Clavius, Christoph, Geometria practica

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        <div xml:id="echoid-div416" type="section" level="1" n="171">
          <p>
            <s xml:id="echoid-s6121" xml:space="preserve">
              <pb o="158" file="188" n="188" rhead="GEOMETR. PRACT."/>
            angulum, vnius in alterum; </s>
            <s xml:id="echoid-s6122" xml:space="preserve">adeo vt in quadrato ſatis ſit ducere vnum latus in
              <lb/>
            ſe, vt eius area cognoſcatur: </s>
            <s xml:id="echoid-s6123" xml:space="preserve">quippe cum duo latera circa vnum angulum re-
              <lb/>
              <figure xlink:label="fig-188-01" xlink:href="fig-188-01a" number="119">
                <image file="188-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/188-01"/>
              </figure>
            ctum æqualia ſint. </s>
            <s xml:id="echoid-s6124" xml:space="preserve">Vtin quadrato A B C D,
              <lb/>
            cuius ſingula latera quinos palmos con-
              <lb/>
            tinent, ſi latus A B, quinque palmorum
              <lb/>
            in ſe ducatur, producentur 25. </s>
            <s xml:id="echoid-s6125" xml:space="preserve">quadrata,
              <lb/>
            quorum quodlibet habet latus vnius pal-
              <lb/>
            mi; </s>
            <s xml:id="echoid-s6126" xml:space="preserve">atque tot palmos quadratos conti-
              <lb/>
            nere dicetur area quadrati A B C D. </s>
            <s xml:id="echoid-s6127" xml:space="preserve">At
              <lb/>
            area rectanguli altera parte longioris
              <lb/>
            EFGH, cuius vnum latus circa rectum an-
              <lb/>
            gulum continet 5. </s>
            <s xml:id="echoid-s6128" xml:space="preserve">pedes, & </s>
            <s xml:id="echoid-s6129" xml:space="preserve">alterum 3. </s>
            <s xml:id="echoid-s6130" xml:space="preserve">dicetur continere 15. </s>
            <s xml:id="echoid-s6131" xml:space="preserve">palmos quadra-
              <lb/>
            tos, propterea quod ex mutua laterum 5. </s>
            <s xml:id="echoid-s6132" xml:space="preserve">& </s>
            <s xml:id="echoid-s6133" xml:space="preserve">3. </s>
            <s xml:id="echoid-s6134" xml:space="preserve">multiplicatione numerus 15.
              <lb/>
            </s>
            <s xml:id="echoid-s6135" xml:space="preserve">procreatur.</s>
            <s xml:id="echoid-s6136" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">Vt camp{us}
            <lb/>
          rectangul{us}
            <lb/>
          menſuretur,
            <lb/>
          quid agen-
            <lb/>
          dum.</note>
          <p>
            <s xml:id="echoid-s6137" xml:space="preserve">2. </s>
            <s xml:id="echoid-s6138" xml:space="preserve">
              <emph style="sc">Itaqve</emph>
            ſi campum aliquem rectangulum, vel parallelo grammum re-
              <lb/>
            ctangulum metiri iubeamur, menſuranda erunt per aliquam menſuram notam,
              <lb/>
            vt per palmum, vel pedem, &</s>
            <s xml:id="echoid-s6139" xml:space="preserve">c. </s>
            <s xml:id="echoid-s6140" xml:space="preserve">duo latera circa angulum rectum. </s>
            <s xml:id="echoid-s6141" xml:space="preserve">Nam vno
              <lb/>
            in alterum ducto, area propoſiti campi, vel parallelogrammi rectanguli produ-
              <lb/>
            cetur, vt dictum eſt.</s>
            <s xml:id="echoid-s6142" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div418" type="section" level="1" n="172">
          <head xml:id="echoid-head175" xml:space="preserve">DE AREA TRIANGVLORVM
            <lb/>
            <emph style="sc">Capvt</emph>
          II.</head>
          <p>
            <s xml:id="echoid-s6143" xml:space="preserve">1. </s>
