Clavius, Christoph
,
In Sphaeram Ioannis de Sacro Bosco commentarius
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: 58
[Note]
Page: 59
[Note]
Page: 59
[Note]
Page: 59
[Note]
Page: 59
[Note]
Page: 59
[Note]
Page: 59
[Note]
Page: 60
[Note]
Page: 60
[Note]
Page: 60
[Note]
Page: 60
[Note]
Page: 60
[Note]
Page: 60
[Note]
Page: 60
[Note]
Page: 60
[Note]
Page: 60
[Note]
Page: 60
[Note]
Page: 61
[Note]
Page: 62
[Note]
Page: 62
[Note]
Page: 63
[Note]
Page: 63
[Note]
Page: 63
[Note]
Page: 63
[Note]
Page: 63
[Note]
Page: 63
[Note]
Page: 63
[Note]
Page: 63
[Note]
Page: 64
[Note]
Page: 64
<
1 - 7
[out of range]
>
page
|<
<
(34)
of 525
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div128
"
type
="
section
"
level
="
1
"
n
="
50
">
<
p
>
<
s
xml:id
="
echoid-s1599
"
xml:space
="
preserve
">
<
pb
o
="
34
"
file
="
070
"
n
="
71
"
rhead
="
Comment. in I. Cap. Sphæræ
"/>
dus, remiſſe autem calidus exiſtit: </
s
>
<
s
xml:id
="
echoid-s1600
"
xml:space
="
preserve
">frigiditatis cum humiditate, ex qua philoſo-
<
lb
/>
phi aquam colligunt, quam frigidam dicunt in ſummo, humidam vero remiſ-
<
lb
/>
ſe: </
s
>
<
s
xml:id
="
echoid-s1601
"
xml:space
="
preserve
">ſiccitatis cum frigiditate, ex qua terra conficitur, quæ in ſummo ſicca, frigi-
<
lb
/>
da uero remiſſe eſſe prædicatur: </
s
>
<
s
xml:id
="
echoid-s1602
"
xml:space
="
preserve
">caliditatis cum frigiditate: </
s
>
<
s
xml:id
="
echoid-s1603
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1604
"
xml:space
="
preserve
">humiditatis cum
<
lb
/>
ſiccitate. </
s
>
<
s
xml:id
="
echoid-s1605
"
xml:space
="
preserve
">Sed quoniam duæ hæ poſtremæ combinationes impoſſibiles ſunt,
<
lb
/>
cum ſint contrariorum; </
s
>
<
s
xml:id
="
echoid-s1606
"
xml:space
="
preserve
">quorum ea eſt natura, vt vnum alterum ſemper expel-
<
lb
/>
lat: </
s
>
<
s
xml:id
="
echoid-s1607
"
xml:space
="
preserve
">Neque enim una, eademq́ue res numero calida, & </
s
>
<
s
xml:id
="
echoid-s1608
"
xml:space
="
preserve
">frigida; </
s
>
<
s
xml:id
="
echoid-s1609
"
xml:space
="
preserve
">neque humida
<
lb
/>
ſimul, & </
s
>
<
s
xml:id
="
echoid-s1610
"
xml:space
="
preserve
">ſicca eſſe poteſt; </
s
>
<
s
xml:id
="
echoid-s1611
"
xml:space
="
preserve
">idcirco inutiles cenſentur, neque quicquam ex eis cõ
<
lb
/>
ſtitui poteſt. </
s
>
<
s
xml:id
="
echoid-s1612
"
xml:space
="
preserve
">Hæ autem omnes combinationes luce clarius in figura propoſi-
<
lb
/>
ta conſpiciuntur. </
s
>
<
s
xml:id
="
echoid-s1613
"
xml:space
="
preserve
">Quod autem diximus, unam qualitatem in quolibet elemẽ
<
lb
/>
to eſſe in ſummo gradu, & </
s
>
<
s
xml:id
="
echoid-s1614
"
xml:space
="
preserve
">in remiſſo alteram, intelligendum eſt ex ſententia
<
lb
/>
@uorunda
<
unsure
/>
m philoſophorum. </
s
>
<
s
xml:id
="
echoid-s1615
"
xml:space
="
preserve
">Multi enim arbitrantur, utramque qualitatem in
<
lb
/>
quouis elemento eſſe in ſummo grad@</
s
>
</
p
>
<
note
position
="
left
"
xml:space
="
preserve
">Digreſſio
<
lb
/>
pulcherri-
<
lb
/>
ma de rerũ
<
lb
/>
cõbinatio--
<
lb
/>
nibus, fiue
<
lb
/>
cõparatio--
<
lb
/>
nibus.</
note
>
<
p
>
<
s
xml:id
="
echoid-s1616
"
xml:space
="
preserve
">
<
emph
style
="
sc
">Qvoniam</
emph
>
vero diximus, inter quatuor res non poſſe fieri plures com-
<
lb
/>
binationes, quàm ſex, ſi binæ tantum ſemper ſumantur, uiſum mihi eſt, paulo
<
lb
/>
