Clavius, Christoph, Geometria practica

Table of contents

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[31.] Rurſus
[32.] XI. LATVS.
[33.] XII. LATVS.
[34.] Deinde.
[35.] Hæc autem tangens hoc etiam modo inuenietur, qui priori præferendus videtur.
[36.] Poſt hæc.
[37.] XIII. LATVS.
[38.] XIIII. ANGVLOS DVOS.
[39.] XV. ANGVLOS DVOS.
[40.] XVI. ANGVLOS OMNES TRES. Ex tribus omnibus lateribus perueſtigare.
[41.] Rurſus.
[42.] XVII. PERPENDICVLAREM IN LATVS quodcunque ex angulo oppoſito cadentem. Ex tribus omnibus lateribus efficere notam.
[43.] FINIS LIBRI PRIMI.
[44.] GEOMETRIÆ PRACTICÆ LIBER SECVNDVS.
[45.] PROBLEMA I.
[46.] ALITER
[47.] ALITER
[48.] ALITER
[49.] LEMMA.
[50.] SCHOLIVM.
[51.] COROLLARIVM I.
[52.] COROLLARIVM II.
[53.] PROBLEMA II.
[54.] 2. ITEM ſi fiat.
[55.] ALITER.
[56.] Ergo ſi fiat,
[57.] Si igitur fiat.
[58.] COROLLARIVM I.
[59.] COROLLARIVM II.
[60.] PROBLEMA III.
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          <pb o="48" file="078" n="78" rhead="GEOMETR. PRACT."/>
          <note style="it" position="right" xml:space="preserve">
            <lb/>
          Vt ſin{us} vtriuſl@bet \\ anguli inuenti # ad lat{us} oppo- \\ ſitum: # ita angul{us} \\ dat{us} # ad lat{us} oppoſitum quod \\ quæritur.
            <lb/>
          </note>
          <note position="left" xml:space="preserve">1. Triang.
            <lb/>
          rectil.</note>
          <p>
            <s xml:id="echoid-s1991" xml:space="preserve">Itaque antequam tertium latus inueniatur, diſquirendi prius ſunt reliqui
              <lb/>
            duo anguli: </s>
            <s xml:id="echoid-s1992" xml:space="preserve">qui commodius videntur poſteriori via Num. </s>
            <s xml:id="echoid-s1993" xml:space="preserve">2. </s>
            <s xml:id="echoid-s1994" xml:space="preserve">exp oſita indagari,
              <lb/>
            quam priori illa ratione Num. </s>
            <s xml:id="echoid-s1995" xml:space="preserve">1 explicata.</s>
            <s xml:id="echoid-s1996" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1997" xml:space="preserve">3. </s>
            <s xml:id="echoid-s1998" xml:space="preserve">Siduo latera ſint æqualia; </s>
            <s xml:id="echoid-s1999" xml:space="preserve"> erunt reliqui duo anguli æquales. </s>
            <s xml:id="echoid-s2000" xml:space="preserve">
              <note symbol="a" position="left" xlink:label="note-078-03" xlink:href="note-078-03a" xml:space="preserve">@5. primi.</note>
            ergo arcus, qui detracto angulo dato ex ſemicirculo relinquitur, dabit vtrum-
              <lb/>
            que, &</s>
            <s xml:id="echoid-s2001" xml:space="preserve">c.</s>
            <s xml:id="echoid-s2002" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div86" type="section" level="1" n="37">
          <head xml:id="echoid-head40" xml:space="preserve">XIII. LATVS.</head>
          <p>
            <s xml:id="echoid-s2003" xml:space="preserve">Ex duobus lareribus, & </s>
            <s xml:id="echoid-s2004" xml:space="preserve">angulo vni eorum oppoſito (ſi modo conſtet ſpe-
              <lb/>
            cies anguli alteri lateri dato oppoſiti, quando datus angulus acutus eſt) ex-
              <lb/>
            quirere.</s>
            <s xml:id="echoid-s2005" xml:space="preserve"/>
          </p>
          <note style="it" position="right" xml:space="preserve">
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          1. Vt lat{us} datum \\ dato angulo oppo- \\ ſitum # ad ſinum angu- \\ li dati: # ita alterum lat{us} \\ datum, # ad ſinum anguli \\ huic alteri late- \\ rioppoſiti.
            <lb/>
          </note>
          <note position="left" xml:space="preserve">13. triang.
