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-div7" type="body" level="1" n="1">
          <div xml:id="echoid-div477" type="chapter" level="2" n="6">
            <div xml:id="echoid-div512" type="section" level="3" n="7">
              <div xml:id="echoid-div513" type="letter" level="4" n="2">
                <pb o="261" rhead="EPISTOL AE." n="273" file="0273" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0273"/>
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              <div xml:id="echoid-div515" type="letter" level="4" n="3">
                <head xml:id="echoid-head390" style="it" xml:space="preserve">Decognitione latitudinum stellarum.</head>
                <head xml:id="echoid-head391" xml:space="preserve">AD EVNDEM.</head>
                <p>
                  <s xml:id="echoid-s3273" xml:space="preserve">AD cognoſcendam latitudinem ſtellæ,
                    <reg norm="eiusque" type="simple">eiusq́</reg>
                  declinationem, Monteregius in
                    <lb/>
                  10. propoſitione .8. li. </s>
                  <s xml:id="echoid-s3274" xml:space="preserve">Almageſti
                    <reg norm="methodum" type="context">methodũ</reg>
                  ſatis docuit, ſed ſi alia aliqua metho
                    <lb/>
                  do hoc idem cognoſcere voluerimus, oportebit nos prius altitudinem poli cogno-
                    <lb/>
                  ſcere, deinde altitudinem meridianam ipſius ſtellæ, nec non horam,
                    <reg norm="quando" type="context">quãdo</reg>
                  ipſa ſtel
                    <lb/>
                  la in meridiano ſupra terram reperitur, qua hora mediante, illicò cognoſcemus pun
                    <lb/>
                  ctum ecclipticæà meridiano interſecto, eo tempore, quo ſtella cœlum mediat ſu-
                    <lb/>
                  pra terram. </s>
                  <s xml:id="echoid-s3275" xml:space="preserve">Et quia ex cognita altitudine poli, illico cognoſcitur altitudo æqua-
                    <lb/>
                  toris, cuius altitudinis differentia ab altitudine ſtellæ eſt declinatio ipſius ſtellæ, ha-
                    <lb/>
                  bebimus ideo eius declinationem cognitam; </s>
                  <s xml:id="echoid-s3276" xml:space="preserve">qua mediante ad
                    <reg norm="cognoſcendum" type="context">cognoſcendũ</reg>
                  etiam
                    <lb/>
                  latitudinem ita faciemus.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3277" xml:space="preserve">Sit exempli gratia
                    <var>.p.o.u.</var>
                  meridianus
                    <var>.u.a.</var>
                  verò æquator
                    <var>.e.a.</var>
                  autem eccliptica, &
                    <lb/>
                  o. centrum aſtri
                    <var>.u.o.</var>
                  verò eius declinatio ab æquatore, et
                    <var>.e.a.</var>
                  arcus ęcclipticæ inter
                    <lb/>
                  æquatorem, & meridianum, hoc eſt minor quarta, et
                    <var>.a.u.</var>
                  aſcenſio recta ipſius arcus,
                    <lb/>
                  et
                    <var>.u.e.</var>
                  ſit declinatio puncti
                    <var>.e.</var>
                  ęcclipticę ab æquatore,
                    <reg norm="reſiduum" type="context">reſiduũ</reg>
                  vero declinationis ſtel-
                    <lb/>
                  lę ſit
                    <var>.o.e.</var>
                  quæ
                    <reg norm="omnia" type="wordlist">oĩa</reg>
                  nobis cognita erunt,
                    <reg norm="ſitque" type="simple">ſitq́;</reg>
                    <var>.t.</var>
                  polus ęcclipticus, à quo per
                    <var>.o.</var>
                  vſque ad
                    <lb/>
                  ęcclipticam tranſeat quarta
                    <var>.t.i.</var>
                  in qua quęrendus erit arcus
                    <var>.o.i.</var>
                  hoc modo.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3278" xml:space="preserve">Primum arcus
                    <var>.o.u</var>
                  :
                    <var>e.u</var>
                  :
                    <var>e.o</var>
                  :
                    <var>a.e</var>
                  : et
                    <var>.a.u.</var>
                  nobis cogniti ſunt, cum angulo
                    <var>.a.</var>
                  declinatio
                    <lb/>
                  nis ęclipticę, & cum angulo
                    <var>.u.</var>
                  recto, vnde ex .4. primi Copernici, cognoſcemus angu
                    <lb/>
                  lum
                    <var>.a.e.u.</var>
                  collateralem, & eius
                    <var>.o.e.i</var>
                  . </s>
                  <s xml:id="echoid-s3279" xml:space="preserve">quare in triangulo
                    <var>.o.e.i.</var>
                  cognoſcemus
                    <reg norm="angulum" type="context">angulũ</reg>
                    <lb/>
                  e. et deinde
                    <var>.i.</var>
                  vt
