Apian, Petrus
,
Instrvmentvm Sinvvm, sev primi mobilis
Text
Text Image
Image
XML
Thumbnail overview
Document information
None
Concordance
Notes
Handwritten
Figures
Content
Thumbnails
Page concordance
<
1 - 30
31 - 60
61 - 90
91 - 97
>
Scan
Original
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
<
1 - 30
31 - 60
61 - 90
91 - 97
>
page
|<
<
of 97
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div41
"
type
="
section
"
level
="
1
"
n
="
25
">
<
p
>
<
s
xml:id
="
echoid-s1523
"
xml:space
="
preserve
">
<
pb
file
="
0038
"
n
="
38
"
rhead
="
GENVINVS VSVS
"/>
igitur habes gradũ Solis ex amplitudine ortiua collectũ. </
s
>
<
s
xml:id
="
echoid-s1524
"
xml:space
="
preserve
">Et ſimili planè modo intelliges
<
lb
/>
omnia de occaſu, ſiquidem amplitudo una alteri reſpondet ſaltem unius ꝓpoſiti gradus.</
s
>
<
s
xml:id
="
echoid-s1525
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div43
"
type
="
section
"
level
="
1
"
n
="
26
">
<
head
xml:id
="
echoid-head30
"
xml:space
="
preserve
">PRONVNCIATVM XIIII.</
head
>
<
p
>
<
s
xml:id
="
echoid-s1526
"
xml:space
="
preserve
">Altitudinem poli in ſingulos dies examplitudine ortiua uel occidua, So-
<
lb
/>
lis ſiue ſtellarum, adpoſite inueſtigare.</
s
>
<
s
xml:id
="
echoid-s1527
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s1528
"
xml:space
="
preserve
">Vno hoc pronunciato tres ſimul uelut uno faſce cõſtrinximus, 12. </
s
>
<
s
xml:id
="
echoid-s1529
"
xml:space
="
preserve
">13. </
s
>
<
s
xml:id
="
echoid-s1530
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1531
"
xml:space
="
preserve
">14. </
s
>
<
s
xml:id
="
echoid-s1532
"
xml:space
="
preserve
">tria enim
<
lb
/>
illa expendenda fuerunt, declinatio, amplitudo, & </
s
>
<
s
xml:id
="
echoid-s1533
"
xml:space
="
preserve
">altitudo poli, ex ijs: </
s
>
<
s
xml:id
="
echoid-s1534
"
xml:space
="
preserve
">quia priora duo
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0038-01
"
xlink:href
="
note-0038-01a
"
xml:space
="
preserve
">
<
emph
style
="
it
">Per aream</
emph
>
<
lb
/>
<
emph
style
="
it
">quadr antis</
emph
>
<
lb
/>
<
emph
style
="
it
">ſimile perſi</
emph
>
<
lb
/>
<
emph
style
="
it
">acs.</
emph
>
</
note
>
iam antea docuimus, reliquum eſt, ut etiã hoc tertium expediamus. </
s
>
<
s
xml:id
="
echoid-s1535
"
xml:space
="
preserve
">Si forte altitudinem
<
lb
/>
poli ex amplitudine ſiue declinatione cognoſcere cupis, propone tibi ſinum amplitudi-
<
lb
/>
nis ſimul cum ſinu declinationis, minorem duc in ſinum totum, productum diuide in ma
<
lb
/>
iorem, arcus quotientis oſtendet complementum altitudinis poli, id ſi ſubtrahas à 90. </
s
>
<
s
xml:id
="
echoid-s1536
"
xml:space
="
preserve
">re
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0038-02
"
xlink:href
="
note-0038-02a
"
xml:space
="
preserve
">EXEM-
<
lb
/>
PLVM
<
lb
/>
E
<
emph
style
="
it
">piſoo
<
unsure
/>
pi.</
emph
>
</