            <lb/>
          rectil.</note>
          <p>
            <s xml:id="echoid-s2006" xml:space="preserve">Hic ſinus inuentus dabit angulum alteri dato lateri oppoſitum, ſi acutus
              <lb/>
            fuerit: </s>
            <s xml:id="echoid-s2007" xml:space="preserve">(erit autem ſemper acutus, quando datus angulus eſt obtuſus) ſi verò
              <lb/>
            fuerit obtuſus, arcus ſinus inuenti ex ſemicirculo demptus, reliquum faciet eum
              <lb/>
            angulum: </s>
            <s xml:id="echoid-s2008" xml:space="preserve">Propterea quando datus angulus eſt acutus, oportet dari huius al-
              <lb/>
            terius ſpeciem, vt ſciamus, num acutus ſit, vel obtuſus. </s>
            <s xml:id="echoid-s2009" xml:space="preserve">Summa autem horum
              <lb/>
            angulorum ex ſemicirculo ſubtracta relinquet tertium angulum quæſito lateri
              <lb/>
            oppoſitum. </s>
            <s xml:id="echoid-s2010" xml:space="preserve">Ergo.</s>
            <s xml:id="echoid-s2011" xml:space="preserve"/>
          </p>
          <note style="it" position="right" xml:space="preserve">
            <lb/>
          Vt ſin{us} dati \\ anguli # ad datum lat{us} \\ ei oppoſitum; # ita ſin{us} tertii anguli inuenti \\ quæſito lateri oppoſiti. # ad lat{us} quæ- \\ ſitum.
            <lb/>
          </note>
          <note position="left" xml:space="preserve">1. triang.
            <lb/>
          rectil.</note>
          <p>
            <s xml:id="echoid-s2012" xml:space="preserve">2. </s>
            <s xml:id="echoid-s2013" xml:space="preserve">Si duo latera data ſint æqualia: </s>
            <s xml:id="echoid-s2014" xml:space="preserve"> erit angulus alteri dato lateri
              <note position="left" xlink:label="note-078-08" xlink:href="note-078-08a" xml:space="preserve">@5. rimi.</note>
            dato angulo æqualis.</s>
            <s xml:id="echoid-s2015" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div88" type="section" level="1" n="38">
          <head xml:id="echoid-head41" xml:space="preserve">XIIII. ANGVLOS DVOS.</head>
          <p>
            <s xml:id="echoid-s2016" xml:space="preserve">Ex duobus lateribus, & </s>
            <s xml:id="echoid-s2017" xml:space="preserve">angulo ab ipſis comprehenſo, reperire.</s>
            <s xml:id="echoid-s2018" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2019" xml:space="preserve">Inuenientur ex iis, quæ data ſunt, duo anguli, vt in priori parte problem atis 12. </s>
            <s xml:id="echoid-s2020" xml:space="preserve">di-
              <lb/>
            ctum eſt: </s>
            <s xml:id="echoid-s2021" xml:space="preserve">ſi nimirum inquiratur tangens differentiæ inter ſemiſſem arc{us}, qui detracto
              <lb/>
            angulo dato ex ſemicirculo relinquitur, & </s>
            <s xml:id="echoid-s2022" xml:space="preserve">alterutrum angulorum, qui quæruntur, &</s>
            <s xml:id="echoid-s2023" xml:space="preserve">c.
              <lb/>
            </s>
            <s xml:id="echoid-s2024" xml:space="preserve">quæ quidem tangens duob{us} modis inuenta est in priori parte problematis 12. </s>
            <s xml:id="echoid-s2025" xml:space="preserve">in quo la-
              <lb/>
            t{us} proponitur inueſtigandum ex duob{us} laterib{us}, & </s>
            <s xml:id="echoid-s2026" xml:space="preserve">angulo ab ipſis comprehenſo. </s>
            <s xml:id="echoid-s2027" xml:space="preserve">
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            Quod vt fier{et}, inuenti pri{us} fuerunt alii duo anguli, qui in hoc problemate 14. </s>
            <s xml:id="echoid-s2028" xml:space="preserve">quæ-
              <lb/>
            runtur.</s>
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        <div xml:id="echoid-div89" type="section" level="1" n="39">
          <head xml:id="echoid-head42" xml:space="preserve">XV. ANGVLOS DVOS.</head>
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            <s xml:id="echoid-s2030" xml:space="preserve">Ex duobus lateribus, & </s>
            <s xml:id="echoid-s2031" xml:space="preserve">angulo vni eorum oppoſito (ſi modo conſtet ſpe-
              <lb/>
            cies anguli alteri lateri dato oppoſiti, quando datus angulus acutus eſt) ex-
              <lb/>
            piſcari.</s>
            <s xml:id="echoid-s2032" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2033" xml:space="preserve">Hic {et}iam adhibenda eſt prior operatio problematis 13. </s>
            <s xml:id="echoid-s2034" xml:space="preserve">in quo lat{us} opponitur inqui-
              <lb/>
            rendum ex iiſdem datis: </s>
            <s xml:id="echoid-s2035" xml:space="preserve">quod vt fier{et}, inuenti pri{us} fuerereliqui
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            duo anguli, qui in hoc
              <lb/>
            problemate 15. </s>
            <s xml:id="echoid-s2036" xml:space="preserve">indagandi proponuntur.</s>
            <s xml:id="echoid-s2037" xml:space="preserve"/>
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