                    <reg norm="rectum" type="context">rectũ</reg>
                  , & latus
                    <var>.o.e.</var>
                  ergò ex
                    <reg norm="eadem" type="context">eadẽ</reg>
                  .4. cognoſcemus
                    <reg norm="arcum" type="context">arcũ</reg>
                    <var>.o.i.</var>
                  quæſitum,
                    <lb/>
                  & ſimiliter arcum
                    <var>.e.i.</var>
                  qui coniunctus vel
                    <reg norm="demptus" type="context">dẽptus</reg>
                  ab
                    <var>.a.e.</var>
                  tribuet nobis longitudinem
                    <lb/>
                  ſtellę, ſed quia huiuſmodi operatio in paruis triangulis valde fallit. </s>
                  <s xml:id="echoid-s3280" xml:space="preserve">Ideo tibi ſua-
                    <lb/>
                  deo alia methodo, hoc facere, hoc eſt inuenire angulum
                    <var>.o.</var>
                  trianguli
                    <var>.t.p.o.</var>
                  cuius duo
                    <lb/>
                  latera
                    <var>.t.p.</var>
                  et
                    <var>.p.o.</var>
                  cognita nobis ſunt, cum angulo
                    <var>.p</var>
                  . </s>
                  <s xml:id="echoid-s3281" xml:space="preserve">Nam
                    <var>.o.p.</var>
                  eſt complementum de
                    <lb/>
                  clinationis ſtellæ, et
                    <var>.p.t.</var>
                  eſt arcus coluri ſolſtitiorum inter duos polos, & angulus
                    <var>.p.</var>
                    <lb/>
                  reſiduum ex recto
                    <var>.t.p.a.</var>
                  duorum colurum dempto angulo. a,
                    <var>p.u.</var>
                  cognito aſcenſionis
                    <lb/>
                  recte, vnde angulus
                    <var>.u.o.s.</var>
                  vt contrapoſitus cognitus remanet. </s>
                  <s xml:id="echoid-s3282" xml:space="preserve">angulus verò
                    <var>.u.</var>
                  rectus
                    <lb/>
                  eſt, & arcus
                    <var>.o.u.</var>
                  cognitus, </s>
                  <s xml:id="echoid-s3283" xml:space="preserve">quare cognitus
                    <lb/>
                  nobis erit arcus
                    <var>.u.s.</var>
                  & angulus
                    <var>.u.s.o.</var>
                  vnde
                    <lb/>
                    <figure xlink:label="fig-0273-01" xlink:href="fig-0273-01a" number="301">
                      <image file="0273-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0273-01"/>
                    </figure>
                  arcus
                    <var>.a.s.</var>
                  nobis cognitus remanebit
                    <reg norm="cum" type="context">cũ</reg>
                  an-
                    <lb/>
                  gulo
                    <var>.a.s.i.</var>
                  reſiduo ex duobus rectis. </s>
                  <s xml:id="echoid-s3284" xml:space="preserve">Et quia
                    <lb/>
                  etiam angulus
                    <var>.s.a.i.</var>
                  cognitus eſt, cum ſit an
                    <lb/>
                  gulus maximę declinationis Zodiaci ab
                    <lb/>
                  æquatore. </s>
                  <s xml:id="echoid-s3285" xml:space="preserve">Ideo in triangulo
                    <var>.a.s.i.</var>
                  cuius
                    <lb/>
                  duo anguli
                    <var>.a.</var>
                  et
                    <var>.s.</var>
                  cum latere
                    <var>.a.s.</var>
                  dantur, fa
                    <lb/>
                  cilè inueniemus arcum
                    <var>.s.i.</var>
                    <reg norm="cum" type="context">cũ</reg>
                  arcu
                    <var>.a.i.</var>
                  ſed
                    <lb/>
                    <var>a.i.</var>
                  erit longitudinis ſtellæ dempto poſtea
                    <var>.
                      <lb/>
                    s.i.</var>
                  ex
                    <var>.s.o.</var>
                  iam inuento habebimus arcum
                    <var>.i.
                      <lb/>
                    o.</var>
                  latitudinis ipſius ſtellæ.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3286" xml:space="preserve">Hæc autem tibi ſcribo non vt ipſis vta-
                    <lb/>
                  ris, ſed potius vt tibi morem
                    <reg norm="geram" type="context">gerã</reg>
                  , cum bre
                    <lb/>
                  uiſſima methodus ſit illa,
                    <reg norm="quam" type="context">quã</reg>
                  Monteregius
                    <lb/>
                  ſcripſit
                    <reg norm="in" type="wordlist">ĩ</reg>
                  .10.
                    <reg norm="propoſitione" type="simple">ꝓpoſitione</reg>
                  .8. li. in Almageſt.</s>
                </p>
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