Apian, Petrus
,
Instrvmentvm Sinvvm, sev primi mobilis
Text
Text Image
Image
XML
Thumbnail overview
Document information
None
Concordance
Notes
Handwritten
Figures
Content
Thumbnails
Table of Notes
<
1 - 7
[out of range]
>
[Note]
Page: 36
[Note]
Page: 36
[Note]
Page: 36
[Note]
Page: 37
[Note]
Page: 37
[Note]
Page: 37
[Note]
Page: 37
[Note]
Page: 37
[Note]
Page: 37
[Note]
Page: 38
[Note]
Page: 38
[Note]
Page: 38
[Note]
Page: 38
[Note]
Page: 38
[Note]
Page: 39
[Note]
Page: 39
[Note]
Page: 39
[Note]
Page: 39
[Note]
Page: 39
[Note]
Page: 40
[Note]
Page: 40
[Note]
Page: 40
[Note]
Page: 40
[Note]
Page: 40
[Note]
Page: 40
[Note]
Page: 40
[Note]
Page: 41
[Note]
Page: 41
[Note]
Page: 41
[Note]
Page: 41
<
1 - 7
[out of range]
>
page
|<
<
of 97
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div133
"
type
="
section
"
level
="
1
"
n
="
71
">
<
p
>
<
s
xml:id
="
echoid-s4385
"
xml:space
="
preserve
">
<
pb
file
="
0063
"
n
="
63
"
rhead
="
TABVLARVM SINVVM PER PET. APIANVM.
"/>
complementi declinationis minoris. </
s
>
<
s
xml:id
="
echoid-s4386
"
xml:space
="
preserve
">ſ. </
s
>
<
s
xml:id
="
echoid-s4387
"
xml:space
="
preserve
">5. </
s
>
<
s
xml:id
="
echoid-s4388
"
xml:space
="
preserve
">gra. </
s
>
<
s
xml:id
="
echoid-s4389
"
xml:space
="
preserve
">25. </
s
>
<
s
xml:id
="
echoid-s4390
"
xml:space
="
preserve
">mi. </
s
>
<
s
xml:id
="
echoid-s4391
"
xml:space
="
preserve
">♌, & </
s
>
<
s
xml:id
="
echoid-s4392
"
xml:space
="
preserve
">quia declinatio eius eſt 18. </
s
>
<
s
xml:id
="
echoid-s4393
"
xml:space
="
preserve
">gra.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s4394
"
xml:space
="
preserve
">58. </
s
>
<
s
xml:id
="
echoid-s4395
"
xml:space
="
preserve
">mi. </
s
>
<
s
xml:id
="
echoid-s4396
"
xml:space
="
preserve
">cõplementũ ipſius erit 71. </
s
>
<
s
xml:id
="
echoid-s4397
"
xml:space
="
preserve
">gra. </
s
>
<
s
xml:id
="
echoid-s4398
"
xml:space
="
preserve
">2. </
s
>
<
s
xml:id
="
echoid-s4399
"
xml:space
="
preserve
">mi. </
s
>
<
s
xml:id
="
echoid-s4400
"
xml:space
="
preserve
">ſinus atit 94570. </
s
>
<
s
xml:id
="
echoid-s4401
"
xml:space
="
preserve
">ꝓductũ ex hac multiplicati
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0063-01
"
xlink:href
="
note-0063-01a
"
xml:space
="
preserve
">
<
emph
style
="
it
">Per latera.</
emph
>
<
lb
/>
<
emph
style
="
it
">lem ingreſ-</
emph
>
<
lb
/>
<
emph
style
="
it
">ſum qua-</
emph
>
<
lb
/>
<
emph
style
="
it
">drans illud</
emph
>
<
lb
/>
<
emph
style
="
it
">demõſtrat.</
emph
>
</
note
>
one diuido in ſinũ totũ, & </
s
>
<
s
xml:id
="
echoid-s4402
"
xml:space
="
preserve
">quotiẽs dabit 74323. </
s
>
<
s
xml:id
="
echoid-s4403
"
xml:space
="
preserve
">arcus eſt 48. </
s
>
<
s
xml:id
="
echoid-s4404
"
xml:space
="
preserve
">gra. </
s
>
<
s
xml:id
="
echoid-s4405
"
xml:space
="
preserve
">altiudo illa poli quæſita
<
lb
/>
in loco intronizationis. </
s
>
<
s
xml:id
="
echoid-s4406
"
xml:space