note
>
manebit altitudo poli quam quæſiuiſti. </
s
>
<
s
xml:id
="
echoid-s1537
"
xml:space
="
preserve
">?</
s
>
<
s
xml:id
="
echoid-s1538
"
xml:space
="
preserve
">? Vis & </
s
>
<
s
xml:id
="
echoid-s1539
"
xml:space
="
preserve
">hic exemplum tibi dari@ Enipſo in-
<
lb
/>
tronizationis die Sol fuit in 2. </
s
>
<
s
xml:id
="
echoid-s1540
"
xml:space
="
preserve
">gra. </
s
>
<
s
xml:id
="
echoid-s1541
"
xml:space
="
preserve
">26. </
s
>
<
s
xml:id
="
echoid-s1542
"
xml:space
="
preserve
">mi. </
s
>
<
s
xml:id
="
echoid-s1543
"
xml:space
="
preserve
">II. </
s
>
<
s
xml:id
="
echoid-s1544
"
xml:space
="
preserve
">ex 5. </
s
>
<
s
xml:id
="
echoid-s1545
"
xml:space
="
preserve
">ergo pronunciato inueni declinatio
<
lb
/>
nem 20. </
s
>
<
s
xml:id
="
echoid-s1546
"
xml:space
="
preserve
">gra. </
s
>
<
s
xml:id
="
echoid-s1547
"
xml:space
="
preserve
">42. </
s
>
<
s
xml:id
="
echoid-s1548
"
xml:space
="
preserve
">mi. </
s
>
<
s
xml:id
="
echoid-s1549
"
xml:space
="
preserve
">ſinus eius eſt 35347. </
s
>
<
s
xml:id
="
echoid-s1550
"
xml:space
="
preserve
">Amplitudinem autem ortiuam Solis in die in-
<
lb
/>
tronizationis inueni 31. </
s
>
<
s
xml:id
="
echoid-s1551
"
xml:space
="
preserve
">gra. </
s
>
<
s
xml:id
="
echoid-s1552
"
xml:space
="
preserve
">53. </
s
>
<
s
xml:id
="
echoid-s1553
"
xml:space
="
preserve
">mi. </
s
>
<
s
xml:id
="
echoid-s1554
"
xml:space
="
preserve
">iam paro elicere inde altitudinem poli. </
s
>
<
s
xml:id
="
echoid-s1555
"
xml:space
="
preserve
">Sinus igitur
<
lb
/>
amplitudinis eſt 52825. </
s
>
<
s
xml:id
="
echoid-s1556
"
xml:space
="
preserve
">iam duco minorem iſtam 3534. </
s
>
<
s
xml:id
="
echoid-s1557
"
xml:space
="
preserve
">à toto ſinu, productum diuido
<
lb
/>
in 52825. </
s
>
<
s
xml:id
="
echoid-s1558
"
xml:space
="
preserve
">tanquam numerum maiorem, quotientis erit 66913. </
s
>
<
s
xml:id
="
echoid-s1559
"
xml:space
="
preserve
">arcus illius 42. </
s
>
<
s
xml:id
="
echoid-s1560
"
xml:space
="
preserve
">eum ubi
<
lb
/>
ſubtraxeris à 90. </
s
>
<
s
xml:id
="
echoid-s1561
"
xml:space
="
preserve
">remanebunt gradus 8. </
s
>
<
s
xml:id
="
echoid-s1562
"
xml:space
="
preserve
">ipſa eleuatio polaris optata.</
s
>
<
s
xml:id
="
echoid-s1563
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div45
"
type
="
section
"
level
="
1
"
n
="
27
">
<
head
xml:id
="
echoid-head31
"
xml:space
="
preserve
">PRONVNCIATVM XV.</
head
>
<
p
>
<
s
xml:id
="
echoid-s1564
"
xml:space
="
preserve
">In qualibet regione differentiam inquirere aſcenſionalem, per quam lon-
<
lb
/>
gitudo dierum & </
s
>
<
s
xml:id
="
echoid-s1565
"
xml:space
="
preserve
">noctium inuenitur, & </
s
>
<
s
xml:id
="
echoid-s1566
"
xml:space
="
preserve
">unde longitudo diurna per uniuer-
<
lb
/>
ſum orbem facile cognoſci poteſt.</
s
>
<
s
xml:id
="
echoid-s1567
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s1568
