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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            <div xml:id="echoid-div642" type="section" level="3" n="28">
              <div xml:id="echoid-div647" type="letter" level="4" n="2">
                <p>
                  <s xml:id="echoid-s4044" xml:space="preserve">
                    <pb o="334" rhead="IO. BABPT. BENED." n="346" file="0346" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0346"/>
                  circunferentijs, ipſas circunferentias inuicem contiguas eſſe oportebit in puncto
                    <var>.b.</var>
                    <lb/>
                  tantummodo.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4045" xml:space="preserve">Eſto primum quod centrum
                    <var>.c.</var>
                  commune exiſtat, vt dictum eſt. </s>
                  <s xml:id="echoid-s4046" xml:space="preserve">ſit etiam centrum
                    <lb/>
                  vnius circuli, cuius diameter ſit
                    <reg norm="idem" type="context">idẽ</reg>
                    <reg norm="cum" type="context">cũ</reg>
                  maiori axe
                    <var>.d.p.</var>
                  & in gyro oxygoniæ accipia-
                    <lb/>
                  tur punctum
                    <var>.f.</var>
                  proximum
                    <var>.b.</var>
                  quantum fieri poterit, </s>
                  <s xml:id="echoid-s4047" xml:space="preserve">tunc protrahatur
                    <var>.f.a.e.</var>
                  parallela
                    <lb/>
                  ipſi
                    <var>.g.c.</var>
                  vſque ad gyrum maioris circuli in puncto
                    <var>.e.</var>
                  quæ cum
                    <var>.d.p.</var>
                  rectos efficiec
                    <lb/>
                  angulos. ex .29. primi Eucli. </s>
                  <s xml:id="echoid-s4048" xml:space="preserve">
                    <reg norm="ſecabitque" type="simple">ſecabitq́;</reg>
                  gyrum circuli
                    <var>.b.o.</var>
                  minoris in puncto
                    <var>.t.</var>
                  quod di
                    <lb/>
                  co eſſe intra oxygoniam,
                    <reg norm="ſeparatumque" type="simple">ſeparatumq́;</reg>
                  ab
                    <var>.f</var>
                  . </s>
                  <s xml:id="echoid-s4049" xml:space="preserve">Quapropter duco
                    <var>.c.e.</var>
                  quæ ſecabit cir-
                    <lb/>
                  cunferentiam circuli minoris in
                    <reg norm="puncto" type="context">pũcto</reg>
                    <var>.o.</var>
                  à quo puncto duco etiam
                    <var>.o.i.</var>
                  parallelam ad
                    <lb/>
                    <var>e.a</var>
                  . </s>
                  <s xml:id="echoid-s4050" xml:space="preserve">Deinde conſidero, quod ex ra-
                    <lb/>
                  tionibus ab Archimede adductis in
                    <lb/>
                    <figure xlink:label="fig-0346-01" xlink:href="fig-0346-01a" number="373">
                      <image file="0346-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0346-01"/>
                    </figure>
                  quinta propoſitione libri de conoi-
                    <lb/>
                  dalibus, & ſphæroidibus, eadem
                    <lb/>
                  proportio erit
                    <reg norm="ipſius" type="simple">ipſiꝰ</reg>
                    <var>.g.c.</var>
                  ad
                    <var>.b.c.</var>
                  quę
                    <lb/>
                  ipſius
                    <var>.e.a.</var>
                  ad
                    <var>.f.a.</var>
                  vnde permutando
                    <lb/>
                  ita erit ipſius
                    <var>.g.c.</var>
                  ad
                    <var>.e.a.</var>
                  vel
                    <var>.b.c.</var>
                  ad
                    <lb/>
                    <var>f.a.</var>
                  hoc eſt ipſius
                    <var>.e.c.</var>
                  ad
                    <var>.e.a.</var>
                  vt
                    <var>.o.c.</var>
                    <lb/>
                  ad
                    <var>.f.a.</var>
                  ſed ex ſimilitudine triangu-
                    <lb/>
                  lorum, & ex .11. quinti, ita
                    <reg norm="etiam" type="context">etiã</reg>
                  erit
                    <lb/>
                  ipſius
                    <var>.o.c.</var>
                  ad
                    <var>.o.i.</var>
                  vt
                    <var>.o.c.</var>
                  ad
                    <var>.f.a</var>
                  . </s>
                  <s xml:id="echoid-s4051" xml:space="preserve">Vn-
                    <lb/>
                  de ſequitur
                    <var>.o.i.</var>
                  æqualem eſſe
                    <var>.f.a.</var>
                    <lb/>
                  ſed ex .14. tertij Eucli
                    <var>.t.a.</var>
                  minor eſt
                    <var>.
