Clavius, Christoph, Geometria practica

Table of Notes

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              <pb o="135" file="165" n="165" rhead="LIBER TERTIVS."/>
              <note style="it" position="right" xlink:label="note-165-01" xlink:href="note-165-01a" xml:space="preserve">
                <lb/>
              Vt differentia vmbrarum \\ verſarum # ad D E, differen- \\ tiam ſtationum # Ita vmbra verſa \\ maior # ad EB,
                <lb/>
              </note>
            fietrurſus nota recta E B, &</s>
            <s xml:id="echoid-s5260" xml:space="preserve">c.</s>
            <s xml:id="echoid-s5261" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5262" xml:space="preserve">3. </s>
            <s xml:id="echoid-s5263" xml:space="preserve">
              <emph style="sc">Si</emph>
            denique in vna ſtatione latus vmbræ rectæ ſecetur, & </s>
            <s xml:id="echoid-s5264" xml:space="preserve">in altera latus
              <lb/>
            vmbræ verſæ, reducenda erit vel vmbra recta ad verſam, vel verſa ad rectam.
              <lb/>
            </s>
            <s xml:id="echoid-s5265" xml:space="preserve">Nam ſi rurſus fiat. </s>
            <s xml:id="echoid-s5266" xml:space="preserve">
              <lb/>
              <note style="it" position="right" xlink:label="note-165-02" xlink:href="note-165-02a" xml:space="preserve">
                <lb/>
              Vt differentia vmbrarum \\ ſiue verſarum, ſiue rectarum, # ad D E, differen- \\ tiam ſtationum: # Ita vmbr a verſa \\ velrecta maior # ad E B.
                <lb/>
              </note>
            iterum producetur recta E B, in partibus differentiæ ſtationum D E, &</s>
            <s xml:id="echoid-s5267" xml:space="preserve">c.</s>
            <s xml:id="echoid-s5268" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5269" xml:space="preserve">
              <emph style="sc">Per</emph>
            vnicam quoque ſtationem aſſe quemur altitudinem putei, quemad-
              <lb/>
            modum in ſcholio probl. </s>
            <s xml:id="echoid-s5270" xml:space="preserve">9. </s>
            <s xml:id="echoid-s5271" xml:space="preserve">ex montis vertice eius altitudinem menſi ſumus: </s>
            <s xml:id="echoid-s5272" xml:space="preserve">ſi
              <lb/>
            videlicet in A, quadratum ita ſtatuatur, vt centruma, dioptræ
              <lb/>
              <figure xlink:label="fig-165-01" xlink:href="fig-165-01a" number="96">
                <image file="165-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/165-01"/>
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            ſuperius ſit, & </s>
            <s xml:id="echoid-s5273" xml:space="preserve">latus infimum A C, ex A, ad punctum C, ver-
              <lb/>
            gat, ad inueniendam diſtantiam, vel hypotenuſam A C, &</s>
            <s xml:id="echoid-s5274" xml:space="preserve">c.
