Clavius, Christoph, Geometria practica

Table of Notes

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          <p>
            <s xml:id="echoid-s6933" xml:space="preserve">
              <pb o="168" file="198" n="198" rhead="GEOMETR. PRACT."/>
            qualis eſt à nobis conſtructus cap. </s>
            <s xml:id="echoid-s6934" xml:space="preserve">2. </s>
            <s xml:id="echoid-s6935" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s6936" xml:space="preserve">1. </s>
            <s xml:id="echoid-s6937" xml:space="preserve">Nam ex his cognitis, vt proxime di-
              <lb/>
            ximus, tota area trianguli cognoſcetur, etiamſi ad alia duo latera accedere non
              <lb/>
            poſsimus.</s>
            <s xml:id="echoid-s6938" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6939" xml:space="preserve">
              <emph style="sc">Qvando</emph>
            in eodem triangulo rectangulo B D C, alterutrum latus datur
              <lb/>
            circa angulum rectum vna cumlatere, quod recto angulo opponitur, nimirum
              <lb/>
            ſi DC, & </s>
            <s xml:id="echoid-s6940" xml:space="preserve">DB, cognita ſint; </s>
            <s xml:id="echoid-s6941" xml:space="preserve"> cognoſcetur quoque alterum latus B C, ſi fiat,
              <note symbol="a" position="left" xlink:label="note-198-01" xlink:href="note-198-01a" xml:space="preserve">3. triang. re-
                <lb/>
              ctil.</note>
            latus DB, angulo recto oppoſitum ad ſinum to tum angulirecti C, ita Iatus datũ
              <lb/>
            DC, ad aliud. </s>
            <s xml:id="echoid-s6942" xml:space="preserve">Productus enim numerus erit ſinus anguli B, quo cognito ex ta-
              <lb/>
              <note position="left" xlink:label="note-198-02" xlink:href="note-198-02a" xml:space="preserve">Area trian-
                <lb/>
              guli rectan-
                <lb/>
              guli ex vno
                <lb/>
              latere circa
                <lb/>
              angulum re-
                <lb/>
              ctum, & late-
                <lb/>
              re quodrecto
                <lb/>
              angulo oppo-
                <lb/>
              nitur.</note>
            bula ſinuum, cognitũ etiam erit eius complementum BDC. </s>
            <s xml:id="echoid-s6943" xml:space="preserve">Siergo rurſus fi-
              <lb/>
            at, vt ſinus totus angulirecti C, ad latus oppoſitum datum DB, ita ſinus anguli
              <lb/>
            BDC, inuentiad aliud, exibit latus oppoſitum B C. </s>
            <s xml:id="echoid-s6944" xml:space="preserve">Ex duobus igitur lateribus
              <lb/>
            DC, CB, cognitis, area triangulinota fiet ex ijs, quæ Num. </s>
            <s xml:id="echoid-s6945" xml:space="preserve">3. </s>
            <s xml:id="echoid-s6946" xml:space="preserve">paulo ante ſcripſi-
              <lb/>
            mus.</s>
            <s xml:id="echoid-s6947" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6948" xml:space="preserve">
              <emph style="sc">Atqve</emph>
            ita in campo, ſi detur portio triangularis, habens angulum rectum;
              <lb/>
            </s>
            <s xml:id="echoid-s6949" xml:space="preserve">ſatis eſt, ſi diligenter menſuretur vnum latus circa angulum rectum, vna cum la-
              <lb/>
            tere, quodrecto angulo opponitur, etiamſi ad tertium latus non pateat acceſ-
              <lb/>
            ſus. </s>
            <s xml:id="echoid-s6950" xml:space="preserve">Exillis enim duobus area cognoſcetur, vt dictum eſt.</s>
            <s xml:id="echoid-s6951" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6952" xml:space="preserve">
              <emph style="sc">Qvod</emph>
            ſi in eodem triangulo rectangulo B D C, notum fuerit vnum latus
              <lb/>
            circa rectum angulum, videlicet DC, vna cum alterutro angulo acuto, vt pote
              <lb/>
            cum C, notum effi cietur alterum latus B C: </s>
            <s xml:id="echoid-s6953" xml:space="preserve">ſi fiat, vt ſinus totus ad datum
              <note symbol="b" position="left" xlink:label="note-198-03" xlink:href="note-198-03a" xml:space="preserve">4. triang.
