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-div477" type="chapter" level="2" n="6">
            <div xml:id="echoid-div726" type="section" level="3" n="40">
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                <p>
                  <s xml:id="echoid-s4407" xml:space="preserve">
                    <pb o="372" rhead="IO. BAPT. BENED." n="384" file="0384" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0384"/>
                  peiæ tam lucida, vt ipſo lucifero videretur rutilantior
                    <reg norm="atque" type="simple">atq;</reg>
                  cæterarum (abſque vlla
                    <lb/>
                  aſpectus diuerſitate) magis ſcintillans. </s>
                  <s xml:id="echoid-s4408" xml:space="preserve">Quî fieri poterat, vt ſtellæ quæ ab illa pa-
                    <lb/>
                  rum diſtant, alioqui multo maiores, non etiam illa clariores apparuerint? </s>
                  <s xml:id="echoid-s4409" xml:space="preserve">ſed ſi ali-
                    <lb/>
                  quis diceret eam exhalationem non ita fortaſſe dilatari, vt inter nos, & aliam ali-
                    <lb/>
                  quam ſtellam interponeretur. </s>
                  <s xml:id="echoid-s4410" xml:space="preserve">Tunc ego reſponderem neceſſariò ſequi debere ta-
                    <lb/>
                  lem exhalationem, tantam latitudinem occupare, quod aliquibus populis aliam
                    <lb/>
                    <reg norm="aliquam" type="context">aliquã</reg>
                    <reg norm="ſtellam" type="context">ſtellã</reg>
                  circunuicinãhac ipſa de qua mentionem ſecimus redderet lucidiorem.
                    <lb/>
                  </s>
                  <s xml:id="echoid-s4411" xml:space="preserve">Sed cum hoc perſpectum fuerit nulli, ſequebatur lucem illam ab ipſis exhalatio-
                    <lb/>
                  nibus elementaribus haud poſſe oriri: </s>
                  <s xml:id="echoid-s4412" xml:space="preserve">quod nobis ſcintillatio illa maxima perma-
                    <lb/>
                  gno fuit inditio, ſi phas eſt credere,
                    <reg norm="nam" type="context">nã</reg>
                  quo magis aliquod coeleſte corpus ſcintillat,
                    <lb/>
                  eo longius à nobis diſtare.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4413" xml:space="preserve">Verum quoniam efflagitaſti à me vt aliquid circa huiuſce rei ſpeculationem tibi
                    <lb/>
                  ſcribam, idcirco tibi morem gerere volens paucis ſubiungam.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4414" xml:space="preserve">Conſidera primo hanc ſubſcriptam primam figuram, in qua
                    <var>.c.a.e.</var>
                  ſignatur pro
                    <lb/>
                  Globo terreſtri cuius
                    <var>.i.</var>
                  centrum ſit et
                    <var>.u.o.n.</var>
                  pro conuexo ignis, ſed
                    <var>.K.x.s.</var>
                  pro orbe
                    <lb/>
                  octauo
                    <var>.x.</var>
                  autem pro ſtella iam ſuperius dicta, quæ ſemper fuit, eſt, & erit, quamuis
                    <lb/>
                  cæteris tribus nunc obſcurior ſit. </s>
                  <s xml:id="echoid-s4415" xml:space="preserve">Accipiantur deinde duo loca in ſuperſicie terræ,
                    <lb/>
                  quę ſint
                    <var>.c.</var>
                  et
                    <var>.e.</var>
                  diametraliter inuicem oppoſita, ita quod circa eorum orizontes poſ
                    <lb/>
                  ſibile ſit ſtellam
                    <var>.x.</var>
                  videre, radijs ipſius ſtellæ mediantibus
                    <var>.x.n.e.</var>
                  et
                    <var>.x.u.c.</var>
                    <reg norm="quorum" type="context">quorũ</reg>
                  par-
                    <lb/>
                  tes
                    <var>.n.c.</var>
                  et
                    <var>.u.e.</var>
                  ita breues ſint, reſpectu eorum
                    <reg norm="totorum" type="context">totorũ</reg>
                  , vt vix ſexcenteſima pars ſit vna
                    <lb/>
                    <reg norm="quæque" type="simple">quæq;</reg>
                  illarum, nec non
                    <var>.c.e.</var>
                  ita breuis reſpectu ſemidiametri octauæ ſphæræ, quod
                    <lb/>
                  vix ſit vna ex partibus decemmillibus, vt ſcis, ſequitur quod recta terminata ab
                    <var>.u.</var>
                    <lb/>
                  et
                    <var>.n.</var>
                  minor ſenſibiliter non ſit ipſo terræ diametro
                    <var>.c.e.</var>
                  cum duo hæc interualla ex
                    <lb/>
                  triangulorum ſimilitudine ſe habeant vt
                    <var>.x.i.</var>
                  ad
                    <var>.x.o.</var>
                  hoc eſt ferè vt .602. ad .601. vn-
                    <lb/>
                  de anguli
                    <var>.n.e.c.</var>
                  et
                    <var>.u.c.e.</var>
                  à rectis minime differre videbuntur, cum eorum differen-
                    <lb/>
                  tia certo modo minima ſit. </s>