              <lb/>
            </s>
            <s xml:id="echoid-s5275" xml:space="preserve">vtin eo ſcholio factum eſt, atque hæc figura appoſita decla-
              <lb/>
            rat. </s>
            <s xml:id="echoid-s5276" xml:space="preserve">Secundo enim quadratumita locandum eſt, vt A, cen-
              <lb/>
            trum dioptræſit in A, & </s>
            <s xml:id="echoid-s5277" xml:space="preserve">latus A D, lateri pueri A B, adhæreat; </s>
            <s xml:id="echoid-s5278" xml:space="preserve">
              <lb/>
            Adeo vt per dioptram puncto C, inſpecto, radius viſualis ab
              <lb/>
            hypotenuſa A C, non differat. </s>
            <s xml:id="echoid-s5279" xml:space="preserve">Itaque ſi fiat. </s>
            <s xml:id="echoid-s5280" xml:space="preserve">
              <lb/>
              <note style="it" position="right" xlink:label="note-165-03" xlink:href="note-165-03a" xml:space="preserve">
                <lb/>
              Vt eb, vmbra verſa # ad lat{us} ba, # ita lat{us}a A, # ad aliud,
                <lb/>
              </note>
            inuenietur hypotenuſa A C. </s>
            <s xml:id="echoid-s5281" xml:space="preserve">Inuenta deinde portione dioptræ A E, in ſecundo
              <lb/>
            quadrato, vt in ſcholio problem. </s>
            <s xml:id="echoid-s5282" xml:space="preserve">7. </s>
            <s xml:id="echoid-s5283" xml:space="preserve">docuimus: </s>
            <s xml:id="echoid-s5284" xml:space="preserve"> Si rurſus
              <note symbol="a" position="right" xlink:label="note-165-04" xlink:href="note-165-04a" xml:space="preserve">2. ſexti. &
                <lb/>
              componendo.</note>
              <note style="it" position="right" xlink:label="note-165-05" xlink:href="note-165-05a" xml:space="preserve">
                <lb/>
              Vt portio dioptræ A E, \\ iuuenta # ad hypotenuſam inuen- \\ tam A C: # {it}a lat{us} \\ A D, # ad aliud,
                <lb/>
              </note>
            prodibit altitudo, ſiue profunditas A B.</s>
            <s xml:id="echoid-s5285" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s5286" xml:space="preserve">4. </s>
            <s xml:id="echoid-s5287" xml:space="preserve">
              <emph style="sc">Qvod</emph>
            ſi latitudo orificij A M, vel fundi B C, cognita fuerit, quæ facile
              <lb/>
            per aliquam menſuram cognoſci poterit facilius per vnam duntaxat ſtationem
              <lb/>
            in D, factam, & </s>
            <s xml:id="echoid-s5288" xml:space="preserve">per vnicam applicationem quadrati, profunditatem A B, conij-
              <lb/>
            ciemus. </s>
            <s xml:id="echoid-s5289" xml:space="preserve">Nam ſi fiat,
              <lb/>
              <note style="it" position="right" xlink:label="note-165-06" xlink:href="note-165-06a" xml:space="preserve">
                <lb/>
              Vt vmbra recta, ſi ea abſciſſa \\ fuerit, # ad lat{us} quadrati: # Ita latitudo cogni- \\ ta B C, # ad AB,
                <lb/>
              #### Vel
                <lb/>
              Vt lat{us} qua- \\ drati # ad vmbram verſam, ſiea \\ fuerit abſciſſa: # Ita latitudo cogni- \\ ta B C, # ad AB,
                <lb/>
              </note>
            pro ducetur AB, profunditas nota in partibus latitudinis.</s>
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          <p>
            <s xml:id="echoid-s5291" xml:space="preserve">Et ſi forte dioptra per punctum C, in quadrato tranſeat, erit latitudo BC, re-
              <lb/>
            ctæ A B, æqualis.</s>
            <s xml:id="echoid-s5292" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s5293" xml:space="preserve">
              <emph style="sc">Hæ</emph>
            porro praxes demonſtratæ ſunt omnes in prædicto problemate 9. </s>
            <s xml:id="echoid-s5294" xml:space="preserve">hac
              <lb/>
            vltima Num. </s>
            <s xml:id="echoid-s5295" xml:space="preserve">4. </s>
            <s xml:id="echoid-s5296" xml:space="preserve">excepta, quamin problemate 8. </s>
            <s xml:id="echoid-s5297" xml:space="preserve">Num. </s>
            <s xml:id="echoid-s5298" xml:space="preserve">4. </s>
            <s xml:id="echoid-s5299" xml:space="preserve">demonſtrauimus.</s>
            <s xml:id="echoid-s5300" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5301" xml:space="preserve">PROFVNDITATEM vallis, eiuſdemque deſcenſum obliquum,
              <lb/>
            ſi non ſit valde inæqualis, & </s>
            <s xml:id="echoid-s5302" xml:space="preserve">eius terminus, vel aliquod in ea ſignum
              <lb/>
            conſpici poſſit, per quadratum cognoſcere.</s>
            <s xml:id="echoid-s5303" xml:space="preserve"/>
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