                <lb/>
              rectil.</note>
            tus DC: </s>
            <s xml:id="echoid-s6954" xml:space="preserve">Ita Tangens anguli BDC, quæſito lateri CB, oppoſiti, (cognoſcetur
              <lb/>
            autem alter hic angulus BDC, ſi angulus C, ex gradibus 90. </s>
            <s xml:id="echoid-s6955" xml:space="preserve">dematur) ad aliud.
              <lb/>
            </s>
            <s xml:id="echoid-s6956" xml:space="preserve">
              <note position="left" xlink:label="note-198-04" xlink:href="note-198-04a" xml:space="preserve">Areatrian-
                <lb/>
              gulirectangu-
                <lb/>
              liex vno late-
                <lb/>
              re circa angu-
                <lb/>
              lum rectum
                <lb/>
              & vno angu-
                <lb/>
              lo acuto.</note>
            Nam inuentus numerus dabit latus CB, quæſitum. </s>
            <s xml:id="echoid-s6957" xml:space="preserve">Vel ſi fiat, vt ſinus anguli C,
              <lb/>
            dato lateri DC, oppoſiti ad latus datum D C: </s>
            <s xml:id="echoid-s6958" xml:space="preserve">Ita ſinus alterius anguli B D C, ad
              <lb/>
            aliud. </s>
            <s xml:id="echoid-s6959" xml:space="preserve">Nam rurſus producetur latus quæſitum B C. </s>
            <s xml:id="echoid-s6960" xml:space="preserve">Ex duobus ergo lateribus
              <lb/>
            D C, C B, aream cognoſcemus, vt Num. </s>
            <s xml:id="echoid-s6961" xml:space="preserve">3. </s>
            <s xml:id="echoid-s6962" xml:space="preserve">traditur.</s>
            <s xml:id="echoid-s6963" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6964" xml:space="preserve">IN Campo ergo aliquo, ſi proponatur portio triangularis angulum habẽs
              <lb/>
            rectum, ſatis erit vnum latus circa rectum angulum, & </s>
            <s xml:id="echoid-s6965" xml:space="preserve">vnum angulum acutum
              <lb/>
            metiri, vt eius trianguli area reperiatur, etiamſi ad alia duo latera acceſſus dene-
              <lb/>
            getur. </s>
            <s xml:id="echoid-s6966" xml:space="preserve">Atque hæc de rectangulis triangulis: </s>
            <s xml:id="echoid-s6967" xml:space="preserve">veniamusiam ab obliquangula.</s>
            <s xml:id="echoid-s6968" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6969" xml:space="preserve">7. </s>
            <s xml:id="echoid-s6970" xml:space="preserve">
              <emph style="sc">Si</emph>
            ergo in triangulo non rectangulo A B D, notum ſit vnum latus, cum
              <lb/>
            duobus angulis quibuſcunque, perueniemus in cognitionem areæ hoc modo.
              <lb/>
            </s>
            <s xml:id="echoid-s6971" xml:space="preserve">Ex duobus angulis cognitus erit quoque tertius, cum ſit complementum alio-
              <lb/>
              <note symbol="c" position="left" xlink:label="note-198-05" xlink:href="note-198-05a" xml:space="preserve">10. triang.
                <lb/>
              rectil.</note>
            rum duorum ad gr. </s>
            <s xml:id="echoid-s6972" xml:space="preserve">180. </s>
            <s xml:id="echoid-s6973" xml:space="preserve"> Igitur alia duo latera cognolcentur: </s>
            <s xml:id="echoid-s6974" xml:space="preserve">ac proinde ex tri- bus lateribus cognitis area fiet nota exijs, quæ Num. </s>
            <s xml:id="echoid-s6975" xml:space="preserve">1. </s>
            <s xml:id="echoid-s6976" xml:space="preserve">& </s>
            <s xml:id="echoid-s6977" xml:space="preserve">2. </s>
            <s xml:id="echoid-s6978" xml:space="preserve">tradita ſunt.
