Clavius, Christoph, Geometria practica

Table of figures

< >
[Figure 111]
[Figure 112]
[Figure 113]
[Figure 114]
[Figure 115]
[Figure 116]
[Figure 117]
[Figure 118]
[Figure 119]
[Figure 120]
[Figure 121]
[Figure 122]
[Figure 123]
[Figure 124]
[Figure 125]
[Figure 126]
[Figure 127]
[Figure 128]
[Figure 129]
[Figure 130]
[Figure 131]
[Figure 132]
[Figure 133]
[Figure 134]
[Figure 135]
[Figure 136]
[Figure 137]
[Figure 138]
[Figure 139]
[Figure 140]
< >
page |< < (163) of 450 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div418" type="section" level="1" n="172">
          <p>
            <s xml:id="echoid-s6454" xml:space="preserve">
              <pb o="163" file="193" n="193" rhead="LIBER QVARTVS."/>
            Quo ſegmento 6. </s>
            <s xml:id="echoid-s6455" xml:space="preserve">dempto ex latere B C, 21. </s>
            <s xml:id="echoid-s6456" xml:space="preserve">remanebit alterum ſegmentum
              <lb/>
            C D, 15.</s>
            <s xml:id="echoid-s6457" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6458" xml:space="preserve">
              <emph style="sc">Deinde</emph>
            in poſteriori triangulo ABD, ducenda ſit perpendicularis ad latus
              <lb/>
              <note position="right" xlink:label="note-193-01" xlink:href="note-193-01a" xml:space="preserve">18. primi.</note>
            A B, non maximum. </s>
            <s xml:id="echoid-s6459" xml:space="preserve">Et quia latus DB, latere AD, maius eſt; </s>
            <s xml:id="echoid-s6460" xml:space="preserve"> erit angulus
              <note position="right" xlink:label="note-193-02" xlink:href="note-193-02a" xml:space="preserve">17. primi.</note>
            maior angulo B. </s>
            <s xml:id="echoid-s6461" xml:space="preserve"> Cum ambo ergo ſimul ſint duobus rectis minores, erit
              <note position="right" xlink:label="note-193-03" xlink:href="note-193-03a" xml:space="preserve">13. primi.</note>
            minor B, acutus: </s>
            <s xml:id="echoid-s6462" xml:space="preserve"> ac proinde quadratum rectæ AD, minus erit quadratis
              <handwritten xlink:label="hd-193-1" xlink:href="hd-193-1a" number="64"/>
              <handwritten xlink:label="hd-193-1" xlink:href="hd-193-1a" number="66"/>
              <handwritten xlink:label="hd-193-1" xlink:href="hd-193-1a" number="67"/>
            rum A B, B D, rectangulo bis comprehenſo ſub latere AB, & </s>
            <s xml:id="echoid-s6463" xml:space="preserve">ſegmento inter B,
              <lb/>
            & </s>
            <s xml:id="echoid-s6464" xml:space="preserve">perpendicularem. </s>
            <s xml:id="echoid-s6465" xml:space="preserve">Siergo quadratum rectę AD, 121. </s>
            <s xml:id="echoid-s6466" xml:space="preserve">ſubtrahatur ex ſumma
              <lb/>
            quadratorum rectarum AB, B D, id eſt, ex 544. </s>
            <s xml:id="echoid-s6467" xml:space="preserve">reliquum fiet rectangulum bis
              <lb/>
            comprehenſum ſub A B, & </s>
            <s xml:id="echoid-s6468" xml:space="preserve">ſegmento, inter B, & </s>
            <s xml:id="echoid-s6469" xml:space="preserve">perpendicularem, nimirum
              <lb/>
            423. </s>
            <s xml:id="echoid-s6470" xml:space="preserve">ideoque eius ſemiſsis 211 {1/2}. </s>
            <s xml:id="echoid-s6471" xml:space="preserve">æqualis erit illi rectangulo ſemel ſumpto. </s>
            <s xml:id="echoid-s6472" xml:space="preserve">Qua-
              <lb/>
            re ſi rectangulum hoc 211 {1/2}. </s>
            <s xml:id="echoid-s6473" xml:space="preserve">diuidatur per latus AB, 12. </s>
            <s xml:id="echoid-s6474" xml:space="preserve">dabit Quotiens 17 {5/8}. </s>
            <s xml:id="echoid-s6475" xml:space="preserve">ſe-
              <lb/>
            gmentum inter B, & </s>
            <s xml:id="echoid-s6476" xml:space="preserve">perpendicularem. </s>
            <s xml:id="echoid-s6477" xml:space="preserve">quod quia maius eſt latere A B, argu-
              <lb/>
            mento eſt, perpendicularem DC, cadere extra triangulum: </s>
            <s xml:id="echoid-s6478" xml:space="preserve">ac proinde angu-
              <lb/>
            lum A, obtuſum eſſe. </s>
            <s xml:id="echoid-s6479" xml:space="preserve">Quod ſi ex hoc ſegmento 17 {5/8}. </s>
            <s xml:id="echoid-s6480" xml:space="preserve">dematur latus AB, 12. </s>
            <s xml:id="echoid-s6481" xml:space="preserve">re-
              <lb/>