"
xml:space
="
preserve
">Differentia aſcenſionalis arcus eſt æquatoris, per quem longitudo diurna agnoſci-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0038-03
"
xlink:href
="
note-0038-03a
"
xml:space
="
preserve
">
<
emph
style
="
it
">Differentia</
emph
>
<
lb
/>
<
emph
style
="
it
">aſcẽſionalis</
emph
>
<
lb
/>
<
emph
style
="
it
">quid ſit.</
emph
>
</
note
>
tur, is autem ſic intelligitur. </
s
>
<
s
xml:id
="
echoid-s1569
"
xml:space
="
preserve
">Quum ab ortu æquinoctiali uſ ad meridianũ 90. </
s
>
<
s
xml:id
="
echoid-s1570
"
xml:space
="
preserve
">gra. </
s
>
<
s
xml:id
="
echoid-s1571
"
xml:space
="
preserve
">ſem-
<
lb
/>
per interſint, deinde in ſingulas horas gradus 15. </
s
>
<
s
xml:id
="
echoid-s1572
"
xml:space
="
preserve
">emergũt ſuper horizontem, 90. </
s
>
<
s
xml:id
="
echoid-s1573
"
xml:space
="
preserve
">illi gra
<
lb
/>
dus præciſe horas 6. </
s
>
<
s
xml:id
="
echoid-s1574
"
xml:space
="
preserve
">cõficiũt, quo dies medius horis 6. </
s
>
<
s
xml:id
="
echoid-s1575
"
xml:space
="
preserve
">uel longior eſt uel breuior, idip
<
lb
/>
ſum uocamus differentiam aſcenſionalem, eam inuenire cupiens, propone tibi ſinus utri
<
lb
/>
uſ complementi, declinationis & </
s
>
<
s
xml:id
="
echoid-s1576
"
xml:space
="
preserve
">amplitudinis, minorem duc in finum totum, produ-
<
lb
/>
ctum diuide in ſinum maiorem, arcu quotientis dehinc ſubtracto à 90. </
s
>
<
s
xml:id
="
echoid-s1577
"
xml:space
="
preserve
">remanebit diffe-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0038-04
"
xlink:href
="
note-0038-04a
"
xml:space
="
preserve
">
<
emph
style
="
it
">Simile per</
emph
>
<
lb
/>
<
emph
style
="
it
">introitum</
emph
>
<
lb
/>
<
emph
style
="
it
">arealem</
emph
>
<
lb
/>
<
emph
style
="
it
">quærenti</
emph
>
<
lb
/>
<
emph
style
="
it
">apparet.</
emph
>
</
note
>
rentia aſcenſionalis: </
s
>
<
s
xml:id
="
echoid-s1578
"
xml:space
="
preserve
">quod ſi declinatio fuerit meridionalis, ſubtrahe differentiam illam
<
lb
/>
aſcenſionalem à 90. </
s
>
<
s
xml:id
="
echoid-s1579
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1580
"
xml:space
="
preserve
">remanebit arcus ſemidiurnus: </
s
>
<
s
xml:id
="
echoid-s1581
"
xml:space
="
preserve
">ſin autem declinatio ſit ſeptentrio-
<
lb
/>
nalis, illam rurſus adde ad 90. </
s
>
<
s
xml:id
="
echoid-s1582
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1583
"
xml:space
="
preserve
">iterum habebis arcum ſemidiurnum. </
s
>
<
s
xml:id
="
echoid-s1584
"
xml:space
="
preserve
">Tantundem eſt, ſi
<
lb
/>
arcum quotientis ſubtrahas à ſemicirculo, nam & </
s
>
<
s
xml:id
="
echoid-s1585
"
xml:space
="
preserve
">tunc manebit arcus ſemidiurnus, illo
<
lb
/>
duplicato, habes arcum diurnum, quem ſi rurſus ſubtrahas à toto circulo, arcus relinque-
<
lb
/>
tur nocturnus. </
s
>
<
s
xml:id
="
echoid-s1586
"
xml:space
="
preserve
">ſemper tamen hic intellige 15. </
