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]
Text
Text Image
Image
XML
Thumbnail overview
Document information
None
Concordance
Notes
Handwritten
Figures
Content
Thumbnails
page
|<
<
(236)
of 445
>
>|
<
echo
version
="
1.0
">
<
text
type
="
book
"
xml:lang
="
la
">
<
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-div495
"
type
="
section
"
level
="
3
"
n
="
5
">
<
div
xml:id
="
echoid-div495
"
type
="
letter
"
level
="
4
"
n
="
1
">
<
p
>
<
s
xml:id
="
echoid-s2951
"
xml:space
="
preserve
">
<
pb
o
="
236
"
rhead
="
IO. BAPT. BENED.
"
n
="
248
"
file
="
0248
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0248
"/>
tali ſitu epicycli ſit baſis vnius trianguli orthogonij, cuius vnum ex illis duobus late-
<
lb
/>
ribus eſt ſemidiameter eccentrici partium .60. pręcisè, aliud eſt interuallum eccen-
<
lb
/>
tricitatis partium .6. eiuſmodi. </
s
>
<
s
xml:id
="
echoid-s2952
"
xml:space
="
preserve
">Angulus ergo
<
var
>.i.o.c.</
var
>
vt dixi, erit partium .40. minu
<
num
value
="
55
">.
<
lb
/>
55.</
num
>
qui angulus continuò variatur ſecundum ſitum epicycli. </
s
>
<
s
xml:id
="
echoid-s2953
"
xml:space
="
preserve
">& cum centrum
<
lb
/>
eius eſt in auge eccentrici. eſt minimus
<
reg
norm
="
quam
"
type
="
context
">quã</
reg
>
eſſe poſſit. </
s
>
<
s
xml:id
="
echoid-s2954
"
xml:space
="
preserve
">
<
reg
norm
="
eſtque
"
type
="
simple
">eſtq́;</
reg
>
tantum grad .36. min
<
num
value
="
46
">.
<
lb
/>
46.</
num
>
& in oppoſito ipſius augis eſt grad .47. min .1. maximus quam alibi vnquam ſit,
<
lb
/>
& ſic continuò variatur, ſecundum ſitum, quem habet epicyclus in eccentrico. </
s
>
<
s
xml:id
="
echoid-s2955
"
xml:space
="
preserve
">Qui
<
lb
/>
quidem angulus inuenitur per doctrinam .27. et .28. libri primi Monteregij de trian
<
lb
/>
gulis. </
s
>
<
s
xml:id
="
echoid-s2956
"
xml:space
="
preserve
">Nam triangulus
<
var
>.c.i.o.</
var
>
eſt ſemper rectangulus in puncto
<
var
>.i.</
var
>
& latus
<
var
>.c.i.</
var
>
reſpectu
<
lb
/>
ſemidiametri eſt datum. </
s
>
<
s
xml:id
="
echoid-s2957
"
xml:space
="
preserve
">Quod
<
var
>.c.i.</
var
>
erit veluti partium .39. cum dimidia, et dictum
<
lb
/>
interuallum
<
var
>.o.c.</
var
>
veluti pat
<
unsure
/>
cium .60. min .18. & quia datur nobis etiam eccentricitas
<
lb
/>
veluti partium .60. talium, & cum
<
var
>.c.o.</
var
>
ſit linea veri motus epicycli, & latus ſimiliter
<
lb
/>
vnius trian guli, cuius duo latera ſunt ſupradicta, ſcilicet ſemidiameter eccentrici, &
<
lb
/>
eccentricitas, inter ſe compræhendentes angulum datum. </
s
>
<
s
xml:id
="
echoid-s2958
"
xml:space
="
preserve
">Nam ſemper præſuppo
<
lb
/>
nitur datus locus centri ipſius epicycli, cum ipſe eſt extra augem aut oppoſitum eius
<
lb
/>
quia in auge linea
<
var
>.o.c.</
var
>
conſtat ex ſemidiametro eccentrici & interualli eccentricita-
<
lb
/>
tis. </
s
>
<
s
xml:id
="
echoid-s2959
"
xml:space
="
preserve
">& in eius oppoſito, ipſa linea
<
var
>.o.c.</
var
>
eſt minor dicto ſemidiametro eccentrici per in
<
lb
/>
teruallum dictæ eccentricitatis. </
s
>
<
s
xml:id
="
echoid-s2960
"
xml:space
="
preserve
">Vnde etiam poſſumus extra augem, vel oppoſitum
<
lb
/>
eius cognoſcere
<
var
>.o.c.</
var
>
tanquam latus dicti trianguli duorum laterum
<
reg
norm
="
cum
"
type
="
context
">cũ</
reg
>
angulo cogni
<
lb
/>
torum. </
s
>
<
s
xml:id
="
echoid-s2961
"
xml:space
="
preserve
">
<
reg
norm
="
Idque
"
type
="
simple
">Idq́;</
reg
>
per .49. propoſitionem libri primi
<
reg
norm
="
eiuſdem
"
type
="
context
">eiuſdẽ</
reg
>
Monteregij cum ſcilicet dictus
<
lb
/>
angulus
<
reg
norm
="
non
"
type
="
context
">nõ</
reg
>
fuerit rectus. </
s
>
<
s
xml:id
="
echoid-s2962
"
xml:space
="
preserve
">Nam ſi fuerit rectus videbitur per .27. et .28. ſupra citatas.</
s
>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s2963
"
xml:space
="
preserve
">Cum igitur hab eamus angulum
<
var
>.c.o.i.</
var
>
gra .40. mi .55. angulus
<
var
>.o.c.i.</
var
>
tanquam reli-
<
lb
/>
quus exrecto, erit grad .49. mi .5. cui reſpondet arcus
<
var
>.i.g.</
var
>
epicycli confectus à Marte
<
lb
/>
in diebus circiter .105. ad rationem min .28. aut circiter in ſingulos dies, prætermiſ-
<
lb
/>
ſis nunc quidem minutijs cum exigui momenti ſit error .15. aut .20. dierum ad verifi
<
lb
/>
cationem longæ morę Martis in vno duodecatemorio, atque per hoc tempus cen-
<
lb
/>
trum epicycli conficit gradus .55. min .7. aut circiter, ad rationem minutorum .31.
