Benedetti, Giovanni Battista de, Io. Baptistae Benedicti ... Diversarvm specvlationvm mathematicarum, et physicarum liber : quarum seriem sequens pagina indicabit ; [annotated and critiqued by Guidobaldo Del Monte]

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EPISTOL AE.
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        <div xml:id="echoid-div7" type="body" level="1" n="1">
          <div xml:id="echoid-div477" type="chapter" level="2" n="6">
            <div xml:id="echoid-div642" type="section" level="3" n="28">
              <div xml:id="echoid-div642" type="letter" level="4" n="1">
                <pb o="333" rhead="EPISTOL AE." n="345" file="0345" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0345"/>
                <p>
                  <s xml:id="echoid-s4035" xml:space="preserve">Si
                    <reg norm="autem" type="context">autẽ</reg>
                  res viſibilis
                    <reg norm="oculusque" type="simple">oculusq́;</reg>
                  ambo fuerint intra circulum,
                    <reg norm="tunc" type="context">tũc</reg>
                  poſſibile eſſet quod
                    <lb/>
                    <reg norm="longitudo" type="context">lõgitudo</reg>
                    <var>.u.b.n.</var>
                  modo maior, modo minor, modo verò æqualis eſſet ipſa
                    <var>.u.o.n.</var>
                    <reg norm="nunc" type="context">nũc</reg>
                  .
                    <lb/>
                  </s>
                  <s xml:id="echoid-s4036" xml:space="preserve">Quod etiam affirmo de
                    <var>.u.b.p.</var>
                  ſimiliter etiam eueniet ſi vnus terminorum
                    <var>.u.</var>
                  vel
                    <var>.n.</var>
                    <lb/>
                  fuerit intra circunferentiam, reliquus verò extra ipſam.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4037" xml:space="preserve">Conſideremus nunc hic inſraſcriptam .4. figuram vbi
                    <var>.d.b.p.</var>
                  ſit circunferentia oxy
                    <lb/>
                  gonia ſeu elliptica (quod idem eſt) cuius maior axis ſit
                    <var>.d.p.</var>
                  in quo, duo termini
                    <var>.u.n.</var>
                    <lb/>
                  ſint centra eius generationis: </s>
                  <s xml:id="echoid-s4038" xml:space="preserve">b.x. verò ſit minor axis. </s>
                  <s xml:id="echoid-s4039" xml:space="preserve">Imaginemur etiam circulum
                    <var>.
                      <lb/>
                    b.o.x.</var>
                  cuius ſemidiameter ſit
                    <var>.c.b.</var>
                  non maior medietate minoris axis, ne circunferen-
                    <lb/>
                  tia huiuſmodi circuli ſecet circunferentiam oxygoniam. </s>
                  <s xml:id="echoid-s4040" xml:space="preserve">Cogitemus etiam circu-
                    <lb/>
                  lum
                    <var>.b.e.</var>
                  cuius ſemidiameter, minor non ſit minori axe
                    <var>.b.x.</var>
                  ipſius oxygoniæ, ne ſe
                    <lb/>
                  inuicem ſecent huiuſmodi circunferentiæ, ſint etiam ambo eorum centra in linea
                    <var>.b.
                      <lb/>
                    x.</var>
                  minoris axis, & punctum
                    <var>.b.</var>
                  ſit commune vnicuique earum periphæriarum, vnde
                    <lb/>
                  minor circulus, totus intra, maior autem, totus extra ipſam
                    <reg norm="figuram" type="context">figurã</reg>
                  oxygoniam erit.
                    <lb/>
                  </s>
                  <s xml:id="echoid-s4041" xml:space="preserve">Nunc ad partem
                    <var>.o.r.e.</var>
                  vbi non communicant inuicem ipſæ circunferentiæ ducan-
                    <lb/>
                  tur
                    <var>.n.o.r.e</var>
                  :
                    <var>u.o</var>
                  :
                    <var>u.r</var>
                  : et
                    <var>.u.e.</var>
                  & per
                    <var>.b.</var>
                  et
                    <var>.r.</var>
                  cogitetur tranſire alium circulum, cuius cen-
                    <lb/>
                  trum in axe
                    <var>.b.x.</var>
                  ſit
                    <var>.t.</var>
                    <reg norm="omnesque" type="simple">omnesq́;</reg>
                  iſti circuli imaginentur trium diuerſorum ſphærico-
                    <lb/>
                  rum ſpeculorum, vnde pro genera
                    <lb/>
                  tione
                    <reg norm="ipſius" type="simple">ipſiꝰ</reg>
                  oxygonię, ſeu ex .52. ter
                    <lb/>
                  tij Pergei, habebis longitudinem
                    <var>.
