Vitruvius
,
De architectura libri decem
,
1567
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 - 120
121 - 150
151 - 180
181 - 210
211 - 240
241 - 270
271 - 300
301 - 330
331 - 360
361 - 390
391 - 412
>
Scan
Original
61
29
62
30
63
31
64
32
65
33
66
34
67
35
68
36
69
37
70
38
71
39
72
40
73
41
74
42
75
43
76
44
77
45
78
46
79
47
80
48
81
49
82
50
83
51
84
52
85
53
86
54
87
55
88
56
89
57
90
58
<
1 - 30
31 - 60
61 - 90
91 - 120
121 - 150
151 - 180
181 - 210
211 - 240
241 - 270
271 - 300
301 - 330
331 - 360
361 - 390
391 - 412
>
page
|<
<
(81)
of 412
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div1
"
type
="
section
"
level
="
1
"
n
="
1
">
<
div
xml:id
="
echoid-div276
"
type
="
section
"
level
="
2
"
n
="
61
">
<
p
style
="
it
">
<
s
xml:id
="
echoid-s7573
"
xml:space
="
preserve
">
<
pb
o
="
81
"
file
="
514.01.113
"
n
="
113
"
rhead
="
TERTIVS.
"/>
Vtriuſque generis proprium eſt, ut ſecundum collationem , comparationemq́; </
s
>
<
s
xml:id
="
echoid-s7574
"
xml:space
="
preserve
">res æquales, uel inæquales´ mutuo
<
lb
/>
dicantur, nam res omnis alteri comparata uel æqualis illi eſſe cernitur, uel inæqualis, nam uel tanta est, quan-
<
lb
/>
ta eſt alia, uel maior, uel minor. </
s
>
<
s
xml:id
="
echoid-s7575
"
xml:space
="
preserve
">Proportio igitur eſt ex earum numero, quæ per ſe nec ſunt, nec intelliguntur ,
<
lb
/>
ſed id, quod ſunt ad aliud referuntur. </
s
>
<
s
xml:id
="
echoid-s7576
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s7577
"
xml:space
="
preserve
">ex proportionibus aliæ inter res æquales, aliæ inter inæquales cadent.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s7578
"
xml:space
="
preserve
">Vnde proportio est determinata rerum duarum, quæ ſub eodem genere continentur, habitudo. </
s
>
<
s
xml:id
="
echoid-s7579
"
xml:space
="
preserve
">Determinata in-
<
lb
/>
quam non ad nos relata, neque in ſe certa , ſed huiuſmodi , ut alia eſſe non poßit. </
s
>
<
s
xml:id
="
echoid-s7580
"
xml:space
="
preserve
">Sub eodem autem genere,
<
lb
/>
quia nemo lineam maiorem, uel minorem, uel æqualem ſuperficiei dixerit, ſed alteri lineæ, nec ſuperficiem cor-
<
lb
/>
pori, ſed alteri plano comparabit. </
s
>
<
s
xml:id
="
echoid-s7581
"
xml:space
="
preserve
">cum ergo proportio in quantitate ſit , duplexq́; </
s
>
<
s
xml:id
="
echoid-s7582
"
xml:space
="
preserve
">ſit quantitatis genus ( ut di-
<
lb
/>
xi ) certe tam in menſuris, quàm in numeris, ac etiam in his rebus, quæ ex menſuris, & </
s
>
<
s
xml:id
="
echoid-s7583
"
xml:space
="
preserve
">numeris componun-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-514.01.113-01
"
xlink:href
="
note-514.01.113-01a
"
xml:space
="
preserve
">10</
note
>