            <s xml:id="echoid-s6144" xml:space="preserve">
              <emph style="sc">Qvando</emph>
            trianguli omnia tria latera cognita ſunt, duabus viis eius area
              <lb/>
              <handwritten xlink:label="hd-188-2" xlink:href="hd-188-2a" number="56"/>
            cognoſci poteſt. </s>
            <s xml:id="echoid-s6145" xml:space="preserve">Prima, quæ accuratiſsima eſt, ita ſe habet.</s>
            <s xml:id="echoid-s6146" xml:space="preserve">
              <unsure/>
            Colligantur omnia
              <lb/>
            latera in vnam ſummam: </s>
            <s xml:id="echoid-s6147" xml:space="preserve">Ex hui{us} ſummæ ſemiſſe ſubtr ahantur ſingula latera, vt ha-
              <lb/>
            beantur tr{es} differentiæ inter illam ſemiſſem, & </s>
            <s xml:id="echoid-s6148" xml:space="preserve">latera ſingula: </s>
            <s xml:id="echoid-s6149" xml:space="preserve">Poſtremo tr{es} hæ diffe-
              <lb/>
            rentiæ, & </s>
            <s xml:id="echoid-s6150" xml:space="preserve">dicta ſemiſſis inter ſe mutuo multiplicentur. </s>
            <s xml:id="echoid-s6151" xml:space="preserve">Producti enim numeriradix
              <lb/>
            quadrata erit area trianguli quæſita.</s>
            <s xml:id="echoid-s6152" xml:space="preserve"/>
          </p>
          <handwritten number="57"/>
          <p>
            <s xml:id="echoid-s6153" xml:space="preserve">Verbigratia, ſi latera ſint 10. </s>
            <s xml:id="echoid-s6154" xml:space="preserve">17. </s>
            <s xml:id="echoid-s6155" xml:space="preserve">21. </s>
            <s xml:id="echoid-s6156" xml:space="preserve">erit ſumma ex illis collecta 48. </s>
            <s xml:id="echoid-s6157" xml:space="preserve">& </s>
            <s xml:id="echoid-s6158" xml:space="preserve">ſemiſsis
              <lb/>
            24. </s>
            <s xml:id="echoid-s6159" xml:space="preserve">Differentiæ autem inter hanc ſemiſſem, & </s>
            <s xml:id="echoid-s6160" xml:space="preserve">latera erunt 147. </s>
            <s xml:id="echoid-s6161" xml:space="preserve">3. </s>
            <s xml:id="echoid-s6162" xml:space="preserve">Hæ inter ſe
              <lb/>
            multip licatæ) ducendo primum 14. </s>
            <s xml:id="echoid-s6163" xml:space="preserve">in 7. </s>
            <s xml:id="echoid-s6164" xml:space="preserve">deinde productum in 3.) </s>
            <s xml:id="echoid-s6165" xml:space="preserve">faciunt
              <lb/>
            294. </s>
            <s xml:id="echoid-s6166" xml:space="preserve">quæ ducta in 24. </s>
            <s xml:id="echoid-s6167" xml:space="preserve">ſemiſſem prædictam, producunt 7056. </s>
            <s xml:id="echoid-s6168" xml:space="preserve">cuius numeriradix
              <lb/>
            quadrata 84. </s>
            <s xml:id="echoid-s6169" xml:space="preserve">erit area dicti trianguli, cuius latera ſunt 10. </s>
            <s xml:id="echoid-s6170" xml:space="preserve">17. </s>
            <s xml:id="echoid-s6171" xml:space="preserve">21. </s>
            <s xml:id="echoid-s6172" xml:space="preserve">Rurſus ſi in alio
              <lb/>
            quopiam triangulo latera ſint 13. </s>
            <s xml:id="echoid-s6173" xml:space="preserve">14. </s>
            <s xml:id="echoid-s6174" xml:space="preserve">15. </s>
            <s xml:id="echoid-s6175" xml:space="preserve">inueniemus eandem a@eam. </s>
            <s xml:id="echoid-s6176" xml:space="preserve">Nam ſ@m̃a
              <lb/>
            laterum eſt 42. </s>
            <s xml:id="echoid-s6177" xml:space="preserve">ſemiſsis 21. </s>
            <s xml:id="echoid-s6178" xml:space="preserve">Differẽtię inter hanc ſemiſſem, & </s>
            <s xml:id="echoid-s6179" xml:space="preserve">tria latera ſunt 8. </s>
            <s xml:id="echoid-s6180" xml:space="preserve">7. </s>
            <s xml:id="echoid-s6181" xml:space="preserve">6.