<
reg
norm
="
cum
"
type
="
context
">cũ</
reg
>
<
lb
/>
dimidio in ſingulos dies. qui numerus graduum .55. min .7: differt à numero
<
reg
norm
="
graduum
"
type
="
context
">graduũ</
reg
>
.
<
lb
/>
40. min .55. maximæ æquationis argumenti gradibus .14. mi .12. nec refert quod gra
<
num
value
="
55
">.
<
lb
/>
55.</
num
>
min .7. habeant reſpectum ad centrum æquantis, magis quam ad centrum
<
reg
norm
="
mundi
"
type
="
context
">mũdi</
reg
>
,
<
lb
/>
quia differentia non eſt tanta, vt poſſit inducere errorem menſium. </
s
>
<
s
xml:id
="
echoid-s2964
"
xml:space
="
preserve
">Hinc ſequitur
<
lb
/>
quod in fine dictorum dierum .105. </
s
>
<
s
xml:id
="
echoid-s2965
"
xml:space
="
preserve
">Mars erit in linea
<
var
>.o.c.</
var
>
veri motus epicycli, ſed
<
lb
/>
gradibus .14. min .12. vlterius quam in primo loco, in quo erat in Zodiaco, & erit in
<
lb
/>
medio ſuæ retrogradationis. </
s
>
<
s
xml:id
="
echoid-s2966
"
xml:space
="
preserve
">Sed quoniam Mars manifeſtè retrogradi non incipit
<
lb
/>
in puncto
<
var
>.i.</
var
>
conting entiæ, imo ab illo puncto vſque ad terminum primæ ſtationis li
<
lb
/>
neæ
<
var
>.o.n.</
var
>
interponitur arcus
<
var
>.i.n.</
var
>
epicycli, qui eſt graduum .32. minu .14. </
s
>
<
s
xml:id
="
echoid-s2967
"
xml:space
="
preserve
">
<
reg
norm
="
Idque
"
type
="
simple
">Idq́;</
reg
>
cogno-
<
lb
/>
ſcitur ſubtrahendo arcum
<
var
>.f.i.n.</
var
>
graduum .163. mi .9. qui eſt inter augem, & primam
<
lb
/>
ſtationem, à gradibus .180. ( qui arcus
<
var
>.f.i.n.</
var
>
erit verum argumentum, quod ſi-
<
lb
/>
militer variatur ſecundum ſitum epicycli, etſi eiuſmodi varietas, nobis
<
reg
norm
="
non
"
type
="
context
">nõ</
reg
>
eſt magni
<
lb
/>
momenti, vnde poſſumus præſupponere, quod
<
var
>.c.</
var
>
centrum epicycli non alteret
<
reg
norm
="
in- teruallum
"
type
="
context
">in-
<
lb
/>
teruallũ</
reg
>
<
var
>.c.o.</
var
>
à centro
<
reg
norm
="
mundi
"
type
="
context
">mũdi</
reg
>
,
<
reg
norm
="
cum
"
type
="
context
">cũ</
reg
>
non posſit intercedere, error
<
reg
norm
="
menſium
"
type
="
context context
">mẽſiũ</
reg
>
reliquum verò
<
var
>.g.
<
lb
/>
n.</
var
>
graduum .16. min .51. ſubtrahendo ex arcu
<
var
>.g.i.</
var
>
graduum .49. minuti .5. vnde reli-
<
lb
/>
quus nobis erit arcus
<
var
>.n.i.</
var
>
graduum .32. min .14. in eiuſmodi tamen ſitu mediocrium
<
lb
/>
longitudinum. </
s
>
<
s
xml:id
="
echoid-s2968
"
xml:space
="
preserve
">Nunc hic arcus epicycli graduum .32. mi .14. fit à ſtella Martis die-
<
lb
/>
bus .69. ad rationem ſupradictam, omittendo quod ipſa ſtella habeat reſpectum ad
<
lb
/>
augem mediocrem epicycli, & quod dicta aux mediocris mutet diſtantiam à vera
<
lb
/>
propter motum epicycli, quod nunc quidem parui refert, in quibus diebus .69. cen- </
s
>
</
p
>
</
div
>
</
div
>
</
div
>
</
div
>
</
text
>
</
echo
>