                      <lb/>
                    o.i</var>
                  . </s>
                  <s xml:id="echoid-s4052" xml:space="preserve">Quare minor etiam erit ipſa
                    <var>.f.
                      <lb/>
                    a</var>
                  . </s>
                  <s xml:id="echoid-s4053" xml:space="preserve">Vnde punctum
                    <var>.t.</var>
                  intra oxygo-
                    <lb/>
                  niam erit, & conſequenter ſepara-
                    <lb/>
                  tum .ab
                    <var>.f</var>
                  .</s>
                </p>
                <p>
                  <s xml:id="echoid-s4054" xml:space="preserve">Sed ſi centrum circuli minoris
                    <lb/>
                  fuerit inter
                    <var>.c.</var>
                  et
                    <var>.b.</var>
                  hoc eſt eccentri-
                    <lb/>
                  cum ipſius oxygoniæ, ipſe tanget concentricum in puncto
                    <var>.b.</var>
                  tantummodò, vt in .3.
                    <lb/>
                  Euclidis libro probatur. </s>
                  <s xml:id="echoid-s4055" xml:space="preserve">Vnde tanto magis diſtans erit punctum
                    <var>.t.</var>
                  à puncto
                    <var>.f.</var>
                  quod
                    <lb/>
                  erit propoſitum.</s>
                </p>
              </div>
              <div xml:id="echoid-div650" type="letter" level="4" n="3">
                <head xml:id="echoid-head499" style="it" xml:space="preserve">Alterius dubitationis ſolutio.</head>
                <head xml:id="echoid-head500" xml:space="preserve">AD EVNDEM.</head>
                <p>
                  <s xml:id="echoid-s4056" xml:space="preserve">VNde autem fiat, quod à ſpeculis planis, obiectorum imagines, ita diſtantes
                    <lb/>
                  vltra ſuperficiem ipſius ſpeculi videantur, vt obiecta citra ipſam ſuperficiem
                    <lb/>
                  reperiuntur.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4057" xml:space="preserve">Pro cuius rei ſcientia, tres cognitiones nos primum habere oportet, quarum pri-
                    <lb/>
                  ma eſt. </s>
                  <s xml:id="echoid-s4058" xml:space="preserve">Vnde fiat, quod obiecti imago in catheto incidentiæ videatur. </s>
                  <s xml:id="echoid-s4059" xml:space="preserve">
                    <reg norm="Secunda" type="context">Secũda</reg>
                  . </s>
                  <s xml:id="echoid-s4060" xml:space="preserve">vn-
                    <lb/>
                  de efficiatur, quod angulus reflexionis, ſemper æqualis ſit angulo incidentiæ.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4061" xml:space="preserve">Terria demum. </s>
                  <s xml:id="echoid-s4062" xml:space="preserve">Vnde naſcatur quod radius incidentiæ ſimul cum radio reflexio-
                    <lb/>
                  nis ſit in quodam plano ſecante ſuperficiem ſpeculi ſemper ad rectos, quod qui-
                    <lb/>
                  dem planum vocatur ſuperficies reflexionis. </s>
                  <s xml:id="echoid-s4063" xml:space="preserve">Huiuſmodi tres paſſiones, ab omnibus
                    <lb/>
                  ſpecularijs conſideratæ ſunt, ſed rationes ab illis traditæ, mihi non ſatisfaciunt.</s>
                </p>
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