Clavius, Christoph, In Sphaeram Ioannis de Sacro Bosco commentarius

Table of figures

< >
< >
page |< < (80) of 525 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div205" type="section" level="1" n="67">
          <p>
            <s xml:id="echoid-s4072" xml:space="preserve">
              <pb o="80" file="116" n="117" rhead="Comment. in I. Cap. Sphæræ"/>
            angulum ſit, quadratum autem & </s>
            <s xml:id="echoid-s4073" xml:space="preserve">æquilaterum, & </s>
            <s xml:id="echoid-s4074" xml:space="preserve">æquiangulum eſt. </s>
            <s xml:id="echoid-s4075" xml:space="preserve">Sit præ-
              <lb/>
            terea aliud parallelogramum rectangulum, cuius unumquodque duorum
              <lb/>
            laterum oppoſitorum ſit 9. </s>
            <s xml:id="echoid-s4076" xml:space="preserve">aliorum uero duorum 3. </s>
            <s xml:id="echoid-s4077" xml:space="preserve">vt quadrati, & </s>
            <s xml:id="echoid-s4078" xml:space="preserve">parallelo-
              <lb/>
            grammi huius ambitus quoque ſint æquales. </s>
            <s xml:id="echoid-s4079" xml:space="preserve">Comprehendet igitur area hu-
              <lb/>
            i
              <unsure/>
            us parallelogrammi ſolum 27. </s>
            <s xml:id="echoid-s4080" xml:space="preserve">quadrata ex illis 36. </s>
            <s xml:id="echoid-s4081" xml:space="preserve">quæ in quadrato diximus
              <lb/>
            contineri. </s>
            <s xml:id="echoid-s4082" xml:space="preserve">Pari ratione, ſi parallelogrammi alicuius unumquodque duorum
              <lb/>
            laterum oppoſitorum eſſet 8. </s>
            <s xml:id="echoid-s4083" xml:space="preserve">& </s>
            <s xml:id="echoid-s4084" xml:space="preserve">aliorum duorum 4. </s>
            <s xml:id="echoid-s4085" xml:space="preserve">eſſet quidem ipſum qua-
              <lb/>
            drato iſoperimetrum, ſed eius area contineret duntaxat 32. </s>
            <s xml:id="echoid-s4086" xml:space="preserve">quadrata. </s>
            <s xml:id="echoid-s4087" xml:space="preserve">Item,
              <lb/>
            ſi duo latera alicuius parallelogrammi oppoſita, ſingula haberent 7. </s>
            <s xml:id="echoid-s4088" xml:space="preserve">alia ue-
              <lb/>
            ro duo ſingula 5. </s>
            <s xml:id="echoid-s4089" xml:space="preserve">eſſet etiam quadrato iſoperimetrum, area autem illius@ in-
              <lb/>
            cluderet tantum 35. </s>
            <s xml:id="echoid-s4090" xml:space="preserve">quadrata, &</s>
            <s xml:id="echoid-s4091" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4092" xml:space="preserve">Vbi clare uides, quo magis figuræ iſoperi-
              <lb/>
            metrę accedunt ad æquilateram, cui ſunt iſoperimetræ, eo etiam maiorem
              <lb/>
            comprehendunt aream, & </s>
            <s xml:id="echoid-s4093" xml:space="preserve">minus differunt in capacitate a figura æquilatera.
              <lb/>
            </s>
            <s xml:id="echoid-s4094" xml:space="preserve">Quod ſi aliquod parallelogrammum rectangulum altera parte longius eiuſ-
              <lb/>
            dem ſit capacitatis cum quadrato, illud maiorem ambitum continere neceſ-
              <lb/>
              <figure xlink:label="fig-116-01" xlink:href="fig-116-01a" number="17">
                <image file="116-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/116-01"/>
              </figure>
            ſe eſt. </s>
            <s xml:id="echoid-s4095" xml:space="preserve">Vt ſi paralle
              <lb/>
            logrammi alicuius
              <lb/>
            quodlibet duorum
              <lb/>
            oppoſitorum late-
              <lb/>
            rum contineat 12.