tur, inuenietur, Quæ igitur ad menſuras proportio pertinet, Geometrarum propria eſt; </
s
>
<
s
xml:id
="
echoid-s7584
"
xml:space
="
preserve
">quæ ad numeros, eorum
<
lb
/>
qui numer andi ſcientiam profitentur; </
s
>
<
s
xml:id
="
echoid-s7585
"
xml:space
="
preserve
">quæ ad utrumque genus Muſicis accommodatur, harmonicaq́; </
s
>
<
s
xml:id
="
echoid-s7586
"
xml:space
="
preserve
">nuncupa-
<
lb
/>
tur. </
s
>
<
s
xml:id
="
echoid-s7587
"
xml:space
="
preserve
">Nos modo de ſimplicibus illis dicemus , ſed libro quinto de permixta illa ex utriſque generibus , cum de
<
lb
/>
muſica ratione tractabimus copioſe diſſeremus. </
s
>
<
s
xml:id
="
echoid-s7588
"
xml:space
="
preserve
">Magnitudines, & </
s
>
<
s
xml:id
="
echoid-s7589
"
xml:space
="
preserve
">numeri inter ſe comparati, aut pares,
<
lb
/>
æqualesq́; </
s
>
<
s
xml:id
="
echoid-s7590
"
xml:space
="
preserve
">ſunt, aut ſe ſe mutuo ſuccedunt . </
s
>
<
s
xml:id
="
echoid-s7591
"
xml:space
="
preserve
">Pares, æqualesq́; </
s
>
<
s
xml:id
="
echoid-s7592
"
xml:space
="
preserve
">intelligo, cum nihil amplius uni ſit, quàm alteri.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s7593
"
xml:space
="
preserve
">impares, & </
s
>
<
s
xml:id
="
echoid-s7594
"
xml:space
="
preserve
">ſe ſe eccedentes, cum quid maius, aut minus in eis eſſe dignoſcitur. </
s
>
<
s
xml:id
="
echoid-s7595
"
xml:space
="
preserve
">Aequalium, pariumq́; </
s
>
<
s
xml:id
="
echoid-s7596
"
xml:space
="
preserve
">nullum
<
lb
/>
aliud genus eſt, nam cum res inter ſe æquabili ratione conferuntur , unius formæ comparatio inter eas cadit. </
s
>
<
s
xml:id
="
echoid-s7597
"
xml:space
="
preserve
">
<
lb
/>
Inæqualium plura ſunt genera, ac totidem, quotres una altera maior eſſe potest . </
s
>
<
s
xml:id
="
echoid-s7598
"
xml:space
="
preserve
">maiorem intelligo contine-
<
lb
/>
re minorem integram, uel amplius aliquid. </
s
>
<
s
xml:id
="
echoid-s7599
"
xml:space
="
preserve
">Inæqualitatis igitur proportio, aut ſimplex est, aut compoſita. </
s
>
<
s
xml:id
="
echoid-s7600
"
xml:space
="
preserve
">ſim
<
lb
/>
plex es
<
unsure
/>
t, cum quod maius est, minus continet uel pluribus uicibus. </
s
>
<
s
xml:id
="
echoid-s7601
"
xml:space
="
preserve
">ſi pluribus uicibus ita , ut ex inte-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-514.01.113-02
"
xlink:href
="
note-514.01.113-02a
"
xml:space
="
preserve
">20</
note
>
gro nihil ſuperſit, tunc proportio ea conficitur, quæ multiplex nominatur. </
s
>
<
s
xml:id
="
echoid-s7602
"
xml:space
="
preserve
">Ita quatuor continet duo bis . </
s
>
<
s
xml:id
="
echoid-s7603
"
xml:space
="
preserve
">Sex
<
lb
/>
continet duo ter. </
s
>
<
s
xml:id
="
echoid-s7604
"
xml:space
="
preserve
">Octo duo quater. </
s
>
<
s
xml:id
