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]

Table of handwritten notes

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          <div xml:id="echoid-div477" type="chapter" level="2" n="6">
            <div xml:id="echoid-div642" type="section" level="3" n="28">
              <div xml:id="echoid-div650" type="letter" level="4" n="3">
                <p>
                  <s xml:id="echoid-s4091" xml:space="preserve">
                    <pb o="337" rhead="EPISTOLAE." n="349" file="0349" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0349"/>
                  oculorum clauderetur, nihilominus cum reliquo obiectum vidiſſemus in
                    <reg norm="eodem" type="context">eodẽ</reg>
                  ipſo
                    <lb/>
                  loco
                    <var>.d.</var>
                  & non in alio ex ſuperius dictis rationibus.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4092" xml:space="preserve">Et ſi ſtantibus ijs terminis volueremus pupillam oculi
                    <var>.u.</var>
                  verſus aliam
                    <var>.a.</var>
                  ad aſpi-
                    <lb/>
                  ciendum punctum
                    <var>.n.</var>
                  in ſuperficie
                    <var>.g.h.</var>
                  ipſius ſpeculi, hoc eſt ſi fecerimus quod axes
                    <lb/>
                  viſuales ſeinuicem ſecarent in ipſo puncto
                    <var>.n</var>
                  . </s>
                  <s xml:id="echoid-s4093" xml:space="preserve">tunc videremur nobis videre duas
                    <lb/>
                  imagines ipſius obiecti
                    <var>.b.</var>
                  intra ſpeculum, eo quod obiectum, propter hoc non
                    <lb/>
                  ceſſaret reflectere ad oculos ab ipſis punctis
                    <var>.n.</var>
                  et
                    <var>.t.</var>
                  quapropter recipiendo ra-
                    <lb/>
                  dium
                    <var>.t.u.</var>
                  in ſitu axis oculi
                    <var>.u.</var>
                  & radium
                    <var>.n.a.</var>
                  in ſitu axis oculi
                    <var>.a.</var>
                  hi axes ex neceſſitate
                    <lb/>
                  (vt probauimus ) ſeinuicem ſecant in puncto
                    <var>.d.</var>
                  vnde vnam tantummodo imaginem
                    <lb/>
                  ipſius obiecti nobis apparebit.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4094" xml:space="preserve">Ex his igitur omnibus potes facilè videre omnem imaginem, cuiuſuis obiecti, re-
                    <lb/>
                  flexam à ſpeculo, reperiri in ipſo catheto incidentiæ, cum ipſe ſemper ſit communis
                    <lb/>
                  ſectio duarum ſuperficierum reflexionis, in quo catheto concurrunt ipſæ axes vi-
                    <lb/>
                  ſuales.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4095" xml:space="preserve">Exijſdem etiam dictis rationibus facile compræhendere poteris, vnde fiat, vt vi-
                    <lb/>
                  deamus imaginem reflexam à ſpeculis ſphęricis concauis citra
                    <reg norm="ipſorum" type="context">ipſorũ</reg>
                  ſuperficiem, &
                    <lb/>
                  non vltra. </s>
                  <s xml:id="echoid-s4096" xml:space="preserve">Quod
                    <reg norm="nunquam" type="context">nunquã</reg>
                  euenit, niſi quando
                    <reg norm="punctum" type="context">punctũ</reg>
                    <var>.d.</var>
                  interſectionis
                    <reg norm="ipſorum" type="context">ipſorũ</reg>
                    <reg norm="radiorum" type="context">radiorũ</reg>
                    <lb/>
                  viſualium (quod alio in loco non fit, niſi in catheto incidentiæ hoc eſt in communi
                    <lb/>
                  ſectione duarum ſuperficierum reflexionis. </s>
                  <s xml:id="echoid-s4097" xml:space="preserve">Dato quod obiectum non ſit in vna ea-
                    <lb/>
                  demq́ue ſuperficie, in qua reperti fuerint axes viſuales, hoc eſt dato,
                    <reg norm="quod" type="simple">ꝙ</reg>
                  ambo axes
                    <lb/>
                  viſuales non ſint in vna
                    <reg norm="eademque" type="simple">eademq́;</reg>
