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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page |< < (343) of 445 > >|
EPISTOL AE.
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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-div660" type="letter" level="4" n="6">
                <p>
                  <s xml:id="echoid-s4162" xml:space="preserve">
                    <pb o="343" rhead="EPISTOL AE." n="355" file="0355" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0355"/>
                  gis erit maior proportio ipſius
                    <var>.g.u.</var>
                  ad
                    <var>.u.e.</var>
                    <lb/>
                    <anchor type="figure" xlink:label="fig-0355-01a" xlink:href="fig-0355-01"/>
                  quam ipſius
                    <var>.g.r.</var>
                  ad
                    <var>.r.e.</var>
                  ergo non æqualis,
                    <lb/>
                  quapropter impoſſibile eſt
                    <var>.u.e.</var>
                  eſſe radium
                    <lb/>
                  reflexum incidentis radij
                    <var>.g.u</var>
                  . </s>
                  <s xml:id="echoid-s4163" xml:space="preserve">Vnde ſequi
                    <lb/>
                  tur concurſum radiorum reflexorum à ſpe-
                    <lb/>
                  culo ſphærico concauo non eſſe in vno, &
                    <lb/>
                  e
                    <unsure/>
                  odem puncto ipſius catheti incidentiæ,
                    <lb/>
                  quando à ſitu non æquidiſtanti ab ipſo ca-
                    <lb/>
                  theto
                    <reg norm="reflectuntur" type="context">reflectũtur</reg>
                  , ex hac ſpeculatione
                    <reg norm="etiam" type="context">etiã</reg>
                    <lb/>
                  videre licet, verum eſſe id quod in .3. Epiſto
                    <lb/>
                  la tibi ſcripſi nempe, quod quotieſcunque
                    <lb/>
                  axes viſuales, vel radij reflexi, in vna ea-
                    <lb/>
                    <reg norm="demque" type="simple">demq́</reg>
                  ſuperficie reflexionis fuerint, </s>
                  <s xml:id="echoid-s4164" xml:space="preserve">tunc
                    <lb/>
                  imago obiecti nullo modo videbitur in ca-
                    <lb/>
                  theto incidentiæ, in ſpeculo ſphærico con-
                    <lb/>
                  cauo.</s>
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                  <figure xlink:label="fig-0355-01" xlink:href="fig-0355-01a">
                    <image file="0355-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0355-01"/>
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              <div xml:id="echoid-div662" type="letter" level="4" n="7">
                <head xml:id="echoid-head507" style="it" xml:space="preserve">Alterius dubit ationis ſolutio.</head>
                <head xml:id="echoid-head508" xml:space="preserve">AD EVNDEM.</head>
                <p>
                  <s xml:id="echoid-s4165" xml:space="preserve">NOn abſque ratione dubitas, vtrum etiam in ſphæricis ſpeculis conuexis idem
                    <lb/>
                  accidat, hoc eſt, an radij reflexi à punctis inęqualis diſtantiæ à catheto inciden
                    <lb/>
                  tiæ conueniant inuicem in eodem catheto.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4166" xml:space="preserve">Ad quod reſpondeo, non concurrere in dicto catheto, ſed extra ipſum, & ſimi-
                    <lb/>
                  liter extra ipſum vide bitur imago.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4167" xml:space="preserve">Pro cuius rei ratione, imaginemur ſuperficiem reflexionis alicuius ſpeculi ſphæ-
                    <lb/>
                  rici conuexi
                    <var>.b.d.h.g.</var>
                  cuius communis ſectio cum ſuperficie ſphærica ſit linea
                    <lb/>
                  circularis
                    <var>.d.e.h.</var>
                  et
                    <var>.o.</var>
                  eius
                    <reg norm="centrum" type="context">cẽtrum</reg>
                  , à quo protrahatur
                    <var>.g.b.</var>
                  indeterminata, et
                    <var>.o.g.</var>
                  ſit ſe
                    <lb/>
                  midiameter circuli
                    <var>.d.g.h.</var>
                  et
                    <var>.o.c.</var>
                  ſit plus medietate ipſius
                    <var>.o.g.</var>
                    <reg norm="accipiaturque" type="simple">accipiaturq́;</reg>
                  linea
                    <var>.e.c.</var>
                    <lb/>
                  minor ipſa
                    <var>.o.c.</var>
                  ſed maior ipſa
                    <var>.c.g.</var>
                    <lb/>
                    <anchor type="figure" xlink:label="fig-0355-02a" xlink:href="fig-0355-02"/>
                  quod difficile non erit, locando im
                    <lb/>
                  mobilem pedem circini in puncto
                    <var>.
                      <lb/>
                    c.</var>
                  aperiendo ipſum aliquantulum
                    <lb/>
                  plus quam
                    <var>.c.g.</var>
                  ſed minus quam
                    <var>.c.
                      <lb/>
                    o.</var>
                  ſignando circunferentiam
                    <var>.d.e.h.</var>
                    <lb/>
                  in puncto
                    <var>.e.</var>
                  quod ex .7. tertij poſſi-
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                  bile eſt, protrahatur poſtea
                    <var>.o.e.f.</var>
                    <lb/>
                  indeterminatè. </s>
                  <s xml:id="echoid-s4168" xml:space="preserve">Facicmus deinde
                    <lb/>
                  angulum
                    <var>.f.e.b.</var>
                  æqualem angulo
                    <var>.o.
                      <lb/>
                    e.c.</var>
                  protracta poſtea cum fuerit
                    <var>.c.
                      <lb/>
                    e.K.</var>
                  indeterminatè,
                    <reg norm="habebimus" type="simple">habebimꝰ</reg>
                  duos
                    <lb/>
                  angulos
                    <var>.b.e.f.</var>
                  et
                    <var>.f.e.K.</var>
                  æquales in-
                    <lb/>
                  uicem mediante .15. primi, ita
                    <reg norm="quod" type="wordlist">qđ</reg>
                  ſi
                    <lb/>
                  radius incidens veniet à puncto
                    <var>.b.</var>
                    <lb/>
                  ad
                    <var>.e.</var>
                  reflexus erit
                    <var>.e.K.</var>
                  qui quidem </s>
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