Clavius, Christoph, Geometria practica

Table of figures

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          <p>
            <s xml:id="echoid-s9131" xml:space="preserve">
              <pb o="205" file="235" n="235" rhead="LIBER QVINTVS."/>
            duo A D E H, B C F G, & </s>
            <s xml:id="echoid-s9132" xml:space="preserve">duo ABGH, DCFE, parallelogramma ſunt inter
              <lb/>
            ſe parallela, & </s>
            <s xml:id="echoid-s9133" xml:space="preserve">æqualia, dicitur parallelepipedum, Huius area ita inueſtigabitur.
              <lb/>
            </s>
            <s xml:id="echoid-s9134" xml:space="preserve">
              <note position="right" xlink:label="note-235-01" xlink:href="note-235-01a" xml:space="preserve">Area paralle-
                <lb/>
              lepipedirectã-
                <lb/>
              guli.</note>
            Sit primò propoſitum parallelepipedum rectangulum habens omnia ſex pa-
              <lb/>
            rallelo gramma rectangula, ac proinde omnes eius angulos ſolidos rectos: </s>
            <s xml:id="echoid-s9135" xml:space="preserve">ſit-
              <lb/>
            que longitudo baſis AB, palm. </s>
            <s xml:id="echoid-s9136" xml:space="preserve">3. </s>
            <s xml:id="echoid-s9137" xml:space="preserve">latitudo AD, palm. </s>
            <s xml:id="echoid-s9138" xml:space="preserve">2. </s>
            <s xml:id="echoid-s9139" xml:space="preserve">& </s>
            <s xml:id="echoid-s9140" xml:space="preserve">altitudo AH, palm. </s>
            <s xml:id="echoid-s9141" xml:space="preserve">4.
              <lb/>
            </s>
            <s xml:id="echoid-s9142" xml:space="preserve">Ducatur ergo latitudo 2. </s>
            <s xml:id="echoid-s9143" xml:space="preserve">in longitudinem 3. </s>
            <s xml:id="echoid-s9144" xml:space="preserve">vt producatur baſis palmorum
              <lb/>
              <handwritten xlink:label="hd-235-1" xlink:href="hd-235-1a" number="70"/>
            6. </s>
            <s xml:id="echoid-s9145" xml:space="preserve">quadratorum, vt lib. </s>
            <s xml:id="echoid-s9146" xml:space="preserve">4. </s>
            <s xml:id="echoid-s9147" xml:space="preserve">cap. </s>
            <s xml:id="echoid-s9148" xml:space="preserve">1. </s>
            <s xml:id="echoid-s9149" xml:space="preserve">traditum eſt. </s>
            <s xml:id="echoid-s9150" xml:space="preserve">Deinde baſis hæc 6. </s>
            <s xml:id="echoid-s9151" xml:space="preserve">palmorum
              <lb/>
            ducatur in altitudinem 4. </s>
            <s xml:id="echoid-s9152" xml:space="preserve">Numerus enim productus 24. </s>
            <s xml:id="echoid-s9153" xml:space="preserve">indicabit in parallele-
              <lb/>
            pipedo contineri 24 cubos, quorũ ſingula latera ſingulos palmos complectun-
              <lb/>
            tur, quod ita planum faciemus. </s>
            <s xml:id="echoid-s9154" xml:space="preserve">Exponatur ſeorſum rectangulum I K L M, æ-
              <lb/>
            quale baſi ABCD, intelligaturque altitudo per-
              <lb/>
              <figure xlink:label="fig-235-01" xlink:href="fig-235-01a" number="151">
                <image file="235-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/235-01"/>
              </figure>
            pendicularis L N, 4. </s>
            <s xml:id="echoid-s9155" xml:space="preserve">palm. </s>
            <s xml:id="echoid-s9156" xml:space="preserve">Si igitur ducatur la-
              <lb/>
            tus I M, palm. </s>
            <s xml:id="echoid-s9157" xml:space="preserve">2. </s>
            <s xml:id="echoid-s9158" xml:space="preserve">in IK, plam. </s>
            <s xml:id="echoid-s9159" xml:space="preserve">3. </s>
            <s xml:id="echoid-s9160" xml:space="preserve">producetur area
              <lb/>
            baſis palmorum quadratorum 6. </s>