="
echoid-s7605
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s7606
"
xml:space
="
preserve
">nihil amplius. </
s
>
<
s
xml:id
="
echoid-s7607
"
xml:space
="
preserve
">ſi una uice quod plus eſt continet minus, uel unã inſuper præ-
<
lb
/>
ter integram partem eius continet, uel plures. </
s
>
<
s
xml:id
="
echoid-s7608
"
xml:space
="
preserve
">ſi unam, uel illa est dimidium, uel tertia pars, uel quarta, & </
s
>
<
s
xml:id
="
echoid-s7609
"
xml:space
="
preserve
">ita
<
lb
/>
in infinitum. </
s
>
<
s
xml:id
="
echoid-s7610
"
xml:space
="
preserve
">Atque hæc proportio ſuperparticularis nominatur. </
s
>
<
s
xml:id
="
echoid-s7611
"
xml:space
="
preserve
">ſeſquialtera ſi dimidium, ſeſquitertia, ſi ter-
<
lb
/>
tiam partem, ſeſquiquarta ſi quartam continet, & </
s
>
<
s
xml:id
="
echoid-s7612
"
xml:space
="
preserve
">ita in infinitum. </
s
>
<
s
xml:id
="
echoid-s7613
"
xml:space
="
preserve
">Si vero maius continet minus integre , & </
s
>
<
s
xml:id
="
echoid-s7614
"
xml:space
="
preserve
">
<
lb
/>
aliquas eius partes, tunc ſuperpartiens nominatur illarum comparatio . </
s
>
<
s
xml:id
="
echoid-s7615
"
xml:space
="
preserve
">aliquas autem partes intelligo, non
<
lb
/>
ut aiunt numerantes , ſed ex illis conſtantes. </
s
>
<
s
xml:id
="
echoid-s7616
"
xml:space
="
preserve
">Pars enim numerans dicitur ea, quæ integram rem certis uicibus
<
lb
/>
deſumpta conſtituit. </
s
>
<
s
xml:id
="
echoid-s7617
"
xml:space
="
preserve
">Cuiuſmodi duo pars est numerans ſenarium, nam ter duo conſtituunt ſex . </
s
>
<
s
xml:id
="
echoid-s7618
"
xml:space
="
preserve
">quatuor item
<
lb
/>
numerat. </
s
>
<
s
xml:id
="
echoid-s7619
"
xml:space
="
preserve
">12. </
s
>
<
s
xml:id
="
echoid-s7620
"
xml:space
="
preserve
">nam ter quatuor duodecim efficiunt . </
s
>
<
s
xml:id
="
echoid-s7621
"
xml:space
="
preserve
">huiuſmodi partes quotas etiam appellare ſolent . </
s
>
<
s
xml:id
="
echoid-s7622
"
xml:space
="
preserve
">ſuper-
<
lb
/>
partiens igitur ratio eſt quotiens maius, minus ſemel continet , & </
s
>
<
s
xml:id
="
echoid-s7623
"
xml:space
="
preserve
">partem ipſius minoris non quotam, & </
s
>
<
s
xml:id
="
echoid-s7624
"
xml:space
="
preserve
">nu-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-514.01.113-03
"
xlink:href
="
note-514.01.113-03a
"
xml:space
="
preserve
">30</
note
>
merantem, ſed ex illis quotis, & </
s
>
<
s
xml:id
="
echoid-s7625
"
xml:space
="
preserve
">numerantibus prouenientem. </
s
>
<
s
xml:id
="
echoid-s7626
"
xml:space
="
preserve
">ſic quinque continet tres ſemel , & </
s
>
<
s
xml:id
="
echoid-s7627
"
xml:space
="
preserve
">duas eius
<
lb
/>
partes, unde appellatur proportio bipartiens tertias, ſeptem continet quatuor, & </
s
>
<