              <lb/>
            </s>
            <s xml:id="echoid-s4096" xml:space="preserve">aliorum vero duo-
              <lb/>
            rum quodlibet 3. </s>
            <s xml:id="echoid-s4097" xml:space="preserve">
              <lb/>
            erit quidem area il
              <lb/>
            lius æqualis areæ
              <lb/>
            quadrati, cum con-
              <lb/>
            tineat 36. </s>
            <s xml:id="echoid-s4098" xml:space="preserve">quadratula: </s>
            <s xml:id="echoid-s4099" xml:space="preserve">At uero ambitus ipſius ſuperabit ambitum quadrati: </s>
            <s xml:id="echoid-s4100" xml:space="preserve">Ille
              <lb/>
            enim erit 30. </s>
            <s xml:id="echoid-s4101" xml:space="preserve">hic autem 24. </s>
            <s xml:id="echoid-s4102" xml:space="preserve">Quæ omnia perſpicua ſunt in appoſitis figuris.</s>
            <s xml:id="echoid-s4103" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4104" xml:space="preserve">
              <emph style="sc">Sit</emph>
            iam parallelogrammum inæqualium angulorum A B C D, & </s>
            <s xml:id="echoid-s4105" xml:space="preserve">a pun-
              <lb/>
            ctis C, D, educantur perpendiculares lineę C F, & </s>
            <s xml:id="echoid-s4106" xml:space="preserve">D E, ad rectam C D: </s>
            <s xml:id="echoid-s4107" xml:space="preserve">Pro
              <lb/>
            ducta igitur A B, vſque ad F, erit parallelogrammum A B C D, æquale paral-
              <lb/>
            lelogrammo C D E F, cum ſint hæc parallelogramma inter eaſdem paralle-
              <lb/>
              <note position="left" xlink:label="note-116-01" xlink:href="note-116-01a" xml:space="preserve">35. primi.</note>
            las C D, A F, & </s>
            <s xml:id="echoid-s4108" xml:space="preserve">ſuper eandem baſim C D, conſtituta. </s>
            <s xml:id="echoid-s4109" xml:space="preserve">Et quoniam latera B C,
              <lb/>
            A D, maiora ſunt lateribus C F, D E, eſtq́ue latus A B, lateri E F, æquale,
              <lb/>
              <note position="left" xlink:label="note-116-02" xlink:href="note-116-02a" xml:space="preserve">19. primi.</note>
            (quod utrumq. </s>
            <s xml:id="echoid-s4110" xml:space="preserve">lateri oppoſito C D, in parallelogrammis A B C D, C D E F,
              <lb/>
              <note position="left" xlink:label="note-116-03" xlink:href="note-116-03a" xml:space="preserve">34. primi.</note>
              <figure xlink:label="fig-116-02" xlink:href="fig-116-02a" number="18">
                <image file="116-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/116-02"/>
              </figure>
            æquale ſit) & </s>
            <s xml:id="echoid-s4111" xml:space="preserve">latus C D, commune, erit
              <lb/>
            ambitus parallelogrammi C D E F, mi-
              <lb/>
            nor ambitu parallelogrammi A B C D.
              <lb/>
            </s>
            <s xml:id="echoid-s4112" xml:space="preserve">Vnde ſi producantur C F, D E, ad G, & </s>
            <s xml:id="echoid-s4113" xml:space="preserve">
              <lb/>
            H, ita ut C G, æqualis ſit ipſi B C, & </s>
            <s xml:id="echoid-s4114" xml:space="preserve">
              <lb/>
            D H, ipſi A D, perficiaturq́ue parallelo-
              <lb/>
            grammum C D H G, (ducta uidelicet re-
              <lb/>
            cta G H,) erit parallelogramum C D
              <lb/>
            H G, iſoperimetrum parallelogrammo
              <lb/>
            A B C D. </s>
            <s xml:id="echoid-s4115" xml:space="preserve">Eſt autem parallelogrammum
              <lb/>
            C D H G, maius quam parallelogram-
              <lb/>
            mum C D E F, hoc eſt, quam parallelo-
              <lb/>
            grammum A B C D, quantitate E F G H. </s>
            <s xml:id="echoid-s4116" xml:space="preserve">
              <lb/>
            Conſtat igitur inter Iſoperimetras figuras rectilineas eam, quæ & </s>
            <s xml:id="echoid-s4117" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum