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-div662" type="letter" level="4" n="7">
                <p>
                  <s xml:id="echoid-s4183" xml:space="preserve">
                    <pb o="345" rhead="EPISTOL AE." n="357" file="0357" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0357"/>
                  puncti
                    <var>.l.</var>
                  clarum igitur nunc habes, quod in ſphærico concauo, ſeu conuexo, non
                    <lb/>
                  omnes radij reflexi conueniunt in vno,
                    <reg norm="eodemque" type="simple">eodemq́;</reg>
                  puncto catheti incidentiæ, quemad
                    <lb/>
                  modum in planis accidit, in quibus ſemper vnum, & idem punctum eſt ipſis commu
                    <lb/>
                  ne in ipſo incidentiæ catheto.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4184" xml:space="preserve">Non prætermittam etiam hunc alium breuiorem modum ſpeculandi
                    <reg norm="æqualita- tem" type="context">æqualita-
                      <lb/>
                    tẽ</reg>
                  depreſſionis imaginis ſub ſpeculo plano, ei quæ ſupra reperitur ipſius obiecti, in ca
                    <lb/>
                  theto incidentiæ, quemadmodum nu nc
                    <lb/>
                  vltimò diximus, hoc eſt quod cum
                    <lb/>
                    <figure xlink:label="fig-0357-01" xlink:href="fig-0357-01a" number="389">
                      <image file="0357-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0357-01"/>
                    </figure>
                  imago obiecti
                    <var>.l.</var>
                  reflexa à puncto
                    <var>.
                      <lb/>
                    x.</var>
                  reperiatur in linea
                    <var>.y.x.t.</var>
                  & ima-
                    <lb/>
                  go eiuſdem obiecti reflexa à pun-
                    <lb/>
                  cto
                    <var>.m.</var>
                  reperiatur in linea
                    <var>.z.m.t.</var>
                  &
                    <lb/>
                  iſtæ duæ lineę ſeinuicem ſecent in
                    <lb/>
                  puncto
                    <var>.t.</var>
                  ipſius catheti, exiſtente
                    <var>.
                      <lb/>
                    r.t.</var>
                  æquali
                    <var>.r.l.</var>
                  vt nunc vidimus, er-
                    <lb/>
                  go ſemper imago reflexa à ſpecu-
                    <lb/>
                  lo plano, nobis apparebit
                    <reg norm="in" type="wordlist">ĩ</reg>
                  ipſo ca
                    <lb/>
                  theto, tam vltra ſpeculum, quam ci
                    <lb/>
                  tra ipſum,
                    <reg norm="repertum" type="simple context">reꝑtũ</reg>
                  fuerit
                    <reg norm="ipsum" type="context">ipsũ</reg>
                    <reg norm="obiectum" type="context">obiectũ</reg>
                    <lb/>
                  quod nec Alhazem, nec Vitellio,
                    <lb/>
                  nec alius aliquis (quod ſciam) ad huc ſcientificè demonſtrauit. </s>
                  <s xml:id="echoid-s4185" xml:space="preserve">exempla enim vel ex
                    <lb/>
                  perientia non faciunt ſcire. </s>
                  <s xml:id="echoid-s4186" xml:space="preserve">Credo etiam te non dubitare quin duæ lineæ
                    <var>.y.x.</var>
                  et
                    <var>.z.
                      <lb/>
                    m.</var>
                  inuicem concurrant, cum anguli
                    <var>.t.x.m.</var>
                  et
                    <var>.t.m.x.</var>
                  minores ſint duobus rectis cum
                    <lb/>
                  æquales ſint angulis
                    <var>.l.x.m.</var>
                  et
                    <var>.l.m.x</var>
                  .</s>
                </p>
              </div>
              <div xml:id="echoid-div666" type="letter" level="4" n="8">
                <head xml:id="echoid-head509" style="it" xml:space="preserve">De rotunditate vmbræterræ in ecclipſibus Lunaribus.</head>
                <head xml:id="echoid-head510" xml:space="preserve">AD EVNDEM.</head>
                <p>
                  <s xml:id="echoid-s4187" xml:space="preserve">ROtunditas vmbræ in ecclipſi-
                    <lb/>
                    <figure xlink:label="fig-0357-02" xlink:href="fig-0357-02a" number="390">
                      <image file="0357-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0357-02"/>
                    </figure>
                  bus lunaribus oritur
                    <reg norm="tam" type="context">tã</reg>
                  à rotun
                    <lb/>
                  ditate maris,
                    <reg norm="quam" type="context">quã</reg>
                  terræ, & ſi terra eſ-
                    <lb/>
                  ſet
                    <reg norm="etiam" type="context">etiã</reg>
                  cuiuſuis alterius figurę,
                    <reg norm="quam" type="context">quã</reg>
                    <lb/>
                  ſphæricę, dummodo aqua impleret
                    <lb/>
                    <reg norm="locum" type="context">locũ</reg>
                  ſphęriceitatis à terra
                    <reg norm="derelictum" type="context">derelictũ</reg>
                  ,
                    <lb/>
                  nihilominus vmbra eſſet rotunda,
                    <lb/>
                  quę quidem ab aqua produceretur,
                    <lb/>
                    <reg norm="quanuis" type="context">quãuis</reg>
                  Alexander Piccolhomineus
                    <lb/>
                    <figure xlink:label="fig-0357-03" xlink:href="fig-0357-03a" number="391">
                      <image file="0357-03" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0357-03"/>
                    </figure>
                  aliter ſentiat in libro de magnitudi-
                    <lb/>
                  ne terrę, & aquæ.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4188" xml:space="preserve">
                    <reg norm="Sciendum" type="context context">Sciẽdũ</reg>
                  enim eſt, quod omne cor
                    <lb/>
                  pus in ſe habens
                    <reg norm="aliquantulum" type="context">aliquantulũ</reg>
                  opaci-
                    <lb/>
                  tatis, ſemper debilitat
                    <reg norm="radium" type="context">radiũ</reg>
                  lumino
                    <lb/>
                  ſum, &
                    <reg norm="tanto" type="context">tãto</reg>
                  magis,
                    <reg norm="quanto" type="context">quãto</reg>
                  magis in ip
                    <lb/>
                  ſo corpore radius penetrat,
                    <reg norm="etiam" type="context">etiã</reg>
                  & ſi
                    <lb/>
                  ad rectos incideret ipſe radius ſupra
                    <lb/>
                    <reg norm="ſuperficiem" type="context">ſuperficiẽ</reg>
                    <reg norm="ipſius" type="simple">ipſiꝰ</reg>
                  corporis. </s>
                  <s xml:id="echoid-s4189" xml:space="preserve">
                    <reg norm="Exempli" type="context">Exẽpli</reg>
                  gra
                    <lb/>
                  tia, eſto
                    <var>.q.p.</var>
                  corpus a
                    <reg norm="queum" type="context">queũ</reg>
                  , cuius pro
                    <lb/>
                  funditas diuidatur in partibus
                    <var>.d.K</var>
                  :
                    <lb/>
                    <var>K.s</var>
                  : et
                    <var>.s.f.</var>
                  à puncto verò lucido
                    <var>.b.</var>
                  </s>
                </p>
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