s
xml:id
="
echoid-s7628
"
xml:space
="
preserve
">tres quartas, & </
s
>
<
s
xml:id
="
echoid-s7629
"
xml:space
="
preserve
">appellatur
<
lb
/>
proportio tripartiens quartas, & </
s
>
<
s
xml:id
="
echoid-s7630
"
xml:space
="
preserve
">nouem continet quinque, & </
s
>
<
s
xml:id
="
echoid-s7631
"
xml:space
="
preserve
">quatuor eius quintas, & </
s
>
<
s
xml:id
="
echoid-s7632
"
xml:space
="
preserve
">appellatur proportio
<
lb
/>
quadripartiens quintas, atque ita in infinitum. </
s
>
<
s
xml:id
="
echoid-s7633
"
xml:space
="
preserve
">Simplices igitur comparationes hæ ſunt, multiplex, ſupraparti-
<
lb
/>
cularis, ſuprapartiens. </
s
>
<
s
xml:id
="
echoid-s7634
"
xml:space
="
preserve
">Compoſitæ autem vim, & </
s
>
<
s
xml:id
="
echoid-s7635
"
xml:space
="
preserve
">naturam ſimplicium tenent , nam vel multiplex eſt, & </
s
>
<
s
xml:id
="
echoid-s7636
"
xml:space
="
preserve
">ſu-
<
lb
/>
praparticularis, vel multiplex, & </
s
>
<
s
xml:id
="
echoid-s7637
"
xml:space
="
preserve
">ſuprapartiens. </
s
>
<
s
xml:id
="
echoid-s7638
"
xml:space
="
preserve
">quatenus multiplex maius continebit rem integram pluri-
<
lb
/>
bus uicibus; </
s
>
<
s
xml:id
="
echoid-s7639
"
xml:space
="
preserve
">quatenus ſupra particularis, continebit amplius, aliquam eius partem, quotam ſcilicet , & </
s
>
<
s
xml:id
="
echoid-s7640
"
xml:space
="
preserve
">nu-
<
lb
/>
merantem; </
s
>
<
s
xml:id
="
echoid-s7641
"
xml:space
="
preserve
">quatenus ſupraparticularis continebit amplius partem non quotam , & </
s
>
<
s
xml:id
="
echoid-s7642
"
xml:space
="
preserve
">numerantem, ſed ex quo-
<
lb
/>
tis, & </
s
>
<
s
xml:id
="
echoid-s7643
"
xml:space
="
preserve
">numerantibus prouenientem. </
s
>
<
s
xml:id
="
echoid-s7644
"
xml:space
="
preserve
">multiplex ſupraparticularis eſt inter decem, & </
s
>
<
s
xml:id
="
echoid-s7645
"
xml:space
="
preserve
">quatuor, nam decem con-
<
lb
/>
tinet quatuor bis, unde multiplicis nomen ſortitur , & </
s
>
<
s
xml:id
="
echoid-s7646
"
xml:space
="
preserve
">dimidium , vnde ſeſquialtera nuncupatur, quare du-
<
lb
/>
plex ſeſquialtera dicetur. </
s
>
<
s
xml:id
="
echoid-s7647
"
xml:space
="
preserve
">multiplex ſuprapartiens est inter octo, & </
s
>
<
s
xml:id
="
echoid-s7648
"
xml:space
="
preserve
">tria, nam octo continet tria bis, unde mul-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-514.01.113-04
"
xlink:href
="
note-514.01.113-04a
"
xml:space
="
preserve
">40</
note
>
tiplicis ratio naſcitur, & </
s
>
<
s
xml:id
="
echoid-s7649
"
xml:space
="
preserve
">duo, unde ſuprapartiens nominatur, atque ita inter octo & </
s
>
<
s
xml:id
="
echoid-s7650
"
xml:space
="
preserve
">tria erit proportio dupla
<
lb
/>
bipartiens tertias . </
s
>
<
s
