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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          <p>
            <s xml:id="echoid-s1963" xml:space="preserve">
              <pb o="47" file="077" n="77" rhead="LIBER PRIMVS."/>
            ſit cum angulis. </s>
            <s xml:id="echoid-s1964" xml:space="preserve">In æquilatero vero triangulo, ſi vnumlatus datum ſit, erunt & </s>
            <s xml:id="echoid-s1965" xml:space="preserve">
              <lb/>
            reliquailli æqualia, data.</s>
            <s xml:id="echoid-s1966" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div80" type="section" level="1" n="32">
          <head xml:id="echoid-head35" xml:space="preserve">XI. LATVS.</head>
          <p>
            <s xml:id="echoid-s1967" xml:space="preserve">Ex duobus reliquis lateribus, & </s>
            <s xml:id="echoid-s1968" xml:space="preserve">duobus quibuſuis angulis, ac proinde o-
              <lb/>
            mnibus tribus, cum tertius ſit aliorum complementum ad ſemicirculum, id eſt,
              <lb/>
            ad grad. </s>
            <s xml:id="echoid-s1969" xml:space="preserve">180. </s>
            <s xml:id="echoid-s1970" xml:space="preserve">addiſcere.</s>
            <s xml:id="echoid-s1971" xml:space="preserve"/>
          </p>
          <note style="it" position="right" xml:space="preserve">
            <lb/>
          Vt ſin{us} anguli alteru- \\ tri lateri dato oppo- \\ ſiti # ad lat{us} oppo- \\ ſitum da@um: # ita ſin{us} anguli \\ quæſito lateri \\ oppoſiti # ad lat{us} quæſi- \\ tum.
            <lb/>
          </note>
          <note position="right" xml:space="preserve">10. Triang.
            <lb/>
          rectil.</note>
        </div>
        <div xml:id="echoid-div81" type="section" level="1" n="33">
          <head xml:id="echoid-head36" xml:space="preserve">XII. LATVS.</head>
          <p>
            <s xml:id="echoid-s1972" xml:space="preserve">Ex duobus lateribus, & </s>
            <s xml:id="echoid-s1973" xml:space="preserve">angulo ab ipſis comprehenſo colligere.</s>
            <s xml:id="echoid-s1974" xml:space="preserve"/>
          </p>
          <note style="it" position="right" xml:space="preserve">
            <lb/>
          1. Vt ſin{us} \\ tot{us} # ad ſecantem complementi ar- \\ c{us}, qui ſemiſſi aggregati da- \\ torum laterum ad ſin{us} re- \\ uocatorum, vt ſinui, debe- \\ tur: # Ita differentia in- \\ ter eam ſemiſ- \\ ſem, & alteru- \\ trum
            <unsure/>
          datorum \\ laterum ad ſin{us} \\ reuocatorum. # ad quar- \\ tũ quen \\ dam nu- \\ merum.
            <lb/>
          </note>
          <note position="right" xml:space="preserve">Problema
            <lb/>
          17. triang.
            <lb/>
          ſphæric.</note>
          <p>
            <s xml:id="echoid-s1975" xml:space="preserve">Latera data ad ſinus reuo cabuntur, ſi vtrumq; </s>
            <s xml:id="echoid-s1976" xml:space="preserve">multiplicetur per 10. </s>
            <s xml:id="echoid-s1977" xml:space="preserve">vel 100.
              <lb/>
            </s>
            <s xml:id="echoid-s1978" xml:space="preserve">vel 1000. </s>
            <s xml:id="echoid-s1979" xml:space="preserve">&</s>
            <s xml:id="echoid-s1980" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1981" xml:space="preserve">ita vt maioris lateris numerus habeat tot figuras, quot continen-
              <lb/>
            tur in maioribus ſinubus tabulæ ſinuum, nimirum 5. </s>
            <s xml:id="echoid-s1982" xml:space="preserve">ſi ſinus totus ſtatuatur
              <lb/>
            100000. </s>
            <s xml:id="echoid-s1983" xml:space="preserve">vel 7. </s>
            <s xml:id="echoid-s1984" xml:space="preserve">ſi ſinus totus ponatur 10000000.</s>
            <s xml:id="echoid-s1985" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div82" type="section" level="1" n="34">
          <head xml:id="echoid-head37" xml:space="preserve">Deinde.</head>
          <note style="it" position="right" xml:space="preserve">
            <lb/>
          Vt ſin{us} \\ tot{us} # ad tangentem ſemiſſis arc{us}, \\ qui d{et}racto dato angulo ex \\ ſemicirculo relinquitur: # ita quart{us} \\ numer{us} \\ inuent{us} # ad tangentem diffe- \\ rentiæ inter ſem ßẽ \\ eiuſdem arc{us}, & \\ alterutrum angulo- \\ rum non datorum.
            <lb/>
          </note>
        </div>
        <div xml:id="echoid-div83" type="section" level="1" n="35">
          <head xml:id="echoid-head38" xml:space="preserve">Hæc autem tangens hoc etiam modo inuenietur, qui priori
            <lb/>
          præferendus videtur.</head>
          <note style="it" position="right" xml:space="preserve">
            <lb/>
          2. Vt ſemiſ- \\ ſis aggre- \\ gati duo- \\ rum late- \\ rum da- \\ torum. # ad tangentem ſe- \\ miſſis arc{us}, qui \\ detracto dato an \\ gulo ex ſemici
            <unsure/>
          r- \\ culo relinquitur. # ita differentia in- \\ ter ſemiſſem ag- \\ gregati duorum \\ datorum laterũ, \\ & vtrumlib{et} \\ laterum # ad tangentem diffe- \\ rentiæ inter ſemiſ@ \\ ſem arc{us} prædi- \\ cti, & alterutrum \\ argulorum non \\ datorum.
            <lb/>
          </note>
          <note position="right" xml:space="preserve">Alio modo
            <lb/>
          qui priori
            <lb/>
          præferendus
            <lb/>
          videtur.</note>
          <p>
            <s xml:id="echoid-s1986" xml:space="preserve">Arcus huius tangentis inuentæ additus ad ſemiſſem eiuſdem arcus (eſt au-
              <lb/>
            tem hic arcus ſumma duorum angulorum non datorum, nimirum dati anguli
              <lb/>
            complementum ad ſemicir culum, hoc eſt, ad grad. </s>
            <s xml:id="echoid-s1987" xml:space="preserve">180.) </s>
            <s xml:id="echoid-s1988" xml:space="preserve">dabit ma@orem angu-
              <lb/>
            lum non datum, qui videlicet maiorilateri dato opponitur: </s>
            <s xml:id="echoid-s1989" xml:space="preserve">ex eadem verò ſe-
              <lb/>
            miſſe detractus reliquum faciet minorem angulum non datum, quinimirum
              <lb/>
            lateri minori dato opponitur.</s>
            <s xml:id="echoid-s1990" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div84" type="section" level="1" n="36">
          <head xml:id="echoid-head39" xml:space="preserve">Poſt hæc.</head>
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