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-div558" type="section" level="3" n="16">
              <div xml:id="echoid-div559" type="letter" level="4" n="2">
                <pb o="291" rhead="EPISTOLAE." n="303" file="0303" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0303"/>
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              <div xml:id="echoid-div561" type="letter" level="4" n="3">
                <head xml:id="echoid-head428" style="it" xml:space="preserve">Quod incendium, ex reflexione radiorum ſolarium, non fiat in cen
                  <lb/>
                tro ſpeculi ſpharici, & aliquid contra Cardanum, &
                  <lb/>
                de moturadiorum ſolarium.</head>
                <head xml:id="echoid-head429" xml:space="preserve">AD EVNDEM.</head>
                <p>
                  <s xml:id="echoid-s3608" xml:space="preserve">ITerum tibi dico, quod radij illi ſolares, quià diuerſis punctis ipſius ſolaris corpo-
                    <lb/>
                  ris veniunt, tranſeuntes per centrum ſpeculi ſphærici concaui, quamuis à ſuper-
                    <lb/>
                  ficie ſpeculi ad centrum ipſum reflectantur, vt alíâs tibi dixi, nihilominus nullo mo
                    <lb/>
                  do poſſunt aliquod obiectum incendere duabus ex cauſis, quarum vna eſt, quia cum
                    <lb/>
                  Sol valde remotus ſit à nobis, valde etiam acutus generatur angulus coni radiorum
                    <lb/>
                  in centro ſpeculi, vnde à parua ſuperficie ipſius ſpeculi reflectuntur, </s>
                  <s xml:id="echoid-s3609" xml:space="preserve">quare pauciſſi-
                    <lb/>
                  mi radij ſunt qui reflectantur in ipſo centro, & propterea non ſufficiunt ad combu
                    <lb/>
                  ſtionem alicuius obiecti. </s>
                  <s xml:id="echoid-s3610" xml:space="preserve">Alia verò cauſa eſt, quod quamuis multi, & ſufficientes
                    <lb/>
                  radij fuiſſentad
                    <reg norm="comburendum" type="context context">cõburendũ</reg>
                  velociter quoduis obiectum. </s>
                  <s xml:id="echoid-s3611" xml:space="preserve">impoſſibile tamen omnino
                    <lb/>
                  eſset, vt aliquod obiectum comburerent, propterea quod cum radij incidentes de-
                    <lb/>
                  beant per centrum tranſire, obiectum combuſtibile, vt opacum, obſtaret ipſis radijs,
                    <lb/>
                  ne vlterius tranſirent, vnde nulla fieret reflexio, ſed etiam ſi dicti radij in centro re
                    <lb/>
                  flexi, ſufficerent ad combuſtionem, incidentes hoc magis eſſicerent. </s>
                  <s xml:id="echoid-s3612" xml:space="preserve">& ita abſque
                    <lb/>
                  vllo ſpeculo, omnia & in quolibet loco comburerentur, quod manifeſtè falſum eſt.
                    <lb/>
                  </s>
                  <s xml:id="echoid-s3613" xml:space="preserve">Deſine igitur mihi citate Lucillum Philalteum, qui in philoſophia mathematica
                    <lb/>
                  fuit omnium imperitiſſimus. </s>
                  <s xml:id="echoid-s3614" xml:space="preserve">Verum ſpeculum vſtorium illud eſt quod ab Alhazem
                    <lb/>
                  </s>
                  <s xml:id="echoid-s3615" xml:space="preserve">Deinde à Vitellìone deſcribitur.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3616" xml:space="preserve">Quod deinde verum ſit,
                    <reg norm="vmbram" type="context">vmbrã</reg>
                  vniuſcuiuſque corporis opaci à Sole productam
                    <lb/>
                  ſemper eſſe centum
                    <reg norm="nouemque" type="simple">nouemq́;</reg>
                  vicibus maiorem diametro eiuſdem corporis, nego.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3617" xml:space="preserve">Imaginemur
                    <var>.s.</var>
                  1. diametrum eſſe illius circuli, quo vltimi radij ſolares veniunt tan
                    <lb/>
                  gentes corpus cuius diameter ſit
                    <var>.c.e.</var>
                  et
                    <var>.a.i.</var>
                  ſit diameter alterius circuli eiuſdem cor-
                    <lb/>
                  poris ſolaris à quo vltimi radij veniunt tangentes corpus, cuius diameter ſit
                    <var>.f.g.</var>
                  in
                    <lb/>
                  eadem diſtantia, & eodem ſitu prioris corporis. </s>
                  <s xml:id="echoid-s3618" xml:space="preserve">Tunc conus vmbræ ipſius
                    <var>.f.g.</var>
                  ſit
                    <var>.f.
                      <lb/>
                    g.q.</var>
                  & ipſius
                    <var>.c.e.</var>
                  ſit
                    <var>.c.n.e.</var>
                  centrum autem ſolare ſit
                    <var>.o.</var>
                  conorum verò axes ſint
                    <var>.t.n.q</var>
                  .
                    <lb/>
                  </s>
                  <s xml:id="echoid-s3619" xml:space="preserve">tunc ex ſuppoſito
                    <var>.q.f.a</var>
                  :
                    <var>n.c.s</var>
                  :
                    <var>n.e.l</var>
                  : et
                    <var>.q.g.i.</var>
                  erunt omnes contigui corpori ſolari, vn-
                    <lb/>
                  de ex .17. tertij Eucli. anguli
                    <var>.o.a.q.</var>
                  et
                    <var>.o.s.n.</var>
                  erunt recti. </s>
                  <s xml:id="echoid-s3620" xml:space="preserve">protracta deinde cum fu erit
                    <lb/>
                    <var>a.s.</var>
                  habebimus angulos
                    <var>.u.a.s.</var>
                  et
                    <var>.u.s.a.</var>
                  minores duobus rectis. </s>
                  <s xml:id="echoid-s3621" xml:space="preserve">Quare
                    <var>.n.s.</var>
                  concurret
                    <lb/>
                    <figure xlink:label="fig-0303-01" xlink:href="fig-0303-01a" number="325">
                      <image file="0303-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0303-01"/>
                    </figure>
                  </s>
                </p>
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