="
preserve
">Quid ſi aũt contingat, ut alter terminus eclypticæ ſit in medie-
<
lb
/>
tate eclypticæ ſeptentrionali, alter uero in meridionali? </
s
>
<
s
xml:id
="
echoid-s4407
"
xml:space
="
preserve
">tunc ſanè duc ſinum differentiæ
<
lb
/>
aſcenſionũ in ſinũ cõplementi de clinationis Borealis, ꝓducto diuiſo in ſinũ totum, quo
<
lb
/>
tiens dabit inuentũ primũ. </
s
>
<
s
xml:id
="
echoid-s4408
"
xml:space
="
preserve
">Sinũ cõplementi huius inuenti propone tibi, & </
s
>
<
s
xml:id
="
echoid-s4409
"
xml:space
="
preserve
">ſimul ſinũ de-
<
lb
/>
clinationis Borealis, minorem duc in totum, & </
s
>
<
s
xml:id
="
echoid-s4410
"
xml:space
="
preserve
">productũ diuide in maiorẽ, arcui quoti-
<
lb
/>
entis adde arcũ declinationis Auſtrinæ, & </
s
>
<
s
xml:id
="
echoid-s4411
"
xml:space
="
preserve
">collectũ hoc uocabit̃ inuentũ ſecundũ. </
s
>
<
s
xml:id
="
echoid-s4412
"
xml:space
="
preserve
">Poſtea
<
lb
/>
duc ſinũ complementi primi inuenti in ſinũ cõplem enti ſecundi inuenti, productũ diui-
<
lb
/>
de in ſinũ totum, quotientis arcu ex 90. </
s
>
<
s
xml:id
="
echoid-s4413
"
xml:space
="
preserve
">ſubtracto, reſidui ſinũ ſeorſim colloca unà cum ſi-
<
lb
/>
nu inuenti primi, minorẽ duc in totũ, productum in maiorem diuide, & </
s
>
<
s
xml:id
="
echoid-s4414
"
xml:space
="
preserve
">quotientem ex di
<
lb
/>
uiſione prouenientem rurſus duc in ſinum cõplementi declinationis Auſtrinæ, & </
s
>
<
s
xml:id
="
echoid-s4415
"
xml:space
="
preserve
">produ
<
lb
/>
ctum diuide cum ſinu toto, tunc arcus quotientis arguet altitudinem poli quam optabas
<
lb
/>
ſcire, nec eſt. </
s
>
<
s
xml:id
="
echoid-s4416
"
xml:space
="
preserve
">ꝙ hic inſuper expectes exemplum, quum neceſſarium non uideatur.</
s
>
<
s
xml:id
="
echoid-s4417
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div135
"
type
="
section
"
level
="
1
"
n
="
72
">
<
head
xml:id
="
echoid-head76
"
xml:space
="
preserve
">PRONVNCIATVM LX.</
head
>
<
p
>
<
s
xml:id
="
echoid-s4418
"
xml:space
="
preserve
">Cognito antea & </
s
>
<
s
xml:id
="
echoid-s4419
"
xml:space
="
preserve
">gradu medij cœli, & </
s
>
<
s
xml:id
="
echoid-s4420
"
xml:space
="
preserve
">ſimul perſpecta amplitudine ortiua
<
lb
/>
aſcendentis, altitudinem poli inde perquirere.</
s
>
<
s
xml:id
="
echoid-s4421
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s4422
"
xml:space
="
preserve
">Iam ſupra præmonuimus, ubi declinatio tanta eſt quanta amplitudo, in ea ciuitate
<
lb
/>
nullã eſſe eleuationẽ poli, q̊d ſanè omnibus cõtingit ſub æquatore habitãtibus, nequit e-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0063-02
"
xlink:href
="
note-0063-02a
"
xml:space
="
preserve
">
<
emph
style
="
it
">Amplitude</
emph
>
<
lb
/>
<
emph
style
="
it
">ortus ſiue</
emph
>
<
lb
/>
<
emph
style
="
it
">occaſus de-</
emph
>
<
lb
/>
<
emph
style
="
it
">clinatione</
emph
>
<
lb
/>
<
emph
style
="
it
">nunquã mi</
emph
>
<
lb
/>
<
emph
style
="
it