                  ſuperficie reflexionis) reperitur citra & non vltra ſu
                    <lb/>
                  perficiem ipſius ſpeculi.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4098" xml:space="preserve">Ad cuius rei euidentiam non
                    <reg norm="prætermittam" type="context">prætermittã</reg>
                  dicere, quod cum debeant ſemper ſu-
                    <lb/>
                  perficies reflexionum perpendiculares eſſe, velad rectos ſecare ſuperficiem ipſius
                    <lb/>
                  ſpeculi, ipſarum communes ſectiones cum ſuperficie ſpeculi ſphęrici, ſemper erunt
                    <lb/>
                  circunferentiæ magnorum circulorum illius ſphæræ, cuius portio eſt ſpeculum
                    <lb/>
                  propoſitum, vt etiam Vitellio affirmat in prima ſexti libri. </s>
                  <s xml:id="echoid-s4099" xml:space="preserve">Vnde vnuſquiſque ca-
                    <lb/>
                  thetus incidentiæ tranſibit per centrum ſpeculi, cum ipſe ſit communis ſectio dua-
                    <lb/>
                  rum ſuperficierum reflexionis, </s>
                  <s xml:id="echoid-s4100" xml:space="preserve">quare in ipſo catheto erit punctum interſectionis ip
                    <lb/>
                  ſorum axium viſualium ex neceſſitate, vt videbimus, ſi vnam tantummodo
                    <reg norm="imaginem" type="context">imaginẽ</reg>
                    <lb/>
                  obiecti nobis videremur videre.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4101" xml:space="preserve">Exempli gratia, ſint duæ ſuperficies reflexionis ſpeculi ſphærici concaui
                    <var>.b.n.c.a.</var>
                    <lb/>
                  et
                    <var>.b.t.c.u.</var>
                    <reg norm="obiectumque" type="simple">obiectumq́;</reg>
                  ſit
                    <var>.b.</var>
                  oculi autem ſint
                    <var>.a.u.</var>
                  punctum verò ſuperficiei ſpeculi, à
                    <lb/>
                  quo obiectum emittit reflexionem ſuę
                    <lb/>
                  imaginis ad oculum
                    <var>.a.</var>
                  ſit
                    <var>.n.</var>
                    <reg norm="punctum" type="context">pũctum</reg>
                  au-
                    <lb/>
                    <figure xlink:label="fig-0349-01" xlink:href="fig-0349-01a" number="376">
                      <image file="0349-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0349-01"/>
                    </figure>
                    <figure xlink:label="fig-0349-02" xlink:href="fig-0349-02a" number="377">
                      <image file="0349-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0349-02"/>
                    </figure>
                  tem à quo eandem reflectit oculo
                    <var>.u.</var>
                  ſit
                    <lb/>
                  t. communis autem ſectio harum dua-
                    <lb/>
                  rum ſuperficierum ſit
                    <var>.b.c.</var>
                  ſed
                    <var>.x.</var>
                    <reg norm="centrum" type="context">centrũ</reg>
                    <lb/>
                  ſit ſpeculi, radius verò incidentię ſuper
                    <lb/>
                  ficiei
                    <var>.b.n.c.</var>
                  erit
                    <var>.b.n.</var>
                  cuius reflexus ſit
                    <var>.n.
                      <lb/>
                    a.</var>
                  radij autem alterius ſuperficiei erunt
                    <lb/>
                    <var>b.t.</var>
                  et
                    <var>.t.u</var>
                  . </s>
                  <s xml:id="echoid-s4102" xml:space="preserve">Imaginemur nunc duos ſemi
                    <lb/>
                  diametros
                    <var>.x.n.</var>
                  et
                    <var>.x.t.</var>
                  quæ angulos
                    <var>.b.n.
                      <lb/>
                    a.</var>
                  et
                    <var>.b.t.u.</var>
                  per æqualia diuidant ex ſup-
                    <lb/>
                  poſito.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4103" xml:space="preserve">Nunc ijs ſuppoſitis, ſi vnam tantum-
                    <lb/>
                  modo obiecti imaginem videbimus, </s>
                </p>
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