIVS.
Page: 151 (114)
< >
page |< < (85) of 525 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div223" type="section" level="1" n="75">
          <pb o="85" file="121" n="122" rhead="Ioan. de Sacro Boſco."/>
        </div>
        <div xml:id="echoid-div225" type="section" level="1" n="76">
          <head xml:id="echoid-head80" style="it" xml:space="preserve">THEOR. 4. PROPOS. 4.</head>
          <p style="it">
            <s xml:id="echoid-s4239" xml:space="preserve">
              <emph style="sc">Area</emph>
            cuiuslibet circuli æqualis eſt rectangulo comprehenſo
              <unsure/>
            ſub ſe-
              <lb/>
              <note position="right" xlink:label="note-121-01" xlink:href="note-121-01a" xml:space="preserve">Circulus
                <lb/>
              quicunque
                <lb/>
              cui rectan
                <unsure/>
              -
                <lb/>
              gulo æqua-
                <lb/>
              lis ſit.</note>
            midiametro, & </s>
            <s xml:id="echoid-s4240" xml:space="preserve">dimidiata circumferentia circuli.</s>
            <s xml:id="echoid-s4241" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4242" xml:space="preserve">
              <emph style="sc">Esto</emph>
            circulus A B C, cuius ſemidiameter D B: </s>
            <s xml:id="echoid-s4243" xml:space="preserve">Rectangulum autem
              <lb/>
              <figure xlink:label="fig-121-01" xlink:href="fig-121-01a" number="22">
                <image file="121-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/121-01"/>
              </figure>
            D B E F, comprehenſum ſub D B, ſemidiametro circuli, & </s>
            <s xml:id="echoid-s4244" xml:space="preserve">B E, recta, quæ
              <lb/>
            æqualis ſit dimidiatæ circunferentiæ circuli. </s>
            <s xml:id="echoid-s4245" xml:space="preserve">Dico aream circuli A B C, æqua
              <lb/>
            lem eſſe rectangulo D B E F. </s>
            <s xml:id="echoid-s4246" xml:space="preserve">Producatur enim B E, in continuum, ponatur-
              <lb/>
            q́ue E G, æqualis ipſi B E, ut ſit B G, recta æqualis toti circunferentiæ circu-
              <lb/>
            li. </s>
            <s xml:id="echoid-s4247" xml:space="preserve">Coniungantur denique puncta D, G, recta D G. </s>
            <s xml:id="echoid-s4248" xml:space="preserve">Quoniam igitur (per 1.
              <lb/>
            </s>
            <s xml:id="echoid-s4249" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s4250" xml:space="preserve">Archimedis de Dimenſione circuli) circulus A B C, æqualis eſt trian
              <lb/>
            gulo D B G: </s>
            <s xml:id="echoid-s4251" xml:space="preserve">Eſt autem triangulum D B G, rectangulo D B E F, æquale, ut in
              <lb/>
            ſcholio propoſ. </s>
            <s xml:id="echoid-s4252" xml:space="preserve">41. </s>
            <s xml:id="echoid-s4253" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s4254" xml:space="preserve">1. </s>
            <s xml:id="echoid-s4255" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s4256" xml:space="preserve">demonſtrauimus, quòd baſis trianguli dupla ſit
              <lb/>
            baſis rectanguli, (Id quod etiam ex demonſtratione antecedentis propoſ. </s>
            <s xml:id="echoid-s4257" xml:space="preserve">li-
              <lb/>
            quet, ubi oſtendimus, triangulum D E F, æquale eſſe rectangulo D E H I:) </s>
            <s xml:id="echoid-s4258" xml:space="preserve">
              <lb/>
            erit quoque circulus A B C, rectangulo D B E F, æqualis. </s>
            <s xml:id="echoid-s4259" xml:space="preserve">Area ergo cuius-
              <lb/>
            libet circuli æqualis eſt rectangulo, &</s>
            <s xml:id="echoid-s4260" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4261" xml:space="preserve">quod oſtendendum erat.</s>
            <s xml:id="echoid-s4262" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div228" type="section" level="1" n="77">
          <head xml:id="echoid-head81" style="it" xml:space="preserve">THEOR. 5. PROPOS. 5.</head>
          <note position="right" xml:space="preserve">Proprietas
            <lb/>
          quædã triã-
            <lb/>
          guli rectan
            <lb/>
          guli.</note>
          <p style="it">
            <s xml:id="echoid-s4263" xml:space="preserve">
              <emph style="sc">In</emph>
            omni triangulo rectangulo, ſi ab uno acutorum angul orum ut-
              <lb/>
            cunque ad latus oppoſitum linea recta ducatur, erit maior proportio
              <lb/>
            huius lateris ad eius ſegmentum, quod prope angulum rectum exi-
              <lb/>
            ſtit, quàm anguli acuti prędicti ad eius partem dicto ſegmento late-
              <lb/>
            ris oppoſitam.</s>
            <s xml:id="echoid-s4264" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4265" xml:space="preserve">
              <emph style="sc">Sit</emph>
            triangulum rectangulum A B C, cuius angulus C, ſit rectus; </s>
            <s xml:id="echoid-s4266" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum