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-div776" type="section" level="3" n="50">
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                <p>
                  <s xml:id="echoid-s5022" xml:space="preserve">
                    <pb o="417" rhead="EPISTOL AE." n="429" file="0429" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0429"/>
                  vmbra reperitur, tantum quantum defectus caloris radij ſolaris fert, qui per vim,
                    <lb/>
                  dictum aerem rarefactum conſeruabat, ſtatim dictum aerem condenſari cognoſces:
                    <lb/>
                  </s>
                  <s xml:id="echoid-s5023" xml:space="preserve">& quia ea condenſatio homogenea non eſt, ob diuerſas rationes, hanc ob cauſam
                    <lb/>
                  percipimus eam aeris impulſionem, & inæqualiter, dum verò eadem vmbra diſce-
                    <lb/>
                  dit, ventus, ferè, ſtatim ceſſat, & ſæpe ante quam dicta vmbra diſcedat; </s>
                  <s xml:id="echoid-s5024" xml:space="preserve">cuius rei cau
                    <lb/>
                  ſa eſt longa mora quam trahi vmbra, ita vt prius abſoluatur reditus aeris ad
                    <reg norm="formam" type="context">formã</reg>
                  ,
                    <lb/>
                  quæ ei conuenit in huiuſmodi vmbra, quam faciet nubes dum Sol deregitur.</s>
                </p>
                <p>
                  <s xml:id="echoid-s5025" xml:space="preserve">Vera non ſunt ea, quæ tibi Arnoldus dixit, vt mihi tuis literis ſignificaſti. </s>
                  <s xml:id="echoid-s5026" xml:space="preserve">Nam ego
                    <lb/>
                  ita dixi, videlicet, quod quoti eſcunque aliquis aſpexerit aliquod punctum in ſuper-
                    <lb/>
                  ficie ſpeculi, </s>
                  <s xml:id="echoid-s5027" xml:space="preserve">tunc imaginem ipſius poſt dictam ſuperficie
                    <unsure/>
                  m videbit duplicatam, ſi
                    <lb/>
                  verò aſpexerit imaginem intra ſpeculum, </s>
                  <s xml:id="echoid-s5028" xml:space="preserve">tunc illud punctum videbit duplicatum,
                    <lb/>
                  huiuſmodi autem rei ratio pendet ab hijs quę ad Franciſcum Vimercatum ſcri-
                    <lb/>
                  pſi, quæ ſi memoria tenes, nullum tibi dubium remanebit. </s>
                  <s xml:id="echoid-s5029" xml:space="preserve">Nam ea tibi omnia
                    <lb/>
                  oſtendi.</s>
                </p>
                <p>
                  <s xml:id="echoid-s5030" xml:space="preserve">Dum verò dicis omnem proportionem rationalem diuidi poſſe duobus numeris
                    <lb/>
                  mediantibus in tres æquas partes, mihi ad memoriam reuocas id quod quidam Vitru
                    <lb/>
                  uij commentator aſſerit ſuper primum cap. noni lib. eiuſdem Authoris, ita dicens.</s>
                </p>
                <quote>
                  <s xml:id="echoid-s5031" xml:space="preserve">Benè eſſe poteſt vt diagonalis (quadrati ſcilicet) numerorum via reperiatur, ſed
                    <lb/>
                  fortaſſe intercedent fracta.</s>
                </quote>
                <p>
                  <s xml:id="echoid-s5032" xml:space="preserve">Miror te non memoria tenere quid ſint numeri rationales quidúe ſurdi,
                    <reg norm="neque" type="simple">neq;</reg>
                  con
                    <lb/>
                  ſideras, non ſolum non eſſe diuiſibilem in tres æquas partes omnem proportionem
                    <lb/>
                  rationabilem, ſed neque in duas, vt ſunt ſuperparticulares proportiones, necnon
                    <lb/>
                  aliæ innumeræ, ſed cum talia ſcribis te nimis parum verſatum in iſtis rebus oſtendis.</s>
                </p>
                <p>
                  <s xml:id="echoid-s5033" xml:space="preserve">Id verò quod tibi dicere volebam nudiustertius de Mercurio erat, quod nullo pa
                    <lb/>
                  cto confidendum eſt calculis qui fiunt de curſu Mercurij, eo quod eius ſitus nullo mo
                    <lb/>
                  do obſeruabilis eſt, nam ipſe nunquam nec vbiuis locorum orbis terrarum viſibilis
                    <lb/>
                  eſt altior .18. gradibus ſupra orizontem, ſed neque confidendum eſſet ſi
                    <reg norm="etiam" type="context">etiã</reg>
                  ipſum
                    <lb/>
                  videremus altum .20. gradibus, </s>
                  <s xml:id="echoid-s5034" xml:space="preserve">propterea quod magna refractio
                    <reg norm="radiorum" type="context">radiorũ</reg>
                  infra hos
                    <lb/>
                  gradus nos valde fallit, quæ quidem refractio, nec
                    <reg norm="vbique" type="simple">vbiq;</reg>
                  , nec omni tempore vnifor-
                    <lb/>
                  mis eſt, propter diformem ſeu inæqualem craſſiciem vaporum quæ continuò muta
                    <lb/>
                  tur. </s>
                  <s xml:id="echoid-s5035" xml:space="preserve">Imo multoties eum. videre putabimus ſupra orizontem, exiſtente ipſo ſub
                    <lb/>
                  orizonte.</s>
                </p>
              </div>
              <div xml:id="echoid-div777" type="letter" level="4" n="2">
                <head xml:id="echoid-head588" style="it" xml:space="preserve">Quod Ouidius tr anſcurrit à motu diurno, ad motum annuum
                  <lb/>
                prater rem.</head>
                <head xml:id="echoid-head589" xml:space="preserve">AD EVNDEM.</head>
                <p>
                  <s xml:id="echoid-s5036" xml:space="preserve">TVus etiam Ouidius ceſpitauit, cum pro itinere vnius diei efficiat, vt Phaeton à
                    <lb/>
                  patre edoctus ſit etiam de itinere annuali.</s>
                </p>
                <p>
                  <s xml:id="echoid-s5037" xml:space="preserve">Nam, quod Phaeton petat pro curſu vnius diei, clarè patet
                    <reg norm="ex" type="conjecture">ẽx</reg>
                  diuerſis locis, & pri-
                    <lb/>
                  mò vbi ita ſcribit Ouidius.</s>
                </p>
                <quote>
                  <s xml:id="echoid-s5038" xml:space="preserve">Currus petit ille paternos.
                    <lb/>
                  </s>
                  <s xml:id="echoid-s5039" xml:space="preserve">
                    <reg norm="Inque" type="simple">Inq;</reg>
                  diem alipedum ius & moderamen equorum.</s>
                </quote>
                <p>
                  <s xml:id="echoid-s5040" xml:space="preserve">Deinde vbi Pater ita loquitur.</s>
                </p>
                <quote>
                  <s xml:id="echoid-s5041" xml:space="preserve">Ardua prima via eſt, & qua vix
                    <reg norm="manem" type="context">manẽ</reg>
                    <unsure/>
                  recentes. </s>
                </quote>
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