xml:id
="
echoid-s7651
"
xml:space
="
preserve
">Oriuntur autem proportiones e numeris certo quodam ordine diſpoſitis , & </
s
>
<
s
xml:id
="
echoid-s7652
"
xml:space
="
preserve
">collocatis. </
s
>
<
s
xml:id
="
echoid-s7653
"
xml:space
="
preserve
">ac
<
lb
/>
primum ſupraparticulares rationes ita fient. </
s
>
<
s
xml:id
="
echoid-s7654
"
xml:space
="
preserve
">Diſpone a ternario numeros ſe ſe ut natura fert, conſequentes. </
s
>
<
s
xml:id
="
echoid-s7655
"
xml:space
="
preserve
">at-
<
lb
/>
que eo in primo , & </
s
>
<
s
xml:id
="
echoid-s7656
"
xml:space
="
preserve
">ſuperiori ordine collocabis , ſubſcribes eoſdem a binario natura ſe conſequentes quem-
<
lb
/>
admodum uides.</
s
>
<
s
xml:id
="
echoid-s7657
"
xml:space
="
preserve
"/>
</
p
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s7658
"
xml:space
="
preserve
">3.</
s
>
<
s
xml:id
="
echoid-s7659
"
xml:space
="
preserve
">#4.</
s
>
<
s
xml:id
="
echoid-s7660
"
xml:space
="
preserve
">#5.</
s
>
<
s
xml:id
="
echoid-s7661
"
xml:space
="
preserve
">#6.</
s
>
<
s
xml:id
="
echoid-s7662
"
xml:space
="
preserve
">#7.</
s
>
<
s
xml:id
="
echoid-s7663
"
xml:space
="
preserve
">#8.</
s
>
<
s
xml:id
="
echoid-s7664
"
xml:space
="
preserve
">#9.</
s
>
<
s
xml:id
="
echoid-s7665
"
xml:space
="
preserve
">#10.</
s
>
<
s
xml:id
="
echoid-s7666
"
xml:space
="
preserve
">#11.</
s
>
<
s
xml:id
="
echoid-s7667
"
xml:space
="
preserve
">#12.</
s
>
<
s
xml:id
="
echoid-s7668
"
xml:space
="
preserve
">#hi ſunt numeri a quibus incipit comparatio.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s7669
"
xml:space
="
preserve
">2.</
s
>
<
s
xml:id
="
echoid-s7670
"
xml:space
="
preserve
">#3.</
s
>
<
s
xml:id
="
echoid-s7671
"
xml:space
="
preserve
">#4.</
s
>
<
s
xml:id
="
echoid-s7672
"
xml:space
="
preserve
">#5.</
s
>
<
s
xml:id
="
echoid-s7673
"
xml:space
="
preserve
">#6.</
s
>
<
s
xml:id
="
echoid-s7674
"
xml:space
="
preserve
">#7.</
s
>
<
s
xml:id
="
echoid-s7675
"
xml:space
="
preserve
">#8.</
s
>
<
s
xml:id
="
echoid-s7676
"
xml:space
="
preserve
">#9.</
s
>
<
s
xml:id
="
echoid-s7677
"
xml:space
="
preserve
">#10.</
s
>
<
s
xml:id
="
echoid-s7678
"
xml:space
="
preserve
">#11.</
s
>
<
s
xml:id
="
echoid-s7679
"
xml:space
="
preserve
">#hi ſunt numeri in quos deſinit comparatio , & </
s
>
<
s
xml:id
="
echoid-s7680
"
xml:space
="
preserve
">ad
<
lb
/>
quos ſuperiores ſe habent in ſupraparticulari proportione, nam. </
s
>
<
s
xml:id
="
echoid-s7681
"
xml:space
="
preserve
">3. </
s
>
<
s
xml:id
="
echoid-s7682
"
xml:space
="
preserve
">ad. </
s
>
<
s
xml:id
="
echoid-s7683
"
xml:space
="
preserve
">2. </
s
>
<
s
xml:id
="
echoid-s7684
"
xml:space
="
preserve
">est ſeſquialtera. </
s
>
<
s
xml:id
="
echoid-s7685