              <lb/>
            </s>
            <s xml:id="echoid-s6182" xml:space="preserve">quæ inter ſe multip licatæ faciunt 336. </s>
            <s xml:id="echoid-s6183" xml:space="preserve">quæ ducta in 21. </s>
            <s xml:id="echoid-s6184" xml:space="preserve">ſemiſſem prædictam effi-
              <lb/>
            ciunt 7056. </s>
            <s xml:id="echoid-s6185" xml:space="preserve">cuius numeri quadrata radix 84. </s>
            <s xml:id="echoid-s6186" xml:space="preserve">dabit aream trianguli, quod lateri-
              <lb/>
            bus 13. </s>
            <s xml:id="echoid-s6187" xml:space="preserve">14. </s>
            <s xml:id="echoid-s6188" xml:space="preserve">15. </s>
            <s xml:id="echoid-s6189" xml:space="preserve">continetur. </s>
            <s xml:id="echoid-s6190" xml:space="preserve">Denique ſi detur triangulum A B C, in quo latus A B,
              <lb/>
            7. </s>
            <s xml:id="echoid-s6191" xml:space="preserve">B C, 10. </s>
            <s xml:id="echoid-s6192" xml:space="preserve">& </s>
            <s xml:id="echoid-s6193" xml:space="preserve">A C, 11. </s>
            <s xml:id="echoid-s6194" xml:space="preserve">ſumma omnium eſt 28. </s>
            <s xml:id="echoid-s6195" xml:space="preserve">& </s>
            <s xml:id="echoid-s6196" xml:space="preserve">ſemiſsis 14. </s>
            <s xml:id="echoid-s6197" xml:space="preserve">quæ latera ſuperat hiſ-
              <lb/>
            ce numeris 7. </s>
            <s xml:id="echoid-s6198" xml:space="preserve">4. </s>
            <s xml:id="echoid-s6199" xml:space="preserve">3. </s>
            <s xml:id="echoid-s6200" xml:space="preserve">qui inter ſemultip licati faciunt 84. </s>
            <s xml:id="echoid-s6201" xml:space="preserve">quę ducta in 14. </s>
            <s xml:id="echoid-s6202" xml:space="preserve">ſemiſſem
              <lb/>
            ſummæ gignunt numerum 1176. </s>
            <s xml:id="echoid-s6203" xml:space="preserve">cuius radix quadrata 34 {20/69}. </s>
            <s xml:id="echoid-s6204" xml:space="preserve">ferè dabit aream
              <lb/>
            trianguli A B C. </s>
            <s xml:id="echoid-s6205" xml:space="preserve">Ex quo colliges, non omnis trianguli aream eſſe numerum ra-
              <lb/>
            tionalem: </s>
            <s xml:id="echoid-s6206" xml:space="preserve">propterea quod numerus vltimo loco productus non eſt ſemper
              <lb/>
            quadratus, vt in poſtremo hoc exemplo @ontigit.</s>
            <s xml:id="echoid-s6207" xml:space="preserve"/>
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