uberius explicare, quotnam combinationes huiuſmodi fieri poſsint inter quot-
<
lb
/>
cunque res propoſitas; </
s
>
<
s
xml:id
="
echoid-s1617
"
xml:space
="
preserve
">Ad multa enim conducit huiuſce rei notitia, eſtq́ue per
<
lb
/>
ſe iucundiſſima. </
s
>
<
s
xml:id
="
echoid-s1618
"
xml:space
="
preserve
">Propoſito ergo numero aliquarum rerum, multiplicetur is
<
lb
/>
per numerum proxime minorem. </
s
>
<
s
xml:id
="
echoid-s1619
"
xml:space
="
preserve
">Nam producti numeri medietas indicabit
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-070-02
"
xlink:href
="
note-070-02a
"
xml:space
="
preserve
">Quot com-
<
lb
/>
binationes
<
lb
/>
fieri poſ-
<
lb
/>
f
<
unsure
/>
int inter
<
lb
/>
quotcunq;
<
lb
/>
res, ſi binæ
<
lb
/>
ſ
<
unsure
/>
umantur.</
note
>
numerum combinationum, quæ fieri poſſunt inter res propoſitas. </
s
>
<
s
xml:id
="
echoid-s1620
"
xml:space
="
preserve
">Vt in propo-
<
lb
/>
ſito exemplo, quoniam ſunt quatuor qualitates primæ, ſi multiplicentur 4. </
s
>
<
s
xml:id
="
echoid-s1621
"
xml:space
="
preserve
">per
<
lb
/>
3. </
s
>
<
s
xml:id
="
echoid-s1622
"
xml:space
="
preserve
">officientur 12. </
s
>
<
s
xml:id
="
echoid-s1623
"
xml:space
="
preserve
">quare ſex combinationes inter ipſas fieri poſſunt. </
s
>
<
s
xml:id
="
echoid-s1624
"
xml:space
="
preserve
">Quòd ſi fue-
<
lb
/>
rint quinque res combinandæ, multiplicanda ſunt 5. </
s
>
<
s
xml:id
="
echoid-s1625
"
xml:space
="
preserve
">per 4. </
s
>
<
s
xml:id
="
echoid-s1626
"
xml:space
="
preserve
">Nam producti me-
<
lb
/>
dietas, nempe 10. </
s
>
<
s
xml:id
="
echoid-s1627
"
xml:space
="
preserve
">oſtendet numerum combinationum: </
s
>
<
s
xml:id
="
echoid-s1628
"
xml:space
="
preserve
">quot uidelicet Porphy
<
lb
/>
rius inter quinque prædicabilia inſtituit.</
s
>
<
s
xml:id
="
echoid-s1629
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s1630
"
xml:space
="
preserve
">
<
emph
style
="
sc
">Potest</
emph
>
hæc regula tradita in duas diſtrahi, prout ſcilicet numerus re-
<
lb
/>
rum par, uel impar fuerit. </
s
>
<
s
xml:id
="
echoid-s1631
"
xml:space
="
preserve
">Sienim numerus rerum fuerit par, multiplicandus
<
lb
/>
erit numerus proxime minor per medietatem numeri rerum: </
s
>
<
s
xml:id
="
echoid-s1632
"
xml:space
="
preserve
">Nam productus
<
lb
/>
numerus continuo oſtendet combinationum numerum. </
s
>
<
s
xml:id
="
echoid-s1633
"
xml:space
="
preserve
">Vt ſi ſcire lubet, quo@
<
lb
/>
fieri poſſint combinationes inter 10. </
s
>
<
s
xml:id
="
echoid-s1634
"
xml:space
="
preserve
">res, multiplicabuntur 9. </
s
>
<
s
xml:id
="
echoid-s1635
"
xml:space
="
preserve
">per 5. </
s
>
<
s
xml:id
="
echoid-s1636
"
xml:space
="
preserve
">ut fiant 45.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s1637
"
xml:space
="
preserve
">quot nimirum combinationes fieri inter decem res poſſunt. </
s
>
<
s
xml:id
="
echoid-s1638
"
xml:space
="
preserve
">Si uero numerus
<
lb
/>
rerum extiterit impar, multiplicandus is erit per medietatem numeri proxime
<
unsure
/>
<
lb
/>
minoris; </
s
>
<
s
xml:id
="
echoid-s1639
"
xml:space
="
preserve
">Hac enim ratione numerus procreatus indicabit, quot fieri poſſintcõ
<
lb
/>
binationes. </
s
>
<
s
xml:id
="
echoid-s1640
"
xml:space
="
preserve
">Vt ſi res fuerint 15. </
s
>
<
s
xml:id
="
echoid-s1641
"
xml:space
="
preserve
">Multiplicatis 15. </
s
>
<
s
xml:id
="
echoid-s1642
"
xml:space