s
>
<
s
xml:id
="
echoid-s1587
"
xml:space
="
preserve
">gra. </
s
>
<
s
xml:id
="
echoid-s1588
"
xml:space
="
preserve
">pro unica hora. </
s
>
<
s
xml:id
="
echoid-s1589
"
xml:space
="
preserve
">?</
s
>
<
s
xml:id
="
echoid-s1590
"
xml:space
="
preserve
">? Sit & </
s
>
<
s
xml:id
="
echoid-s1591
"
xml:space
="
preserve
">hic exem-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0038-05
"
xlink:href
="
note-0038-05a
"
xml:space
="
preserve
">EXEM-
<
lb
/>
PLVM
<
lb
/>
E
<
emph
style
="
it
">piſoo
<
unsure
/>
pi.</
emph
>
</
note
>
plum tibi huiuſmodi: </
s
>
<
s
xml:id
="
echoid-s1592
"
xml:space
="
preserve
">Inuenturus longitudinem diei intronizationis, iam antea habeo
<
lb
/>
perfectam declinationem Solis ex pronunciato 5. </
s
>
<
s
xml:id
="
echoid-s1593
"
xml:space
="
preserve
">quoniam ille in 2. </
s
>
<
s
xml:id
="
echoid-s1594
"
xml:space
="
preserve
">gra. </
s
>
<
s
xml:id
="
echoid-s1595
"
xml:space
="
preserve
">26. </
s
>
<
s
xml:id
="
echoid-s1596
"
xml:space
="
preserve
">mi. </
s
>
<
s
xml:id
="
echoid-s1597
"
xml:space
="
preserve
">fuit II. </
s
>
<
s
xml:id
="
echoid-s1598
"
xml:space
="
preserve
">ea
<
lb
/>
declinatio eſt 20. </
s
>
<
s
xml:id
="
echoid-s1599
"
xml:space
="
preserve
">gra. </
s
>
<
s
xml:id
="
echoid-s1600
"
xml:space
="
preserve
">42. </
s
>
<
s
xml:id
="
echoid-s1601
"
xml:space
="
preserve
">mi. </
s
>
<
s
xml:id
="
echoid-s1602
"
xml:space
="
preserve
">ex 12. </
s
>
<
s
xml:id
="
echoid-s1603
"
xml:space
="
preserve
">pronunciato quo inuentam habeo amplitudinem
<
lb
/>
ad eundem ipſum gradum Solis, puta 31. </
s
>
<
s
xml:id
="
echoid-s1604
"
xml:space
="
preserve
">gra. </
s
>
<
s
xml:id
="
echoid-s1605
"
xml:space
="
preserve
">53. </
s
>
<
s
xml:id
="
echoid-s1606
"
xml:space
="
preserve
">mi. </
s
>
<
s
xml:id
="
echoid-s1607
"
xml:space
="
preserve
">Nunc iam colligo complementa,
<
lb
/>
alterum eſt 58. </
s
>
<
s
xml:id
="
echoid-s1608
"
xml:space
="
preserve
">gra. </
s
>
<
s
xml:id
="
echoid-s1609
"
xml:space
="
preserve
">7. </
s
>
<
s
xml:id
="
echoid-s1610
"
xml:space
="
preserve
">mi. </
s
>
<
s
xml:id
="
echoid-s1611
"
xml:space
="
preserve
">ſinus eius 849 12. </
s
>
<
s
xml:id
="
echoid-s1612
"
xml:space
="
preserve
">alterum porrò complementum eſt 69. </
s
>
<
s
xml:id
="
echoid-s1613
"
xml:space
="
preserve
">gra. </
s
>
<
s
xml:id
="
echoid-s1614
"
xml:space
="
preserve
">18.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s1615
"
xml:space
="
preserve
">mi. </
s
>
<
s
xml:id
="
echoid-s1616
"
xml:space
="
preserve
">arcus ipſius 93544. </
s
>
<
s
xml:id
="
echoid-s1617
"
xml:space
="
preserve
">ſinum minorem multiplica cum toto ſinu, productum diuide in
<
lb
/>
maximum, & </
s
>
<
s
xml:id
="
echoid-s1618
"
xml:space
="
preserve
">quotiens erit 90772, arcus eius eſt 65. </
s
>
<
s
xml:id
="
echoid-s1619
"
xml:space
="
preserve
">gra. </
s
>
<
s
