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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                    <pb o="237" rhead="EPISTOLAE." n="249" file="0249" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0249"/>
                  trum epicycli conficit gra .36. min .13. ad rationem ſupradictam. </s>
                  <s xml:id="echoid-s2969" xml:space="preserve">Reſtat nunc no-
                    <lb/>
                  bis inuenire angulum
                    <var>.b.o.c.</var>
                  in centro
                    <reg norm="mundi" type="context">mũdi</reg>
                  inter duas lineas,
                    <var>b.o.</var>
                  et
                    <var>.c.o.</var>
                    <reg norm="quarum" type="context">quarũ</reg>
                  prior
                    <lb/>
                  eſt primæ ſtationis, altera eſt veri motus epicycli, quod facilè intelligemus per di-
                    <lb/>
                  ctam .49. lib. 1. Monteregij, cum duo latera
                    <var>.n.c.</var>
                  et
                    <var>.c.o.</var>
                  & angulus
                    <var>.n.c.o.</var>
                  ſint nobis no
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                  ta. </s>
                  <s xml:id="echoid-s2970" xml:space="preserve">Hoc autem fiet fingendo lineam
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                  perpendiculerem ad
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                  quæ tanquam ſi-
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                  nus anguli
                    <var>.n.c.h.</var>
                  erit partium .28986. talium qualium
                    <var>.n.c.</var>
                  eſſet partium .100000. &
                    <lb/>
                    <var>c.h.</var>
                  tanquam ſinus anguli
                    <var>.c.n.h.</var>
                  reſtantis ex vno recto, erit partium .95706. dicendo
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                  poſtea ſi
                    <var>.n.e.</var>
                  tanquam ſinus totalis partium .100000. dat nobis
                    <var>.n.h.</var>
                  partium .28986
                    <lb/>
                  quid dabit nobis diameter
                    <var>.n.c.</var>
                  tanquam partium .39. mi .30. inueniemus
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                  venire
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                  nobis ex partibus 11. mi .27. & idem faciendo de
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                  inueniemus quod veniet no-
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                  bis partium .37. mi .48. quibus ſubtractis extota
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                  quę eſt
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                  .60. mi .18. reliqua
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                  erit nobis
                    <var>.h.o.</var>
                  partium .22. min .30. capiendo poſtea radicem
                    <reg norm="quadratam" type="context">quadratã</reg>
                  ſummæ qua
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                  drati
                    <var>.n.h.</var>
                  cum quadrato
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                  veniet nobis
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                  partium .25. min .12. talium qualis
                    <var>.n.
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                    h.</var>
                  eſt partium .11. min .27. ſi igitur ad
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                  tanquam partium .25. min .12. reſpondet
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                    n.h.</var>
                  partium .11. minuti .27. linea
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                  ad
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                  tanquam partium 100000. reſpon
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                  debit part .45436. tanquam ſinus anguli
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                  qui angulus erit gra .27. minut .1. ſub
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                  tracto poſtea hoc angulo ab angulo
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                  graduum .40. minut .55. remanebit an
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                  gulus
                    <var>.n.o.i.</var>
                  graduum .13. minut .54. inter lineam contingentiæ, & lineam primæ
                    <lb/>
                  ſtationis in eiuſmodi ſitu. </s>
                  <s xml:id="echoid-s2971" xml:space="preserve">Et ideo Mars acceſſerit ad lineam
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                  veri motus epi-
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                  cycli. </s>
                  <s xml:id="echoid-s2972" xml:space="preserve">Sed quia linea
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                  contingentiæ, propter motum centri epicycli, in dictis die-
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                  bus .69. confecerit gradus .36. minut .13. ( præſuppoſita ſemper eadem di-
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                  ſtantia
                    <var>.o.c.</var>
                  quamuis nonnulla ſit differentia, quam nunc prætermittemus ) & Mars in
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                  dicto tempore retrogreſſus fuerit per dictum angulum gra .13. mi .54. quibus dedu-
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                  ctis, ex .36. & min .13. reſtabunt gra .22. min .19. itaque in diebus .69. </s>
                  <s xml:id="echoid-s2973" xml:space="preserve">Mars promo-
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                  tus fuerit a primo ſitu gra .22. min .19. aut circiter, prius quam retrogradatio eius in-
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                  cipiat eſſe appa-
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                  rens.</s>
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                  <s xml:id="echoid-s2974" xml:space="preserve">Nunc à prima
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                  ſtatione vſque ad
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                  veri motus
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                  epicycli ſunt gra
                    <num value="16">.
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                    16.</num>
                  min .51. ipſius
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                  epicycli, vt ſupra
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                    <reg norm="vidimus" type="simple">vidimꝰ</reg>
                  quos Mars
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                  tranſit in diebus
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                  36. aut circiter ad
                    <lb/>
                  rationem min .28.
                    <lb/>
                  in ſingulos dies,
                    <lb/>
                  quo tempore cen
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                  trum epicycli, in
                    <lb/>
                  tali diſtantia à
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                    tro</reg>
                  mundi confice
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                  ret gra .18. mi .54.
                    <lb/>
                  ad rationem min
                    <num value="31">.
                      <lb/>
                    31.</num>
                  cum dimidio
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                  in ſingulos dies,
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                    <reg norm="quibus" type="simple">quibꝰ</reg>
                  deductis ex
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                  gra .27. min .1. an- </s>
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