            <s xml:id="echoid-s9161" xml:space="preserve">ſupra quæ ſi
              <lb/>
            concipiantur extructi 6. </s>
            <s xml:id="echoid-s9162" xml:space="preserve">cubiæquales, imple-
              <lb/>
            bunt ij parallelepipedum vſq; </s>
            <s xml:id="echoid-s9163" xml:space="preserve">ad primum pal-
              <lb/>
            mum L Q, altitudinis. </s>
            <s xml:id="echoid-s9164" xml:space="preserve">Si deinde alij 6. </s>
            <s xml:id="echoid-s9165" xml:space="preserve">cubi æ-
              <lb/>
            quales prioribus ſuperimp onantur, implebit@r parallelepipedum vſq; </s>
            <s xml:id="echoid-s9166" xml:space="preserve">ad ſecun-
              <lb/>
            dum palmum altitudinis QP. </s>
            <s xml:id="echoid-s9167" xml:space="preserve">Et alij 6. </s>
            <s xml:id="echoid-s9168" xml:space="preserve">@ubi æquales parallelepipedum vſq;
              <lb/>
            </s>
            <s xml:id="echoid-s9169" xml:space="preserve">tertium palmum P O, altitudinis implebunt. </s>
            <s xml:id="echoid-s9170" xml:space="preserve">Denique alij 6. </s>
            <s xml:id="echoid-s9171" xml:space="preserve">cubi appoſiti to-
              <lb/>
            tum parallelepipedum explebunt vſque ad quartũ altitudinis palmum O N. </s>
            <s xml:id="echoid-s9172" xml:space="preserve">
              <lb/>
            Conſtat ergo in toto parallelepipedo exiſtere toties 6. </s>
            <s xml:id="echoid-s9173" xml:space="preserve">cubospalmares, quoties
              <lb/>
            palmus in altitudine continetur, hoc eſt cubos 24.</s>
            <s xml:id="echoid-s9174" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9175" xml:space="preserve">2. </s>
            <s xml:id="echoid-s9176" xml:space="preserve">
              <emph style="sc">Intelligatvr</emph>
            deinde parallelepipedum ABCE, cuius baſes ABCD,
              <lb/>
              <note position="right" xlink:label="note-235-02" xlink:href="note-235-02a" xml:space="preserve">Area paralle
                <unsure/>
              -
                <lb/>
              lepipedi nõre
                <unsure/>
              -
                <lb/>
              ctanguli.</note>
            EFGH, ſint Rhombi, vel Rhomboides, ac latera AH, DE, DE, BG, CF, ad ba-
              <lb/>
            ſem A B C D, recta, ita vt altitudo ſit A H. </s>
            <s xml:id="echoid-s9177" xml:space="preserve">Primum ergo inquiratur area baſis
              <lb/>
            ABCD, vt lib. </s>
            <s xml:id="echoid-s9178" xml:space="preserve">4. </s>
            <s xml:id="echoid-s9179" xml:space="preserve">cap. </s>
            <s xml:id="echoid-s9180" xml:space="preserve">3. </s>
            <s xml:id="echoid-s9181" xml:space="preserve">Num. </s>
            <s xml:id="echoid-s9182" xml:space="preserve">1. </s>
            <s xml:id="echoid-s9183" xml:space="preserve">docuimus. </s>
            <s xml:id="echoid-s9184" xml:space="preserve">Hæc deinde in altitudinem AH, du-
              <lb/>
            catur. </s>
            <s xml:id="echoid-s9185" xml:space="preserve">Productus namq; </s>
            <s xml:id="echoid-s9186" xml:space="preserve">numerus erit parallelepipedi area. </s>
            <s xml:id="echoid-s9187" xml:space="preserve">Nam ſi fiat rectan-
              <lb/>
            gulum IL, baſi AC, æquale, & </s>
            <s xml:id="echoid-s9188" xml:space="preserve">ſupra illud concipiatur parallelepipedũ rectan-
              <lb/>
            gulũ, cuius altitudo LN, altitudini AH, ſit æqualis erit hoc
              <note symbol="a" position="right" xlink:label="note-235-03" xlink:href="note-235-03a" xml:space="preserve">31. duodec.</note>
            parallelepipedo ACE, æquale. </s>
            <s xml:id="echoid-s9189" xml:space="preserve">Cum ergo parallelepipedum, cuius baſis rectan-
