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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249237EPISTOLAE. trum epicycli conficit gra .36. min .13. ad rationem ſupradictam. Reſtat nunc no-
bis inuenire angulum .b.o.c. in centro mundi inter duas lineas, b.o. et .c.o. quarum prior
eſt primæ ſtationis, altera eſt veri motus epicycli, quod facilè intelligemus per di-
ctam .49. lib. 1. Monteregij, cum duo latera .n.c. et .c.o. & angulus .n.c.o. ſint nobis no
ta.
Hoc autem fiet fingendo lineam .n.h. perpendiculerem ad .o.c. quæ tanquam ſi-
nus anguli .n.c.h. erit partium .28986. talium qualium .n.c. eſſet partium .100000. &
c.h. tanquam ſinus anguli .c.n.h. reſtantis ex vno recto, erit partium .95706. dicendo
poſtea ſi .n.e. tanquam ſinus totalis partium .100000. dat nobis .n.h. partium .28986
quid dabit nobis diameter .n.c. tanquam partium .39. mi .30. inueniemus .n.h. venire
nobis ex partibus 11. mi .27. & idem faciendo de .c.h. inueniemus quod veniet no-
bis partium .37. mi .48. quibus ſubtractis extota .c.o. quę eſt partium .60. mi .18. reliqua
erit nobis .h.o. partium .22. min .30. capiendo poſtea radicem quadratam ſummæ qua
drati .n.h. cum quadrato .h.o. veniet nobis .n.o. partium .25. min .12. talium qualis .n.
h.
eſt partium .11. min .27. ſi igitur ad .o.n. tanquam partium .25. min .12. reſpondet .
n.h.
partium .11. minuti .27. linea .n.h. ad .o.n. tanquam partium 100000. reſpon
debit part .45436. tanquam ſinus anguli .n.o.h. qui angulus erit gra .27. minut .1. ſub
tracto poſtea hoc angulo ab angulo .c.o.i. graduum .40. minut .55. remanebit an
gulus .n.o.i. graduum .13. minut .54. inter lineam contingentiæ, & lineam primæ
ſtationis in eiuſmodi ſitu.
Et ideo Mars acceſſerit ad lineam .o.c. veri motus epi-
cycli.
Sed quia linea .o.i. contingentiæ, propter motum centri epicycli, in dictis die-
bus .69. confecerit gradus .36. minut .13. ( præſuppoſita ſemper eadem di-
ſtantia .o.c. quamuis nonnulla ſit differentia, quam nunc prætermittemus ) & Mars in
dicto tempore retrogreſſus fuerit per dictum angulum gra .13. mi .54. quibus dedu-
ctis, ex .36. & min .13. reſtabunt gra .22. min .19. itaque in diebus .69.
Mars promo-
tus fuerit a primo ſitu gra .22. min .19. aut circiter, prius quam retrogradatio eius in-
cipiat eſſe appa-
rens.
290[Figure 290]
Nunc à prima
lineam veri motus
epicycli ſunt gra .
16.
min .51. ipſius
epicycli, vt ſupra
vidimus quos Mars
tranſit in diebus
rationem min .28.
in ſingulos dies,
quo tempore cen
trum epicycli, in
tali diſtantia à cen-
tro
mundi confice
ret gra .18. mi .54.
31.
cum dimidio
in ſingulos dies,
quibus deductis ex
gra .27. min .1. an-