            manebit exterius ſegmentum 5 {5/8}.</s>
            <s xml:id="echoid-s6482" xml:space="preserve"/>
          </p>
          <handwritten number="65"/>
          <p>
            <s xml:id="echoid-s6483" xml:space="preserve">
              <emph style="sc">Qvando</emph>
            conſtat, angulum A, eſſe obtuſum, ideoque perpendicularem
              <lb/>
            DC, extra triangulum cadere, reperiemus eadem ſegmenta BC, CA, hoc etiam
              <lb/>
              <note symbol="d" position="right" xlink:label="note-193-04" xlink:href="note-193-04a" xml:space="preserve">12. ſecundi.</note>
            modo. </s>
            <s xml:id="echoid-s6484" xml:space="preserve"> Quoniam quadratum lateris BD, ſuperat quadrata laterum A B,
              <handwritten xlink:label="hd-193-1" xlink:href="hd-193-1a" number="64"/>
              <handwritten xlink:label="hd-193-1" xlink:href="hd-193-1a" number="66"/>
              <handwritten xlink:label="hd-193-1" xlink:href="hd-193-1a" number="67"/>
            rectangulo bis comprehenſo ſub latere A B, & </s>
            <s xml:id="echoid-s6485" xml:space="preserve">ſegmento exteriore AC; </s>
            <s xml:id="echoid-s6486" xml:space="preserve">ſi ſum-
              <lb/>
            mam quadratorum rectarum AB, AD, 265. </s>
            <s xml:id="echoid-s6487" xml:space="preserve">detrahatur ex quadrato lateris BD,
              <lb/>
            400. </s>
            <s xml:id="echoid-s6488" xml:space="preserve">reliquum erit rectangulum 135. </s>
            <s xml:id="echoid-s6489" xml:space="preserve">bis comprehenſum ſub AB, AC: </s>
            <s xml:id="echoid-s6490" xml:space="preserve">& </s>
            <s xml:id="echoid-s6491" xml:space="preserve">eius ſe-
              <lb/>
            miſsis 67 {1/2}. </s>
            <s xml:id="echoid-s6492" xml:space="preserve">illi rectangulo ſemel ſumpto æqualis erit; </s>
            <s xml:id="echoid-s6493" xml:space="preserve">ac proinde hocrectan-
              <lb/>
            gulo 67 {1/2}. </s>
            <s xml:id="echoid-s6494" xml:space="preserve">diuiſo per latus A B, 12. </s>
            <s xml:id="echoid-s6495" xml:space="preserve">indicabit Quotiens 5 {5/8}. </s>
            <s xml:id="echoid-s6496" xml:space="preserve">ſegmentum exterius
              <lb/>
              <note position="right" xlink:label="note-193-05" xlink:href="note-193-05a" xml:space="preserve">Quæ ratio te-
                <lb/>
              nenda in ſe-
                <lb/>
              gmentis ex-
                <lb/>
              quirendis.
                <lb/>
              Perpendicu-
                <lb/>
              laris in trian-
                <lb/>
              gulo quo pa-
                <lb/>
              cto reperia-
                <lb/>
              tur.</note>
            CD; </s>
            <s xml:id="echoid-s6497" xml:space="preserve">cui ſi addatur latus A B, 12. </s>
            <s xml:id="echoid-s6498" xml:space="preserve">conflabitur ſegmentum BC, 17 {5/8}. </s>
            <s xml:id="echoid-s6499" xml:space="preserve">Sed prior
              <lb/>
            ratio, quæ exlibr. </s>
            <s xml:id="echoid-s6500" xml:space="preserve">2. </s>
            <s xml:id="echoid-s6501" xml:space="preserve">Euclid. </s>
            <s xml:id="echoid-s6502" xml:space="preserve">non pendet, expeditior eſt, ac proinde tenenda:
              <lb/>
            </s>
            <s xml:id="echoid-s6503" xml:space="preserve">quamuis auctores alij poſteriorem hanc viam plerunque ſequantur.</s>
            <s xml:id="echoid-s6504" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6505" xml:space="preserve">
              <emph style="sc">Inventis</emph>
            ſegmentis à perpendiculari factis, ita magnitudinem perpendi-
              <lb/>
            cularis cognoſcemus.</s>
            <s xml:id="echoid-s6506" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s6507" xml:space="preserve">DIFFERENTIA inter vtrumuis ſegmentum, & </s>
            <s xml:id="echoid-s6508" xml:space="preserve">lat{us} adiacens ducatur in
              <lb/>
            ſummam ex eodem ſegmento & </s>
            <s xml:id="echoid-s6509" xml:space="preserve">later@ conflatam. </s>
            <s xml:id="echoid-s6510" xml:space="preserve">Radix enim quadrata nume-
              <lb/>
            ri producti perpendicularem exhibebit notam, vt lib. </s>
            <s xml:id="echoid-s6511" xml:space="preserve">1. </s>
            <s xml:id="echoid-s6512" xml:space="preserve">cap. </s>