              <lb/>
            </s>
            <s xml:id="echoid-s6979" xml:space="preserve">
              <note position="left" xlink:label="note-198-06" xlink:href="note-198-06a" xml:space="preserve">Area trian-
                <lb/>
              guli obliquã-
                <lb/>
              guli ex vno
                <lb/>
              latere ac duo-
                <lb/>
              bus angulis.</note>
            </s>
          </p>
          <p>
            <s xml:id="echoid-s6980" xml:space="preserve">
              <emph style="sc">Vt</emph>
            ergo campus triangularis nullum habens angulũ rectum cognitus fiat,
              <lb/>
            ſatis erit, ſi vnum latus cum duobus angulis accuratè menſuretur. </s>
            <s xml:id="echoid-s6981" xml:space="preserve">Exijs enim
              <lb/>
            duo reliqua latera nota efficientur, &</s>
            <s xml:id="echoid-s6982" xml:space="preserve">c. </s>
            <s xml:id="echoid-s6983" xml:space="preserve">vt dictum eſt.</s>
            <s xml:id="echoid-s6984" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6985" xml:space="preserve">
              <emph style="sc">Rvrsvs</emph>
            ſi in eodem triangulo ABD, nonrectangulo nota ſint duo late-
              <lb/>
            ra, vna cum angulo abipſis comprehenſo; </s>
            <s xml:id="echoid-s6986" xml:space="preserve"> inuenietur tertium latus: </s>
            <s xml:id="echoid-s6987" xml:space="preserve">ac
              <note symbol="d" position="left" xlink:label="note-198-07" xlink:href="note-198-07a" xml:space="preserve">12. triang.
                <lb/>
              rectil.</note>
            inde, vt prius, ex omnibus tribus lateribus area trianguli efficietur cognita.</s>
            <s xml:id="echoid-s6988" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6989" xml:space="preserve">
              <emph style="sc">Itaqve</emph>
            ſatis erit, ſi in campo quouis triangulari duo latera, vna eum an-
              <lb/>
              <note position="left" xlink:label="note-198-08" xlink:href="note-198-08a" xml:space="preserve">Area trian-
                <lb/>
              guliobliquan-
                <lb/>
              guli ex duo-
                <lb/>
              b{us} laterib{us}
                <lb/>
              & angulo ab
                <lb/>
              ipſis compre-
                <lb/>
              henſo.</note>
            gulo abipſis comprehenſo menſurentur: </s>
            <s xml:id="echoid-s6990" xml:space="preserve">vt areaipſius nota reddatur.</s>
            <s xml:id="echoid-s6991" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6992" xml:space="preserve">8. </s>
            <s xml:id="echoid-s6993" xml:space="preserve">
              <emph style="sc">Neqve</emph>
            vero hoc omittendum videtur: </s>
            <s xml:id="echoid-s6994" xml:space="preserve">ſi videlicet vnum latus trian-
              <lb/>
            guli, vel cuiuſuis figuræ rectilineæ in partes quotlibet æquales ſecetur, reliqua
              <lb/>
            latera in eiſdem partibus fieri poſſe cognita, beneficio inſtrumenti partium, vt ad
              <lb/>
            finem Num. </s>
            <s xml:id="echoid-s6995" xml:space="preserve">1. </s>
            <s xml:id="echoid-s6996" xml:space="preserve">cap. </s>
            <s xml:id="echoid-s6997" xml:space="preserve">1. </s>
            <s xml:id="echoid-s6998" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s6999" xml:space="preserve">1. </s>
            <s xml:id="echoid-s7000" xml:space="preserve">declarauimus. </s>
            <s xml:id="echoid-s7001" xml:space="preserve">Ve@um vt magis exquiſite </s>
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