"
xml:space
="
preserve
">4. </
s
>
<
s
xml:id
="
echoid-s7686
"
xml:space
="
preserve
">ad. </
s
>
<
s
xml:id
="
echoid-s7687
"
xml:space
="
preserve
">3. </
s
>
<
s
xml:id
="
echoid-s7688
"
xml:space
="
preserve
">
<
lb
/>
ſeſquitertia. </
s
>
<
s
xml:id
="
echoid-s7689
"
xml:space
="
preserve
">5. </
s
>
<
s
xml:id
="
echoid-s7690
"
xml:space
="
preserve
">ad. </
s
>
<
s
xml:id
="
echoid-s7691
"
xml:space
="
preserve
">4. </
s
>
<
s
xml:id
="
echoid-s7692
"
xml:space
="
preserve
">ſeſquiquarta, & </
s
>
<
s
xml:id
="
echoid-s7693
"
xml:space
="
preserve
">ita in infinitum. </
s
>
<
s
xml:id
="
echoid-s7694
"
xml:space
="
preserve
">Superpartiens oritur imparibus numeris ſua ſe-
<
lb
/>
rie ſuprapoſitis, modo a quinario incipias, & </
s
>
<
s
xml:id
="
echoid-s7695
"
xml:space
="
preserve
">a numeris naturali ordine, ſi conſequentibus a ternario in
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-514.01.113-05
"
xlink:href
="
note-514.01.113-05a
"
xml:space
="
preserve
">50</
note
>
hunc modum.</
s
>
<
s
xml:id
="
echoid-s7696
"
xml:space
="
preserve
"/>
</
p
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s7697
"
xml:space
="
preserve
">5.</
s
>
<
s
xml:id
="
echoid-s7698
"
xml:space
="
preserve
">#7.</
s
>
<
s
xml:id
="
echoid-s7699
"
xml:space
="
preserve
">#9.</
s
>
<
s
xml:id
="
echoid-s7700
"
xml:space
="
preserve
">#11.</
s
>
<
s
xml:id
="
echoid-s7701
"
xml:space
="
preserve
">#13.</
s
>
<
s
xml:id
="
echoid-s7702
"
xml:space
="
preserve
">#15.</
s
>
<
s
xml:id
="
echoid-s7703
"
xml:space
="
preserve
">#17.</
s
>
<
s
xml:id
="
echoid-s7704
"
xml:space
="
preserve
">#19.</
s
>
<
s
xml:id
="
echoid-s7705
"
xml:space
="
preserve
">#21.</
s
>
<
s
xml:id
="
echoid-s7706
"
xml:space
="
preserve
">#numeri a quibus incipit comparatio.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s7707
"
xml:space
="
preserve
">3.</
s
>
<
s
xml:id
="
echoid-s7708
"
xml:space
="
preserve
">#4.</
s
>
<
s
xml:id
="
echoid-s7709
"
xml:space
="
preserve
">#5.</
s
>
<
s
xml:id
="
echoid-s7710
"
xml:space
="
preserve
">#6.</
s
>
<
s
xml:id
="
echoid-s7711
"
xml:space
="
preserve
">#7.</
s
>
<
s
xml:id
="
echoid-s7712
"
xml:space
="
preserve
">#8.</
s
>
<
s
xml:id
="
echoid-s7713
"
xml:space
="
preserve
">#9.</
s
>
<
s
xml:id
="
echoid-s7714
"
xml:space
="
preserve
">#10.</
s
>
<
s
xml:id
="
echoid-s7715
"
xml:space
="
preserve
">#11.</
s
>
<
s
xml:id
="
echoid-s7716
"
xml:space
="
preserve
">#numeri in quos deſinit comparatio. </
s
>
<
s
xml:id
="
echoid-s7717
"
xml:space
="
preserve
">atque ita. </
s
>
<
s
xml:id
="
echoid-s7718
"
xml:space
="
preserve
">5. </
s
>
<
s
xml:id
="
echoid-s7719
"
xml:space
="
preserve
">
<
lb
/>
ad 3. </
s
>
<
s
xml:id
="
echoid-s7720
"
xml:space