            <s xml:id="echoid-s6513" xml:space="preserve">3. </s>
            <s xml:id="echoid-s6514" xml:space="preserve">Num. </s>
            <s xml:id="echoid-s6515" xml:space="preserve">17. </s>
            <s xml:id="echoid-s6516" xml:space="preserve">demonſtra-
              <lb/>
            uim{us}.</s>
            <s xml:id="echoid-s6517" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6518" xml:space="preserve">
              <emph style="sc">Verbi</emph>
            gratia. </s>
            <s xml:id="echoid-s6519" xml:space="preserve">In priori triangulo ABC, ſi differentia 4. </s>
            <s xml:id="echoid-s6520" xml:space="preserve">inter ſegmentum B D,
              <lb/>
              <handwritten xlink:label="hd-193-1" xlink:href="hd-193-1a" number="64"/>
              <handwritten xlink:label="hd-193-1" xlink:href="hd-193-1a" number="66"/>
              <handwritten xlink:label="hd-193-1" xlink:href="hd-193-1a" number="67"/>
            & </s>
            <s xml:id="echoid-s6521" xml:space="preserve">latus AB, hoc eſt, inter 6. </s>
            <s xml:id="echoid-s6522" xml:space="preserve">& </s>
            <s xml:id="echoid-s6523" xml:space="preserve">10. </s>
            <s xml:id="echoid-s6524" xml:space="preserve">multip licetur per 16. </s>
            <s xml:id="echoid-s6525" xml:space="preserve">nempe per ſummam eiuſ-
              <lb/>
            dem ſegmenti BD, & </s>
            <s xml:id="echoid-s6526" xml:space="preserve">lateris AB; </s>
            <s xml:id="echoid-s6527" xml:space="preserve">gignetur numerus 64. </s>
            <s xml:id="echoid-s6528" xml:space="preserve">cuius radix quadrata
              <lb/>
            8. </s>
            <s xml:id="echoid-s6529" xml:space="preserve">dabit perpendicularem AD. </s>
            <s xml:id="echoid-s6530" xml:space="preserve">Pari ratione ſi diſſerentia 2. </s>
            <s xml:id="echoid-s6531" xml:space="preserve">inter ſegmentum
              <lb/>
            CD, & </s>
            <s xml:id="echoid-s6532" xml:space="preserve">latus AC, hoc eſt, 15. </s>
            <s xml:id="echoid-s6533" xml:space="preserve">& </s>
            <s xml:id="echoid-s6534" xml:space="preserve">17. </s>
            <s xml:id="echoid-s6535" xml:space="preserve">ducaturin 32. </s>
            <s xml:id="echoid-s6536" xml:space="preserve">id eſt, in ſummam eiuſdem ſeg-
              <lb/>
            menti CD, & </s>
            <s xml:id="echoid-s6537" xml:space="preserve">lateris AC: </s>
            <s xml:id="echoid-s6538" xml:space="preserve">procreabitur numerus 64. </s>
            <s xml:id="echoid-s6539" xml:space="preserve">cuius radix quadrata 8.
              <lb/>
            </s>
            <s xml:id="echoid-s6540" xml:space="preserve">præbebit perpendicularem AD, vt prius.</s>
            <s xml:id="echoid-s6541" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6542" xml:space="preserve">
              <emph style="sc">In</emph>
            poſteriori autem triangulo ABD, ſi differentia 5 {3/8}. </s>
            <s xml:id="echoid-s6543" xml:space="preserve">inter
              <lb/>
            ſegmentum AC, & </s>
            <s xml:id="echoid-s6544" xml:space="preserve">latus AD, nimirũ inter 5 {5/8}. </s>
            <s xml:id="echoid-s6545" xml:space="preserve">& </s>
            <s xml:id="echoid-s6546" xml:space="preserve">11. </s>
            <s xml:id="echoid-s6547" xml:space="preserve">ducatur
              <lb/>
              <figure xlink:label="fig-193-01" xlink:href="fig-193-01a" number="124">
                <image file="193-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/193-01"/>
              </figure>
            in 16 {5/8}. </s>
            <s xml:id="echoid-s6548" xml:space="preserve">hoc eſt, in ſum̃am eiuſdem ſegmenti AC, & </s>
            <s xml:id="echoid-s6549" xml:space="preserve">latus AD:
              <lb/>
            </s>
            <s xml:id="echoid-s6550" xml:space="preserve">producetur numerus {5719/64}. </s>
            <s xml:id="echoid-s6551" xml:space="preserve">ſiue 89 {23/64}. </s>
            <s xml:id="echoid-s6552" xml:space="preserve">cuius radix quadrata
              <lb/>
            in numeris exhiberi non poteſt, ſed paulo maior eſt, quãap-
              <lb/>
            poſita fractio cuius numerator eſt 75 {94/151}. </s>
            <s xml:id="echoid-s6553" xml:space="preserve">denominator aũt 8.</s>
            <s xml:id="echoid-s6554" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>