                      <lb/>
                      <anchor type="figure" xlink:label="fig-0345-01a" xlink:href="fig-0345-01"/>
                    u.r.n.</var>
                  ęqualem eſſe longitudini
                    <var>.u.b.
                      <lb/>
                    n.</var>
                  & ei, quæ eſt
                    <var>.u.o.n.</var>
                  (vt minor ip
                    <lb/>
                  ſa
                    <var>.u.r.n.</var>
                  ex .21. primi Euclidis) mi-
                    <lb/>
                  nor ipſa
                    <var>.u.b.n.</var>
                  & longitudinem
                    <var>.u.
                      <lb/>
                    e.n.</var>
                  (vt maior ipſa
                    <var>.u.r.n.</var>
                  ex eadem
                    <num value="21">.
                      <lb/>
                    21.</num>
                  primi Eucli.) maior ipſa
                    <var>.u.b.n</var>
                  .
                    <lb/>
                  </s>
                  <s xml:id="echoid-s4042" xml:space="preserve">Sed ſi quis vellet hoc demonſtrare
                    <lb/>
                  ope circuli,
                    <reg norm="vnius" type="simple">vniꝰ</reg>
                    <reg norm="tantummodo" type="context context">tãtũmodo</reg>
                  ſpeculi,
                    <lb/>
                    <reg norm="multiplicando" type="context">multiplicãdo</reg>
                  ipſas oxygonias
                    <reg norm="quem- admodum" type="wordlist">quẽ-
                      <lb/>
                    admodum</reg>
                  de ipſis circulis fecimus, obtineret ſimiliter propoſitum.</s>
                </p>
                <div xml:id="echoid-div645" type="float" level="5" n="4">
                  <figure xlink:label="fig-0345-01" xlink:href="fig-0345-01a">
                    <image file="0345-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0345-01"/>
                  </figure>
                </div>
              </div>
              <div xml:id="echoid-div647" type="letter" level="4" n="2">
                <head xml:id="echoid-head497" style="it" xml:space="preserve">Solutio dubitationis.</head>
                <head xml:id="echoid-head498" xml:space="preserve">AD EVNDEM.</head>
                <p>
                  <s xml:id="echoid-s4043" xml:space="preserve">RAtionalis eſt dubitatio tua,
                    <lb/>
                    <anchor type="figure" xlink:label="fig-0345-02a" xlink:href="fig-0345-02"/>
                  vtrum (
                    <reg norm="cum" type="context">cũ</reg>
                  circulus minor hoc
                    <lb/>
                  eſt
                    <var>.b.o.</var>
                  habeat ſuum centrum in mi
                    <lb/>
                  nori axe inter centrum oxygoniæ,
                    <lb/>
                  et .b: exiſtente
                    <var>.b.</var>
                  extremo axis mi-
                    <lb/>
                  noris,
                    <reg norm="communeque" type="simple">communeq́;</reg>
                  ambobus circun-
                    <lb/>
                  ferentijs circuli ſcilicet & oxigonię)
                    <lb/>
                  dictus circulus minor, plura puncta
                    <lb/>
                  communia habeat cum ipſis circun-
                    <lb/>
                  ferentijs.</s>
                </p>
                <div xml:id="echoid-div647" type="float" level="5" n="1">
                  <figure xlink:label="fig-0345-02" xlink:href="fig-0345-02a">
                    <image file="0345-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0345-02"/>
                  </figure>
                </div>
                <p>
                  <s xml:id="echoid-s4044" xml:space="preserve">Cui dubitationi
                    <reg norm="reſpondeo" type="context">reſpõdeo</reg>
                  quod
                    <lb/>
                  quotieſcunque centrum alicuius cir
                    <lb/>
                  culi fuerit idem cum
                    <var>.c.</var>
                  centro oxy-
                    <lb/>
                  goniæ, vel inter
                    <var>.c.</var>
                  et
                    <var>.b.</var>
                  in interual-
                    <lb/>
                  lo ſcilicet minoris axis, exiſtente
                    <var>.b.</var>
                    <lb/>
                  ſua extremitate communi ambabus </s>
                </p>
              </div>
            </div>
          </div>
        </div>
      </text>
    </echo>