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-div642" type="section" level="3" n="28">
              <div xml:id="echoid-div666" type="letter" level="4" n="8">
                <p>
                  <s xml:id="echoid-s4201" xml:space="preserve">
                    <pb o="347" rhead="EPISTOL AE." n="359" file="0359" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0359"/>
                  mine deſtitutæ
                    <reg norm="interuallumque" type="simple">interuallumq́;</reg>
                  tantummodò inter
                    <var>.y.x.</var>
                  illuminatum erit, ſed ſi in
                    <lb/>
                  loco
                    <var>.c.u.</var>
                  poſitum fuerit, </s>
                  <s xml:id="echoid-s4202" xml:space="preserve">tunc totum
                    <var>.c.u.</var>
                  illuminatum erit, ſed debili modo propter
                    <lb/>
                  detractionem factam à reflexione in ſuperficie corporis ſphærici, vt ſupra diximus.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4203" xml:space="preserve">Poſito deinde obiecto in loco
                    <var>.i.z.H.f.</var>
                  tunc partes
                    <var>.z.i.</var>
                  et
                    <var>.H.f.</var>
                  rectos Solis radios
                    <lb/>
                  habebunt cum aliquibus refractis, ſed
                    <var>.z.H.</var>
                  pauciſſimum habebit lumen, pro-
                    <lb/>
                  pter diſgregationem radiorum. </s>
                  <s xml:id="echoid-s4204" xml:space="preserve">Poſito poſtea ipſo obiecto in loco
                    <var>.t.l.r.s.</var>
                  tanto
                    <lb/>
                  minus lumen habebit pars
                    <var>.l.r.</var>
                  propter dictam
                    <reg norm="diſgregationem" type="context">diſgregationẽ</reg>
                  , ſeu
                    <reg norm="diſſipationem" type="context">diſſipationẽ</reg>
                  radio
                    <lb/>
                  rum, & ſic ſucceſſiuè quanto remotius poſitum fuerit ipſum obiectum, tanto minus
                    <lb/>
                  illuminabitur. </s>
                  <s xml:id="echoid-s4205" xml:space="preserve">vnde ita remotum poterit locari, ut nullus actus luminis in eo
                    <lb/>
                  videatur, de radijs ſcilicet, qui per ſphæram chryſtallinam tranſibunt, ſed videbi-
                    <lb/>
                  tur vmbra ipſius ſphęrę in obiecto propoſito, cum nullum actum illuminationis in
                    <lb/>
                  eo loco obiecti habeant radij tranſeuntes per dictam ſphęram. </s>
                  <s xml:id="echoid-s4206" xml:space="preserve">quapropter partes
                    <var>.
                      <lb/>
                    t.l.</var>
                  et
                    <var>.r.s.</var>
                  illuminatæ erunt à Sole, et
                    <var>.l.r.</var>
                  omnino lumine deſtituta.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4207" xml:space="preserve">Quòd vero tolerabilior ſit oculis radius reflexus Solis à ſuperſicie aquæ, quàm
                    <lb/>
                  à ſuperficie alicuius ſpeculi, oritur ab eo, quod ſupra diximus, hoc eſt, quod ma-
                    <lb/>
                  gna parsipſius luminis penetrat in aquam, & non totum reflectit, quod quidem non
                    <lb/>
                  accidit ſpeculis opacis.</s>
                </p>
              </div>
            </div>
            <div xml:id="echoid-div670" type="section" level="3" n="29">
              <div xml:id="echoid-div670" type="letter" level="4" n="1">
                <head xml:id="echoid-head511" xml:space="preserve">DE LONGITVDINE DVORVM LATERVM
                  <lb/>
                cuiuſuis trianguli ſupra tertium.</head>
                <head xml:id="echoid-head512" style="it" xml:space="preserve">Hieronymo Fenarolo.</head>
                <p>
                  <s xml:id="echoid-s4208" xml:space="preserve">
                    <emph style="sc">
                      <reg norm="QVod" type="conjecture">QVo'd</reg>
                    </emph>
                  quælibet duo latera continentia rectum angulum cuiuſuis triangu-
                    <lb/>
                  li orthogonij, longiora ſint tertio latere, per diametrum circuli in eo in-
                    <lb/>
                  ſcripti, ab alijs iam demonſtratum fuit. </s>
                  <s xml:id="echoid-s4209" xml:space="preserve">Sed quòd quælibet duo latera
                    <lb/>
                  cuiuſuis trianguli longiora ſint tertio per latus tetragonicum, quadrupli
                    <lb/>
                  producti cuiuſuis lineæ deſcendentis ab angulo contento à dictis duobus lateribus
                    <lb/>
                  ad oppoſitam partem circuli inſcripti, in partem extrinſecam ipſius lineæ, nullus
                    <lb/>
                  (quod ſciam) vnquam ſcripſit, vel animaduertit.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4210" xml:space="preserve">Sit exempli gratia triangulus
                    <var>.a.b.c.</var>
                  quem volueris, in quo deſcribatur circulus
                    <var>.
                      <lb/>
                    u.s.n.</var>
                  & puncta contingentiæ ſint eadem
                    <var>.u.s.n.</var>
                  à puncto vero
                    <var>.a.</var>
                  deſcendat linea
                    <var>.a.
                      <lb/>
                    i.e.</var>
                  quæ terminetur à circunferentia in puncto
                    <var>.e.</var>
                  ipſius circunferentiæ, vbi volue-
                    <lb/>
                  ris. </s>
                  <s xml:id="echoid-s4211" xml:space="preserve">Dico nunc latera
                    <var>.a.b.</var>
                  et
                    <var>.a.c.</var>
                  longiora eſſe latere
                    <var>.b.c.</var>
                  per latus
                    <reg norm="tetragonicum" type="context">tetragonicũ</reg>
                  qua-
                    <lb/>
                  drupli producti ipſius
                    <var>.a.e.</var>
                  in
                    <var>.a.i</var>
                  . </s>
                  <s xml:id="echoid-s4212" xml:space="preserve">Nam certi ſamus ex vltima parte penultimæ ter-
                    <lb/>
                  tij Eucli
                    <var>.n.c.</var>
                  et
                    <var>.s.c.</var>
                  æquales inuicem eſſe, & ſimiliter
                    <var>.b.s.</var>
                  et
                    <var>.b.u.</var>
                  vnde ex communi
                    <lb/>
                  conceptu dicta latera maiora erunt
                    <lb/>
                    <figure xlink:label="fig-0359-01" xlink:href="fig-0359-01a" number="394">
                      <image file="0359-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0359-01"/>
                    </figure>
                  ipſo
                    <var>.b.c.</var>
                  per
                    <var>.a.u.</var>
                  et
                    <var>.a.n.</var>
                  quæ duæ
                    <lb/>
                  partes ſunt inuicem æquales di-
                    <lb/>
                  cta ratione, & quadratum lineæ
                    <lb/>
                  æqualis aggregato earum, eſſet qua
                    <lb/>
                  druplum quadrato cuiuſuis earum
                    <lb/>
                  ex .4. ſecundi, ſed ex penultima ter
                    <lb/>
                  tij, productum
                    <var>.a.e.</var>
                  in
                    <var>.a.i.</var>
                  æquale eſt
                    <lb/>
                  quadrato ipſius
                    <var>.a.u.</var>
                  vel ipſius
                    <var>.a.n</var>
                  .</s>
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