="
preserve
">per 7. </
s
>
<
s
xml:id
="
echoid-s1643
"
xml:space
="
preserve
">efficietur numerus con
<
lb
/>
binationum inter ipſas, nempe 105. </
s
>
<
s
xml:id
="
echoid-s1644
"
xml:space
="
preserve
">Inter 9. </
s
>
<
s
xml:id
="
echoid-s1645
"
xml:space
="
preserve
">uero res fient combinationes 36. </
s
>
<
s
xml:id
="
echoid-s1646
"
xml:space
="
preserve
">
<
lb
/>
& </
s
>
<
s
xml:id
="
echoid-s1647
"
xml:space
="
preserve
">fic de cæteris.</
s
>
<
s
xml:id
="
echoid-s1648
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s1649
"
xml:space
="
preserve
">
<
emph
style
="
sc
">Qvod</
emph
>
ſi ſcire placuerit, quotcunque rebus propoſitis, quot fimpliciter
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-070-03
"
xlink:href
="
note-070-03a
"
xml:space
="
preserve
">Quot com-
<
lb
/>
binationes
<
lb
/>
fieri poſ-
<
lb
/>
fint inter
<
lb
/>
quotcunq;
<
lb
/>
res abſolu-
<
lb
/>
te, ſi non ſo
<
lb
/>
l
<
unsure
/>
um binæ,
<
lb
/>
ſed etiam
<
lb
/>
@ernæ, qua-
<
lb
/>
ternæ, qui-
<
lb
/>
@æ, &c. ſu-
<
lb
/>
mantur
<
unsure
/>
.</
note
>
coniunctiones ex ipſis poſſint fieri, non ſolum intelligendo, quando binæ ſu-
<
lb
/>
muntur, ut in præcedenti regula, ſed etiam quando ternæ, quaternæ, quinæ,
<
lb
/>
&</
s
>
<
s
xml:id
="
echoid-s1650
"
xml:space
="
preserve
">c. </
s
>
<
s
xml:id
="
echoid-s1651
"
xml:space
="
preserve
">hoc eſt, quotnã modis diſtinctis inter ſeſe poſſint cõparari; </
s
>
<
s
xml:id
="
echoid-s1652
"
xml:space
="
preserve
">efficietur id hac
<
lb
/>
arte, & </
s
>
<
s
xml:id
="
echoid-s1653
"
xml:space
="
preserve
">regula. </
s
>
<
s
xml:id
="
echoid-s1654
"
xml:space
="
preserve
">Accipiantur tot numeri, incipiendo ab unitate, in dupla propo@
<
lb
/>
tione, quot res ſunt propoſitæ, & </
s
>
<
s
xml:id
="
echoid-s1655
"
xml:space
="
preserve
">à ſumma omnium illorum ſubtrahatur nume
<
lb
/>
rus rerum: </
s
>
<
s
xml:id
="
echoid-s1656
"
xml:space
="
preserve
">Reliquus enim numerus indicabit, quotnam comparationes diuerſę
<
lb
/>
effici poſſint.</
s
>
<
s
xml:id
="
echoid-s1657
"
xml:space
="
preserve
">|Facile aũt habebitur ſumma quotcunq. </
s
>
<
s
xml:id
="
echoid-s1658
"
xml:space
="
preserve
">numerorum duplæ pro-
<
lb
/>
portionis ab 1. </
s
>
<
s
xml:id
="
echoid-s1659
"
xml:space
="
preserve
">incipientis, ſi ultimus numerus duplicetur, & </
s
>
<
s
xml:id
="
echoid-s1660
"
xml:space
="
preserve
">ex producto unitas
<
lb
/>
abijciatur. </
s
>
<
s
xml:id
="
echoid-s1661
"
xml:space
="
preserve
">Vt ſi lubeat ſcire ſummam horum numerorum in dupla proportio-
<
lb
/>
ne, 1. </
s
>
<
s
xml:id
="
echoid-s1662
"
xml:space
="
preserve
">2. </
s
>
<
s
xml:id
="
echoid-s1663
"
xml:space
="
preserve
">4. </
s
>
<
s
xml:id
="
echoid-s1664
"
xml:space
="
preserve
">8. </
s
>
<
s
xml:id
="
echoid-s1665
"
xml:space
="
preserve
">16. </
s
>
<
s
xml:id
="
echoid-s1666
"
xml:space
="
preserve
">32. </
s
>
<
s
xml:id
="
echoid-s1667
"
xml:space
="
preserve
">64. </
s
>
<
s
xml:id
="
echoid-s1668
"
xml:space
="
preserve
">duplicandus erit numerus ultimus 64. </
s
>
<
s
xml:id
="
echoid-s1669
"
xml:space
="
preserve
">ut fiant 128. </
s
>
<
s
xml:id
="
echoid-s1670
"
xml:space
="
preserve
">@
<
lb
/>
quibus reiecta unitate, remanent 127. </
s
>
<
s
xml:id
="
echoid-s1671
"
xml:space
="
preserve
">pro ſumma omnium illorum </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>