Clavius, Christoph, Geometria practica

Table of Notes

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              <pb o="113" file="143" n="143" rhead="LIBER TERTIVS."/>
            60. </s>
            <s xml:id="echoid-s4443" xml:space="preserve">pedes. </s>
            <s xml:id="echoid-s4444" xml:space="preserve">Si verò a A, ponatur 1000. </s>
            <s xml:id="echoid-s4445" xml:space="preserve">comperietur eadem AF, particularum
              <lb/>
            200000. </s>
            <s xml:id="echoid-s4446" xml:space="preserve">qualium 1000. </s>
            <s xml:id="echoid-s4447" xml:space="preserve">in a A, comprehenduntur.</s>
            <s xml:id="echoid-s4448" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4449" xml:space="preserve">2. </s>
            <s xml:id="echoid-s4450" xml:space="preserve">
              <emph style="sc">Post</emph>
            hæc deprimatur Quadratum, ita vt latus AD, Horizonti æquidi-
              <lb/>
            ſtet, centrum que dioptrę ſit in A. </s>
            <s xml:id="echoid-s4451" xml:space="preserve">quo poſito, videbitur cacumen F, per inuen-
              <lb/>
            tam hypotenuſam AF, quæ primum ſecet vmbram verſam C D, in E, vt in pri-
              <lb/>
            mo quadrato, inquiratur que portio dioptrę AE, in partibus laterum A D, D E,
              <lb/>
              <note symbol="a" position="right" xlink:label="note-143-01" xlink:href="note-143-01a" xml:space="preserve">6. Triang.
                <lb/>
              rectil.</note>
            quod fiet vel ex vtro que latere A D, D E, cognito: </s>
            <s xml:id="echoid-s4452" xml:space="preserve"> Vel ex cognito per pro- blema 1. </s>
            <s xml:id="echoid-s4453" xml:space="preserve">ex vmbra D E, angulo D A E, ex latere DE, noto: </s>
            <s xml:id="echoid-s4454" xml:space="preserve"> Vel denique ſi
              <note symbol="b" position="right" xlink:label="note-143-02" xlink:href="note-143-02a" xml:space="preserve">5. Triang.
                <lb/>
              rectil.</note>
            ſumma quadratorum ex AD, DE, deſcriptorum radix quadrata extrahatur. </s>
            <s xml:id="echoid-s4455" xml:space="preserve">In-
              <lb/>
            uenta portione A E, in partibus milleſimis lateris A D, ductaque EM, ipſi A G,
              <lb/>
              <note symbol="c" position="right" xlink:label="note-143-03" xlink:href="note-143-03a" xml:space="preserve">47. primi.</note>
            parallela, ſi fiat,</s>
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          <note symbol="d" position="right" xml:space="preserve">2. ſexti &
            <lb/>
          componendo.</note>
          <note style="it" position="right" xml:space="preserve">
            <lb/>
          Vt AE, inuenta in partib{us} \\ milleſimis AD, # ad AF, in iiſdem par- \\ tib{us} inuentam # Ita G M, in iiſdem par- \\ tib{us} cognita, cum æ- \\ qualis ſit ipſi D E, # ad GF,
            <lb/>
          </note>
          <p>
            <s xml:id="echoid-s4456" xml:space="preserve">nota effi cietur GF, in partibus milleſimis lateris AD. </s>
            <s xml:id="echoid-s4457" xml:space="preserve">Quod ſi rurſus fiat,</s>
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          <note style="it" position="right" xml:space="preserve">
            <lb/>
          Vt lat{us} AD, \\ 1000. # ad 3. ped{es}, quos \\ ponim{us} in AD, \\ contineri: # Ita G F, in milleſimis parti- \\ b{us} lateris AD, inuenta, # ad GF,
            <lb/>
          </note>
          <p>
            <s xml:id="echoid-s4458" xml:space="preserve">reperietur eadem GF, in menſura pedum. </s>
            <s xml:id="echoid-s4459" xml:space="preserve">Et ſi adiiciatur, ſtatura menſoris GI,
              <lb/>
            nota in eadem menſura, cognita fiet tota altitudo I F, in menſura pedum.</s>
            <s xml:id="echoid-s4460" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4461" xml:space="preserve">Vbi vides, nos eadem opera inueniſſe quo que diſtantiam AF, ab oculo A, ad
              <lb/>
            cacumen vſque F.</s>
            <s xml:id="echoid-s4462" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4463" xml:space="preserve">3. </s>
            <s xml:id="echoid-s4464" xml:space="preserve">
              <emph style="sc">Secet</emph>
            deinde hypotenuſa a F, inuenta (inuenietur autem vt Num. </s>
            <s xml:id="echoid-s4465" xml:space="preserve">7.