              <lb/>
            gulum IL, & </s>
            <s xml:id="echoid-s9190" xml:space="preserve">altitudo LN, producatur ex altitudine LN, in baſem IL, vt oſten-
              <lb/>
            ſem eſt, producetur quoque parallelepipedum ACE, ex altitudine AH, in ba-
              <lb/>
            ſem AC, baſi IL, æqualem.</s>
            <s xml:id="echoid-s9191" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9192" xml:space="preserve">
              <emph style="sc">Si</emph>
            nullum latus parallelepipedi rectum eſt ad baſem, demittenda erit ex ali-
              <lb/>
            quo angulo ſupremi parallogrammi ad planum, in quo baſis, linea perpendi-
              <lb/>
            cularis, pro altitudine parallelepipedi, eaque diligenter metienda. </s>
            <s xml:id="echoid-s9193" xml:space="preserve">Sinamq; </s>
            <s xml:id="echoid-s9194" xml:space="preserve">area
              <lb/>
            baſis inueſtigetur vel per cap. </s>
            <s xml:id="echoid-s9195" xml:space="preserve">1. </s>
            <s xml:id="echoid-s9196" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s9197" xml:space="preserve">4. </s>
            <s xml:id="echoid-s9198" xml:space="preserve">quando eſt rectangula, vel per cap. </s>
            <s xml:id="echoid-s9199" xml:space="preserve">3.
              <lb/>
            </s>
            <s xml:id="echoid-s9200" xml:space="preserve">eiuſdem lib. </s>
            <s xml:id="echoid-s9201" xml:space="preserve">quando non eſtrectangula, eaque in altitudinem inuentam duca-
              <lb/>
            tur, producetur area propoſiti parallelepipedi. </s>
            <s xml:id="echoid-s9202" xml:space="preserve">Nam ſi ſupra baſem intelligatur
              <lb/>
            parallelepipedum rectum eiuſdem altitudinis cum propoſito parallelepipedo,
              <lb/>
              <note symbol="b" position="right" xlink:label="note-235-04" xlink:href="note-235-04a" xml:space="preserve">29. vel 30.
                <lb/>
              vndec.</note>
            erunt duo hæc parallelepipeda inter ſeæqualia. </s>
            <s xml:id="echoid-s9203" xml:space="preserve">Conſtat autẽ ex Num. </s>
            <s xml:id="echoid-s9204" xml:space="preserve">1. </s>
            <s xml:id="echoid-s9205" xml:space="preserve">& </s>
            <s xml:id="echoid-s9206" xml:space="preserve">2.</s>
            <s xml:id="echoid-s9207" xml:space="preserve"> parallelepipedum rectum gigni ex ductu bafis in altitudinem.</s>
            <s xml:id="echoid-s9208" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9209" xml:space="preserve">3. </s>
            <s xml:id="echoid-s9210" xml:space="preserve">
              <emph style="sc">Cvbvs</emph>
            , qui etiam parallelepipedum quoddam eſt rectangulum, eo dem
              <lb/>
              <note position="right" xlink:label="note-235-05" xlink:href="note-235-05a" xml:space="preserve">Area c ubi.</note>
            modo producitur, nimirum ex latere in ſe, & </s>
            <s xml:id="echoid-s9211" xml:space="preserve">iterum in productum. </s>
            <s xml:id="echoid-s9212" xml:space="preserve">Vt ſi latus
              <lb/>
            cubi ſit 10. </s>
            <s xml:id="echoid-s9213" xml:space="preserve">erit eius area 1000. </s>
            <s xml:id="echoid-s9214" xml:space="preserve">quod decies decem decies procreent 1000.</s>
            <s xml:id="echoid-s9215" xml:space="preserve"/>
          </p>
          <note symbol="c" position="right" xml:space="preserve">13. defin.
            <lb/>
          vndec.</note>
          <p>
            <s xml:id="echoid-s9216" xml:space="preserve">4. </s>
            <s xml:id="echoid-s9217" xml:space="preserve">
              <emph style="sc">Prisma</emph>
            eſt figura ſolida, quæplanis continetur, quorum aduerſa </s>
          </p>
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