">nor, ſed ma</
emph
>
<
lb
/>
<
emph
style
="
it
">ior aut æ-</
emph
>
<
lb
/>
<
emph
style
="
it
">qualis repe</
emph
>
<
lb
/>
<
emph
style
="
it
">ritur.</
emph
>
</
note
>
nim amplitudo eſſe declinatione minor, ſed bene maior, ſi igitur maior illa fuerit, quære
<
lb
/>
angulũ quẽ facit eclyptica cũ meridiano iuxta gradũ medij cœli ꝑ 26. </
s
>
<
s
xml:id
="
echoid-s4423
"
xml:space
="
preserve
">27. </
s
>
<
s
xml:id
="
echoid-s4424
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s4425
"
xml:space
="
preserve
">28. </
s
>
<
s
xml:id
="
echoid-s4426
"
xml:space
="
preserve
">ꝓnuncia
<
lb
/>
ta, angulus ille ſi fuerit quadrãte minor, tunc erit ad hanc operationẽ adcõ modatus. </
s
>
<
s
xml:id
="
echoid-s4427
"
xml:space
="
preserve
">ſin
<
lb
/>
autem maior extiterit, ſubtrahe eũ à ſemicirculo, & </
s
>
<
s
xml:id
="
echoid-s4428
"
xml:space
="
preserve
">remanebit numerus quo uteris in hac
<
lb
/>
conſideratione loco anguli. </
s
>
<
s
xml:id
="
echoid-s4429
"
xml:space
="
preserve
">Sinum arcus illius ſeorſim pone unà cũ ſinu cõplementi am-
<
lb
/>
plitudinis ortiuæ, ſicut per 12. </
s
>
<
s
xml:id
="
echoid-s4430
"
xml:space
="
preserve
">pronunc. </
s
>
<
s
xml:id
="
echoid-s4431
"
xml:space
="
preserve
">inueniſti, minorẽ exijs duc in totũ, productum
<
lb
/>
diuide in maiorem, & </
s
>
<
s
xml:id
="
echoid-s4432
"
xml:space
="
preserve
">arcus quotientis tibi dabit arcũ à medio cœli uſ ad gradũ horo-
<
lb
/>
ſcopi numerãdo ſecũdũ ordinẽ ſignorũ. </
s
>
<
s
xml:id
="
echoid-s4433
"
xml:space
="
preserve
">At hoc uerum eſt ſi angulus medij cœli minor
<
lb
/>
fuerit quadrante, fit aũt id, quando gradus eclypticæ aſcendens eſt in ſignis meridionali
<
lb
/>
bus. </
s
>
<
s
xml:id
="
echoid-s4434
"
xml:space
="
preserve
">Si autẽ angulus meridiani & </
s
>
<
s
xml:id
="
echoid-s4435
"
xml:space
="
preserve
">eclypticæ maior ſit recto, q̊d fit, quũ aſcendens eſt in
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0063-03
"
xlink:href
="
note-0063-03a
"
xml:space
="
preserve
">
<
emph
style
="
it
">Per aream</
emph
>
<
lb
/>
<
emph
style
="
it
">patet.</
emph
>
</
note
>
ſignis ſeptentrionalibus, arcũ quotiẽtis minue de ſemicirculo, & </
s
>
<
s
xml:id
="
echoid-s4436
"
xml:space
="
preserve
">reliquus manebit arcus
<
lb
/>
eclypticæ à medio cœli uſ ad caput horoſcopi. </
s
>
<
s
xml:id
="
echoid-s4437
"
xml:space
="
preserve
">Porrò etiã tibi propone ſinũ amplitudi
<
lb
/>
nis ortiuæ & </
s
>
<
s
xml:id
="
echoid-s4438
"
xml:space
="
preserve
">ſinum declinationis aſcendentis, minorẽ duc in ſinũ totum, & </
s
>
<
s
xml:id
="
echoid-s4439
"
xml:space
="
preserve
">ꝓductum di-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0063-04
"
xlink:href
="
note-0063-04a
"
xml:space
="
preserve
">
<
emph
style
="
it
">Per aream</
emph
>
</
note
>
uide in maiorem. </
s
>
<
s
xml:id
="
echoid-s4440
"
xml:space
="
preserve
">arcus à 90. </
s
>
<
s
xml:id
="
echoid-s4441
"
xml:space