              <lb/>
            </s>
            <s xml:id="echoid-s4466" xml:space="preserve">dictum eſt) vtrumque latus vmbræ in C, vt in 2. </s>
            <s xml:id="echoid-s4467" xml:space="preserve">quadrato. </s>
            <s xml:id="echoid-s4468" xml:space="preserve"> Si igitur fiat,</s>
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          <note symbol="e" position="right" xml:space="preserve">2. ſexti. &
            <lb/>
          componendo.</note>
          <note style="it" position="right" xml:space="preserve">
            <lb/>
          Vt portio dioptræ a c, inuenta in par- \\ tib{us} a d, lateris, 1000. vt Num. 2. \\ dixim{us}. # ad a F, hypotenuſam \\ in iiſdem partib{us} \\ inuentam: # Ita GK, \\ 1000. # ad GF,
            <lb/>
          </note>
          <p>
            <s xml:id="echoid-s4469" xml:space="preserve">prodibit GF, nota in partibus milleſimis lateris d c: </s>
            <s xml:id="echoid-s4470" xml:space="preserve">Et ſi rurſus fiat,</s>
          </p>
          <note style="it" position="right" xml:space="preserve">
            <lb/>
          Vt lat{us} d c, \\ 1000. # ad 3. ped{es}, quib{us} æquale \\ ponim{us} lat{us} d c, # Ita GK, 1000. cum æqua- \\ le ſit ipſi d c, # ad GF,
            <lb/>
          </note>
          <p>
            <s xml:id="echoid-s4471" xml:space="preserve">inuenta erit eadem GF, in menſura pedum. </s>
            <s xml:id="echoid-s4472" xml:space="preserve">Et ſi addatur ſtatura menſoris G I,
              <lb/>
            nota in eadem menſura, cognoſcetur tota altitudo IF, in menſura pedum.</s>
            <s xml:id="echoid-s4473" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4474" xml:space="preserve">4. </s>
            <s xml:id="echoid-s4475" xml:space="preserve">
              <emph style="sc">Tertio</emph>
            ſecet hypotenuſa inuenta AF, (quę inuenietur vt Num. </s>
            <s xml:id="echoid-s4476" xml:space="preserve">7. </s>
            <s xml:id="echoid-s4477" xml:space="preserve">do-
              <lb/>
            cuimus) vmbram rectam in E, vt in tertio quadrato. </s>
            <s xml:id="echoid-s4478" xml:space="preserve"> Siergo fiat,</s>
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          <note symbol="f" position="right" xml:space="preserve">2. ſexti. &
            <lb/>
          componendo.</note>
          <note style="it" position="right" xml:space="preserve">
            <lb/>
          Vt portio dioptræ A E, inuenta, \\ vt Num. 2. docuim{us}. # ad AF, hypotenuſam \\ inuentam # Ita G K, \\ 1000. # ad G F,
            <lb/>
          </note>
          <p>
            <s xml:id="echoid-s4479" xml:space="preserve">exibit GF, nota in partibus milleſimis lateris DC. </s>
            <s xml:id="echoid-s4480" xml:space="preserve">Et ſi iterum fiat,</s>
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          <note style="it" position="right" xml:space="preserve">
            <lb/>
          Vt lat{us} D C, \\ 1000. # ad 3. ped{es} in D C, \\ contentos # Ita GK, 1000. cum ſit æqua- \\ lis ipſi D C, # ad G F,
            <lb/>
          </note>
          <p>
            <s xml:id="echoid-s4481" xml:space="preserve">cognita erit eadem GF, in menſura pedum, & </s>
            <s xml:id="echoid-s4482" xml:space="preserve">c.</s>
            <s xml:id="echoid-s4483" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4484" xml:space="preserve">
              <emph style="sc">Atqve</emph>
            hac eadem ratione omnes aliæ lineæ inuentę in partibus milleſimis
              <lb/>
            lateris Quadratireuo cabuntur ad quamcunque aliam menſuram, vt ad pedes,
              <lb/>
            vel cubitos, &</s>
            <s xml:id="echoid-s4485" xml:space="preserve">c.</s>
            <s xml:id="echoid-s4486" xml:space="preserve"/>
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