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-div579" type="section" level="3" n="19">
              <div xml:id="echoid-div581" type="letter" level="4" n="3">
                <p>
                  <s xml:id="echoid-s3708" xml:space="preserve">
                    <pb o="300" rhead="IO. BAPT. BENED." n="312" file="0312" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0312"/>
                  dictum lumen conſpiceretur, quia non ſufficit extenſio luminis, cum eiuſdem inten
                    <lb/>
                  ſio ſit etiam neceſſaria. </s>
                  <s xml:id="echoid-s3709" xml:space="preserve">Sed id quoque tibi dico, quod etiam ſi dicta ſexageſima
                    <lb/>
                  pars totius luminis lunaris, eadem intenſione ſplendoris, & luminis Veneris, in tali
                    <lb/>
                  diſtantia trium graduum à Sole prædita eſſet, non eam
                    <reg norm="tamen" type="wordlist">tamẽ</reg>
                  videremus, ratione ob
                    <lb/>
                  liquitatis curuę, & ſphæricę ſuperficiei Lunæ, reſpectu noſtri, in huiuſmodi ſitu: </s>
                  <s xml:id="echoid-s3710" xml:space="preserve">id
                    <reg norm="qui" type="simple">ꝗ</reg>
                    <lb/>
                  tibi ita demonſtratum volo.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3711" xml:space="preserve">Pars ſuperficialis lunaris globi, quæ nos reſpicit ſit
                    <var>.a.p.u.</var>
                  quam accipere poſſu-
                    <lb/>
                  mus pro medietate ipſius ſuperficiei totalis, eo quod reſpectu noſtri viſus, inſenſibi
                    <lb/>
                  liter, ab ipſa medietate differat, pars autem à Sole viſa ſit
                    <var>.u.q.a.</var>
                  cogitemus etiam cir
                    <lb/>
                  culum
                    <var>.a.p.u.q.</var>
                  vnum eſſe ex maioribus ipſius globi, cuius ſuperficies
                    <reg norm="tranſeat" type="context">trãſeat</reg>
                  per ocu
                    <lb/>
                  lum vidontis, vnde pars eius
                    <var>.a.p.u.</var>
                  diuidet vmbram per æqualia, reliqua verò pars
                    <var>.
                      <lb/>
                    a.q.u.</var>
                  diuidet per æqualia lumen ipſius Lunæ à Sole receptum, ita quod pars illumi
                    <lb/>
                  nata, erit medietas
                    <var>.u.q.a.</var>
                  exceſſus verò, cum noſtro viſui incompræhenſibilis ſit, pro
                    <lb/>
                  nihilo reputetur, cuius cauſa eſt, maxima illa diſtantia, quæ inter Solem, & Lunam
                    <lb/>
                  reperitur, quamuis Sol maior ſit Luna multis millibus vicium, eo quod tunc inter So
                    <lb/>
                  lem, & Lunam reperiantur plus quam .570. diametri terræ.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3712" xml:space="preserve">Supponamus nunc Lunam remotam eſſe à loco ipſius
                    <reg norm="coniunctionis" type="context">cõiunctionis</reg>
                  cum Sole per
                    <lb/>
                  3. gradus. </s>
                  <s xml:id="echoid-s3713" xml:space="preserve">vnde
                    <reg norm="quemadmodum" type="wordlist">quẽadmodum</reg>
                  prius
                    <lb/>
                    <figure xlink:label="fig-0312-01" xlink:href="fig-0312-01a" number="334">
                      <image file="0312-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0312-01"/>
                    </figure>
                  lumen erat in gyro
                    <var>.a.q.u.</var>
                  nunc re-
                    <lb/>
                  periatur in gyro
                    <var>.x.q.t.</var>
                  ita quod
                    <var>.t.u.</var>
                    <lb/>
                  erit ſexageſima pars ipſius
                    <var>.a.p.u.</var>
                    <reg norm="quod" type="wordlist">qđ</reg>
                    <lb/>
                  à vero ſenſibiliter non diſcedit.
                    <lb/>
                  </s>
                  <s xml:id="echoid-s3714" xml:space="preserve">Imaginentur nunc duæ rectæ lineæ
                    <lb/>
                  ductæ ab oculo
                    <var>.d.</var>
                  ad puncta
                    <var>.t.</var>
                  et
                    <var>.u.</var>
                    <lb/>
                  verum tamen eſt quod linea
                    <var>.d.u.</var>
                  ſe-
                    <lb/>
                  cabit
                    <reg norm="arcum" type="context">arcũ</reg>
                    <var>.t.u.</var>
                  ſed ita propinqua
                    <reg norm="pum" type="context">pũ</reg>
                    <lb/>
                  cto
                    <var>.u.</var>
                  quod erit ei ferè contingens,
                    <lb/>
                  vnde abſque ſenſibili errore poſſu-
                    <lb/>
                  mus arcum
                    <var>.t.u.</var>
                  intelligere inter duas
                    <lb/>
                  lineas
                    <var>.d.t.</var>
                  et
                    <var>.d.u.</var>
                  quapropter tale lu-
                    <lb/>
                  men compræhendetur, ferè, ſub an-
                    <lb/>
                  gulo
                    <var>.t.d.u.</var>
                  quem quidem angulum
                    <lb/>
                  oportet nos videre, cuius magnitu-
                    <lb/>
                  dinis exiſtat, reſpectu totalis anguli
                    <lb/>
                    <var>a.d.u.</var>
                  protracta cum fuerit
                    <var>.d.a</var>
                  .</s>
                </p>
                <p>
                  <s xml:id="echoid-s3715" xml:space="preserve">Producatur primo
                    <var>.d.t.</var>
                  vſque ad
                    <lb/>
                  diametrum in puncto
                    <var>.i.</var>
                  deinde per
                    <lb/>
                  puncta
                    <var>.a.</var>
                  et
                    <var>.u.</var>
                  ducatur arcus
                    <var>.a.e.u.</var>
                  cir
                    <lb/>
                  ca
                    <var>.d.</var>
                    <reg norm="centrum" type="context">cẽtrum</reg>
                  , ad quem ducatur linea
                    <var>.
                      <lb/>
                    d.t.i.</var>
                  in puncto
                    <var>.e.</var>
                  ſed quia, cum dia-
                    <lb/>
                  meter
                    <var>.a.u.</var>
                  tam breuis ſit reſpectu di
                    <lb/>
                  ſtantiæ à terra, tempore interlunij,
                    <lb/>
                  vnde minor
                    <reg norm="centeſima" type="context">cẽteſima</reg>
                  parte ipſius di-
                    <lb/>
                  ſtantiæ exiſtit,
                    <reg norm="ſequitur" type="simple">ſequit̃</reg>
                  nos poſſe
                    <reg norm="abſque" type="simple">abſq;</reg>
                    <lb/>
                  ſenſibili errore cogitare, à puncto
                    <var>.d.</var>
                    <lb/>
                  ad quoduis punctum ipſius diametri
                    <lb/>
                  omnes lineas ad angulos rectos cum
                    <lb/>
                  ipſo diametro, & inſenſibilis inæqua­ </s>
                </p>
              </div>
            </div>
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