xml:id
="
echoid-s1620
"
xml:space
="
preserve
">12. </
s
>
<
s
xml:id
="
echoid-s1621
"
xml:space
="
preserve
">mi. </
s
>
<
s
xml:id
="
echoid-s1622
"
xml:space
="
preserve
">Arcũ illum ſi ſubtrahas à
<
lb
/>
90. </
s
>
<
s
xml:id
="
echoid-s1623
"
xml:space
="
preserve
">remanebit differentia aſcenſionalis 24. </
s
>
<
s
xml:id
="
echoid-s1624
"
xml:space
="
preserve
">gra. </
s
>
<
s
xml:id
="
echoid-s1625
"
xml:space
="
preserve
">49. </
s
>
<
s
xml:id
="
echoid-s1626
"
xml:space
="
preserve
">mi. </
s
>
<
s
xml:id
="
echoid-s1627
"
xml:space
="
preserve
">differentiam hanc adde, & </
s
>
<
s
xml:id
="
echoid-s1628
"
xml:space
="
preserve
">habe-
<
lb
/>
bis arcum ſemidiurnum 114. </
s
>
<
s
xml:id
="
echoid-s1629
"
xml:space
="
preserve
">gra. </
s
>
<
s
xml:id
="
echoid-s1630
"
xml:space
="
preserve
">49. </
s
>
<
s
xml:id
="
echoid-s1631
"
xml:space
="
preserve
">mi. </
s
>
<
s
xml:id
="
echoid-s1632
"
xml:space
="
preserve
">Vel ſubtrahe 65. </
s
>
<
s
xml:id
="
echoid-s1633
"
xml:space
="
preserve
">gra. </
s
>
<
s
xml:id
="
echoid-s1634
"
xml:space
="
preserve
">11. </
s
>
<
s
xml:id
="
echoid-s1635
"
xml:space
="
preserve
">mi. </
s
>
<
s
xml:id
="
echoid-s1636
"
xml:space
="
preserve
">de ſemicirculo, & </
s
>
<
s
xml:id
="
echoid-s1637
"
xml:space
="
preserve
">
<
lb
/>
rurſus manebit arcus ſemidiurnus, eũ ſi reſoluas in horas, habebis horas 7. </
s
>
<
s
xml:id
="
echoid-s1638
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1639
"
xml:space
="
preserve
">48. </
s
>
<
s
xml:id
="
echoid-s1640
"
xml:space
="
preserve
">mi. </
s
>
<
s
xml:id
="
echoid-s1641
"
xml:space
="
preserve
">Sin
<
lb
/>
autem duplaris numerum, habebis arcũ diurnum 15. </
s
>
<
s
xml:id
="
echoid-s1642
"
xml:space
="
preserve
">horas 36. </
s
>
<
s
xml:id
="
echoid-s1643
"
xml:space
="
preserve
">mi. </
s
>
<
s
xml:id
="
echoid-s1644
"
xml:space
="
preserve
">Ad extremum ſi ſub-
<
lb
/>
trahas arcum diurnum à 24. </
s
>
<
s
xml:id
="
echoid-s1645
"
xml:space
="
preserve
">horis, reliquæ tibi manebunt horæ 8. </
s
>
<
s
xml:id
="
echoid-s1646
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1647
"
xml:space
="
preserve
">24. </
s
>
<
s
xml:id
="
echoid-s1648
"
xml:space
="
preserve
">mi. </
s
>
<
s
xml:id
="
echoid-s1649
"
xml:space
="
preserve
">tempus ſcili-
<
lb
/>
cet nocturnum. </
s
>
<
s
xml:id
="
echoid-s1650
"
xml:space
="
preserve
">At hoc modo cuiuslibet puncti uel ſtellæ fixæ potes arcum inuenire
<
lb
/>
diurnum, hoc eſt, quot horis & </
s
>
<
s
xml:id
="
echoid-s1651
"
xml:space
="
preserve
">minutis maneat ſuper horizontem, ſiue interdiu tandem
<
lb
/>
ſiue noctu id fiat. </
s
>
<
s
xml:id
="
echoid-s1652
"
xml:space
="
preserve
">Quod autem ad puncta eclypticæ tantum pertinet, ſequenti pronun
<
lb
/>
ciato explicabimus.</
s
>
<
s
xml:id
="
echoid-s1653
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
</
text
>
</
echo
>