="
preserve
">ſubtractus, relinquet altitudinem poli eius loci in quo am-
<
lb
/>
plitudinem obſeruaſti. </
s
>
<
s
xml:id
="
echoid-s4442
"
xml:space
="
preserve
">Potes idem diuerſa paulo operatione ſic exequi, ſinum ampli
<
lb
/>
tudinis ortiuæ & </
s
>
<
s
xml:id
="
echoid-s4443
"
xml:space
="
preserve
">ſinũ cõplementi tibi propone, ſimul etiã ſinum complementi arcus in-
<
lb
/>
ter medium cœli & </
s
>
<
s
xml:id
="
echoid-s4444
"
xml:space
="
preserve
">aſcendentis gradum, minorem duc in totum, productum in maiorem
<
lb
/>
diuide, & </
s
>
<
s
xml:id
="
echoid-s4445
"
xml:space
="
preserve
">quotiens dabit diſtantiã medij cœli à 90. </
s
>
<
s
xml:id
="
echoid-s4446
"
xml:space
="
preserve
">gradu ab aſcendente, ad eã diſtantiã
<
lb
/>
adde declinationem medij cœli, ſi Borealis fuerit, uel ſubtrahe, ſi Auſtrina extiterit, quic
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0063-05
"
xlink:href
="
note-0063-05a
"
xml:space
="
preserve
">
<
emph
style
="
it
">Per latera.</
emph
>
</
note
>
quid inde ꝓuenerit, erit altitudo poli quæſita, ſed hic quo exemplum non negabimus
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0063-06
"
xlink:href
="
note-0063-06a
"
xml:space
="
preserve
">EXEM-
<
lb
/>
PLVM
<
lb
/>
<
emph
style
="
it
">Epiſoo
<
unsure
/>
pi.</
emph
>
</
note
>
tibi. </
s
>
<
s
xml:id
="
echoid-s4447
"
xml:space
="
preserve
">?</
s
>
<
s
xml:id
="
echoid-s4448
"
xml:space
="
preserve
">?Ecce ex 25. </
s
>
<
s
xml:id
="
echoid-s4449
"
xml:space
="
preserve
">pronunc. </
s
>
<
s
xml:id
="
echoid-s4450
"
xml:space
="
preserve
">inueni 16. </
s
>
<
s
xml:id
="
echoid-s4451
"
xml:space
="
preserve
">gra. </
s
>
<
s
xml:id
="
echoid-s4452
"
xml:space
="
preserve
">40. </
s
>
<
s
xml:id
="
echoid-s4453
"
xml:space
="
preserve
">mi. </
s
>
<
s
xml:id
="
echoid-s4454
"
xml:space
="
preserve
">♈ in medio cœli fuiſſe hora & </
s
>
<
s
xml:id
="
echoid-s4455
"
xml:space
="
preserve
">lo-
<
lb
/>
co factæ intronizationis, angulũ quo eclypticæ & </
s
>
<
s
xml:id
="
echoid-s4456
"
xml:space
="
preserve
">meridiani iuxta illum gradum eſſe
<
lb
/>
112. </
s
>
<
s
xml:id
="
echoid-s4457
"
xml:space
="
preserve
">gra. </
s
>
<
s
xml:id
="
echoid-s4458
"
xml:space
="
preserve
">37. </
s
>
<
s
xml:id
="
echoid-s4459
"
xml:space
="
preserve
">mi. </
s
>
<
s
xml:id
="
echoid-s4460
"
xml:space
="
preserve
">cognoui ꝑ 26. </
s
>
<
s
xml:id
="
echoid-s4461
"
xml:space
="
preserve
">27. </
s
>
<
s
xml:id
="
echoid-s4462
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s4463
"
xml:space
="
preserve
">28. </
s
>
<
s
xml:id
="
echoid-s4464
"
xml:space
="
preserve
">ꝓnunciata, & </
s
>
<
s
xml:id
="
echoid-s4465
"
xml:space
="
preserve
">quia angulus hic maior eſt qua-
<
lb
/>
drãte, ſubtraxi eũ de ſemicirculo, & </
s
>
<
s
xml:id
="
echoid-s4466
"
xml:space
="
preserve
">remanſerunt 67. </
s
>
<
s
xml:id
="
echoid-s4467
"
xml:space
="
preserve
">gra. </
s
>
<
s
xml:id
="