="
preserve
">bipartiens tertias. </
s
>
<
s
xml:id
="
echoid-s7721
"
xml:space
="
preserve
">7. </
s
>
<
s
xml:id
="
echoid-s7722
"
xml:space
="
preserve
">ad 4. </
s
>
<
s
xml:id
="
echoid-s7723
"
xml:space
="
preserve
">tripartiens quartas. </
s
>
<
s
xml:id
="
echoid-s7724
"
xml:space
="
preserve
">9. </
s
>
<
s
xml:id
="
echoid-s7725
"
xml:space
="
preserve
">ad. </
s
>
<
s
xml:id
="
echoid-s7726
"
xml:space
="
preserve
">5, quadripartiens quintas, & </
s
>
<
s
xml:id
="
echoid-s7727
"
xml:space
="
preserve
">ſic de
<
lb
/>
ſingulis. </
s
>
<
s
xml:id
="
echoid-s7728
"
xml:space
="
preserve
">quod ſi ſuperiorem imparium numerorum ordinem a quinario orſus adſcribes, inferius autem a bina-
<
lb
/>
rio natur ali ordine præcedentes numeros ſubſcribes , differentias multiplicis ſupraparticularis , ſub ratione
<
lb
/>
dupla, content as conficies.</
s
>
<
s
xml:id
="
echoid-s7729
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s7730
"
xml:space
="
preserve
">5.</
s
>
<
s
xml:id
="
echoid-s7731
"
xml:space
="
preserve
">#7.</
s
>
<
s
xml:id
="
echoid-s7732
"
xml:space
="
preserve
">#9.</
s
>
<
s
xml:id
="
echoid-s7733
"
xml:space
="
preserve
">#11.</
s
>
<
s
xml:id
="
echoid-s7734
"
xml:space
="
preserve
">#13.</
s
>
<
s
xml:id
="
echoid-s7735
"
xml:space
="
preserve
">#15.</
s
>
<
s
xml:id
="
echoid-s7736
"
xml:space
="
preserve
">#17.</
s
>
<
s
xml:id
="
echoid-s7737
"
xml:space
="
preserve
">#19.</
s
>
<
s
xml:id
="
echoid-s7738
"
xml:space
="
preserve
">#21.</
s
>
<
s
xml:id
="
echoid-s7739
"
xml:space
="
preserve
"/>
</
p
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s7740
"
xml:space
="
preserve
">2.</
s
>
<
s
xml:id
="
echoid-s7741
"
xml:space
="
preserve
">#3.</
s
>
<
s
xml:id
="
echoid-s7742
"
xml:space
="
preserve
">#4.</
s
>
<
s
xml:id
="
echoid-s7743
"
xml:space
="
preserve
">#5.</
s
>
<
s
xml:id
="
echoid-s7744
"
xml:space
="
preserve
">#6.</
s
>
<
s
xml:id
="
echoid-s7745
"
xml:space
="
preserve
">#7.</
s
>
<
s
xml:id
="
echoid-s7746
"
xml:space
="
preserve
">#8.</
s
>
<
s
xml:id
="
echoid-s7747
"
xml:space
="
preserve
">#9.</
s
>
<
s
xml:id
="
echoid-s7748
"
xml:space
="
preserve
">#10. </
s
>
<
s
xml:id
="
echoid-s7749
"
xml:space
="
preserve
">Siaſeptenario incœperis per impares procedendo,
<
lb
/>
& </
s
>
<
s
xml:id
="
echoid-s7750
"
xml:space
="
preserve
">eandem in inferiori ſerie ſucceſſionem a binario ſeruaueris, multiplicis ſuperparticularis formas , ſub ratio-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-514.01.113-06
"
xlink:href
="
note-514.01.113-06a
"
xml:space
="
preserve
">60</
note
>
ne tripla constitues.</
s
>
<
s
xml:id
="
echoid-s7751
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
</
div
>
</
text
>
</
echo
>