                  <s xml:id="echoid-s4416" xml:space="preserve">ductę poſtea
                    <reg norm="cum" type="context">cũ</reg>
                  fuerint duæ diagonales
                    <var>.e.u.</var>
                  et
                    <var>.n.c.</var>
                    <reg norm="termi- nabunt" type="context">termi-
                      <lb/>
                    nabũt</reg>
                  angulos
                    <var>.n.e.u.</var>
                  et
                    <var>.e.n.c.</var>
                    <reg norm="inuicem" type="context">inuicẽ</reg>
                  ferè ęquales,
                    <reg norm="idem" type="context">idẽ</reg>
                  aſſero de angulis
                    <var>.u.c.n.</var>
                  et
                    <var>.e.u.c</var>
                  .</s>
                </p>
                <p>
                  <s xml:id="echoid-s4417" xml:space="preserve">Supponatur nunc primò tuam exhalationem ſublimatam eſſe ad ſupremas par-
                    <lb/>
                  tes elementaris regionis circum circa lineam
                    <var>.o.i</var>
                  : </s>
                  <s xml:id="echoid-s4418" xml:space="preserve">tunc clarum eſſet quod ſi ratione hu
                    <lb/>
                  iuſmodi exhalationis ſtella
                    <var>.x.</var>
                  ita lucida viſa fuerit tam aſpicientibus ab
                    <var>.e.</var>
                  quam ab
                    <lb/>
                  c. exhalatio minoris latitudinis quam
                    <var>.u.n.</var>
                  eſſe non poterat, hoc eſt, quam terræ dia-
                    <lb/>
                  meter, cum idem in longitudine ferè ſit, ſed punctum
                    <var>.u.</var>
                  ſatis videri poteſt ab oculo
                    <lb/>
                  in
                    <var>.e.</var>
                  & punctum
                    <var>.n.</var>
                  ab oculo in
                    <var>.c.</var>
                  vt alias tibi probaui, ratione refractionis radiorum
                    <lb/>
                  per diuerſa diafana tranſeuntium. </s>
                  <s xml:id="echoid-s4419" xml:space="preserve">Nunc producti cum fuerint ij duo radij
                    <var>.e.u.</var>
                  et
                    <var>.c.
                      <lb/>
                    n.</var>
                  vſque ad octauum orbem ad puncta
                    <var>.s.</var>
                  et
                    <var>.K.</var>
                  reliquum erit nos videre quantitates
                    <lb/>
                  graduum arcus
                    <var>.s.x.</var>
                  et
                    <var>.k.x.</var>
                  ſed
                    <var>.s.x.</var>
                  ſubiacet a ngulo
                    <var>.s.e.x.</var>
                  et
                    <var>.k.x.</var>
                  angulo
                    <var>.k.c.x.</var>
                  qui qui
                    <lb/>
                  quidem anguli nihil differunt ſenſibiliter ac ſi eſſent in centro
                    <var>.i</var>
                  . </s>
                  <s xml:id="echoid-s4420" xml:space="preserve">Et cum ſuperius di-
                    <lb/>
                  xerimus angulos
                    <var>.s.e.x.</var>
                  et
                    <var>.k.c.x.</var>
                  ſenſibiliter mi nime differre ab angulis
                    <var>.c.n.e.</var>
                  et
                    <var>.e.
                      <lb/>
                    u.c.</var>
                  ſi cognouerimus quantitatem iſtorum, cognita etiam nobis erit quantitas
                    <lb/>
                  ill orum.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4421" xml:space="preserve">Cum igitur ſemidiameter elementaris regionis maior ſit ſemidiametro terræ, vt
                    <lb/>
                  33. ad vnum, & cogitata
                    <var>.c.n.</var>
                  vt dicta ſemidiameter, quia ſenſibiliter ab ea minime
                    <lb/>
                  diffe
                    <unsure/>
                  rt, nunc ſi ſupponatur dicta
                    <var>.n.c.</var>
                  vt
                    <reg norm="baſistrianguli" type="context">baſistriãguli</reg>
                  orthogonij eſſe
                    <reg norm="partium" type="context">partiũ</reg>
                  .100000
                    <lb/>
                  & dixerimus ſi
                    <var>.c.n.</var>
                  vt partium .33. præbet nobis
                    <var>.c.e.</var>
                  duarum partium, quid nobis
                    <lb/>
                  pręſtabit eadem
                    <var>.c.n.</var>
                  vt partium .100000. vnde proueniet nobis
                    <var>.c.e.</var>
                  vt
                    <reg norm="partium" type="context">partiũ</reg>
                  .6060.
                    <lb/>
                  cuius angulus
                    <var>.c.n.e.</var>
                  erit graduum .3. & min .29. ita etiam erit angulus
                    <var>.k.</var>
                  e
                    <unsure/>
                    <var>.x.</var>
                  cuius ar- </s>
                </p>
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