echoid-s4468
"
xml:space
="
preserve
">23. </
s
>
<
s
xml:id
="
echoid-s4469
"
xml:space
="
preserve
">mi ſinus eorũ uoco nume℞
<
lb
/>
introitualem. </
s
>
<
s
xml:id
="
echoid-s4470
"
xml:space
="
preserve
">ſ. </
s
>
<
s
xml:id
="
echoid-s4471
"
xml:space
="
preserve
">92309. </
s
>
<
s
xml:id
="
echoid-s4472
"
xml:space
="
preserve
">At quum ſinus cõplementi amplitudinis aſcendentis 87405.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s4473
"
xml:space
="
preserve
">minimus fuerit, nume℞ illum duxi in totũ, ꝓductũ diuiſi in ſinum introitualem, & </
s
>
<
s
xml:id
="
echoid-s4474
"
xml:space
="
preserve
">in quo
<
lb
/>
tiente ꝓdierunt 94687. </
s
>
<
s
xml:id
="
echoid-s4475
"
xml:space
="
preserve
">arcus eius eſt 71. </
s
>
<
s
xml:id
="
echoid-s4476
"
xml:space
="
preserve
">gra. </
s
>
<
s
xml:id
="
echoid-s4477
"
xml:space
="
preserve
">15. </
s
>
<
s
xml:id
="
echoid-s4478
"
xml:space
="
preserve
">mi. </
s
>
<
s
xml:id
="
echoid-s4479
"
xml:space
="
preserve
">quibus à ſemicirculo ſubtractis, re-
<
lb
/>
manent 108. </
s
>
<
s
xml:id
="
echoid-s4480
"
xml:space
="
preserve
">gra. </
s
>
<
s
xml:id
="
echoid-s4481
"
xml:space
="
preserve
">43. </
s
>
<
s
xml:id
="
echoid-s4482
"
xml:space
="
preserve
">mi. </
s
>
<
s
xml:id
="
echoid-s4483
"
xml:space
="
preserve
">arcus ille eclypticæ à medio cœli uſ ad gradum aſcendentis,
<
lb
/>
tantũ quo ſi numeres â 16. </
s
>
<
s
xml:id
="
echoid-s4484
"
xml:space
="
preserve
">gra. </
s
>
<
s
xml:id
="
echoid-s4485
"
xml:space
="
preserve
">40. </
s
>
<
s
xml:id
="
echoid-s4486
"
xml:space
="
preserve
">mi. </
s
>
<
s
xml:id
="
echoid-s4487
"
xml:space
="
preserve
">♈, iuxta uerum ſignorũ ordinem, numerus tan
<
lb
/>
get 5. </
s
>
<
s
xml:id
="
echoid-s4488
"
xml:space
="
preserve
">gra. </
s
>
<
s
xml:id
="
echoid-s4489
"
xml:space
="
preserve
">25. </
s
>
<
s
xml:id
="
echoid-s4490
"
xml:space
="
preserve
">mi. </
s
>
<
s
xml:id
="
echoid-s4491
"
xml:space
="
preserve
">♌, & </
s
>
<
s
xml:id
="
echoid-s4492
"
xml:space
="
preserve
">ſic quidẽ gradũ aſcendentẽ adhuc diuerſo â ſuꝑioribus modo in-
<
lb
/>
ueni. </
s
>
<
s
xml:id
="
echoid-s4493
"
xml:space
="
preserve
">Inſuper ſi ꝑ 5. </
s
>
<
s
xml:id
="
echoid-s4494
"
xml:space
="
preserve
">ꝓnunc. </
s
>
<
s
xml:id
="
echoid-s4495
"
xml:space
="
preserve
">quæro declinationẽ, inuenio uti 18. </
s
>
<
s
xml:id
="
echoid-s4496
"
xml:space
="
preserve
">gra. </
s
>
<
s
xml:id
="
echoid-s4497
"
xml:space
="
preserve
">58. </
s
>
<
s
xml:id
="
echoid-s4498
"
xml:space
="
preserve
">mi ſinum eius
<
lb
/>
declinationis. </
s
>
<
s
xml:id
="
echoid-s4499
"
xml:space
="
preserve
">ſ. </
s
>
<
s
xml:id
="
echoid-s4500
"
xml:space
="
preserve
">32501. </
s
>
<
s
xml:id
="
echoid-s4501
"
xml:space
="
preserve
">quia minorem duco in ſinũ totũ, & </
s
>
<
s
xml:id
="
echoid-s4502
"
xml:space
="
preserve
">productũ diuido in ſinũ </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>