Apian, Petrus
,
Instrvmentvm Sinvvm, sev primi mobilis
Text
Text Image
Image
XML
Thumbnail overview
Document information
None
Concordance
Notes
Handwritten
Figures
Content
Thumbnails
List of thumbnails
<
1 - 10
11 - 20
21 - 30
31 - 40
41 - 50
51 - 60
61 - 70
71 - 80
81 - 90
91 - 97
>
31
32
33
34
35
36
37
38
39
40
<
1 - 10
11 - 20
21 - 30
31 - 40
41 - 50
51 - 60
61 - 70
71 - 80
81 - 90
91 - 97
>
page
|<
<
of 97
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div19
"
type
="
section
"
level
="
1
"
n
="
13
">
<
pb
file
="
0031
"
n
="
31
"
rhead
="
TABVLARVM SIVVM PER PET. APIAVM.
"/>
</
div
>
<
div
xml:id
="
echoid-div20
"
type
="
section
"
level
="
1
"
n
="
14
">
<
head
xml:id
="
echoid-head17
"
xml:space
="
preserve
">PRONVNCIATVM II.</
head
>
<
p
>
<
s
xml:id
="
echoid-s749
"
xml:space
="
preserve
">Sphæram octauam æquare cum nona & </
s
>
<
s
xml:id
="
echoid-s750
"
xml:space
="
preserve
">decima, & </
s
>
<
s
xml:id
="
echoid-s751
"
xml:space
="
preserve
">ſtellas fixas, ſimul ac
<
lb
/>
planetarum auges per hocuerificare.</
s
>
<
s
xml:id
="
echoid-s752
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s753
"
xml:space
="
preserve
">Ad æquandã octauã ſphæram cũ nona, operæpreciũ eſt principio ſcire, ꝙ initiũ octa
<
lb
/>
uæ ſphæræ incipit ꝓpe punctũ parui circuli, quẽ trepidationis ſeu titubatiõis dicimus,
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0031-01
"
xlink:href
="
note-0031-01a
"
xml:space
="
preserve
">
<
emph
style
="
it
">Quẽ in lo-</
emph
>
<
lb
/>
<
emph
style
="
it
">cũ nonæ</
emph
>
<
lb
/>
<
emph
style
="
it
">ſphæræ prĩ</
emph
>
<
lb
/>
<
emph
style
="
it
">apiũ trepi-</
emph
>
<
lb
/>
<
emph
style
="
it
">dationis re</
emph
>
<
lb
/>
<
emph
style
="
it
">ferri debent</
emph
>
</
note
>
qui´ omniũ remotiſsime uergit ad ſeptẽtrionẽ, & </
s
>
<
s
xml:id
="
echoid-s754
"
xml:space
="
preserve
">is ordinẽ motus ſuihabet uerſus ortũ
<
lb
/>
☉(sun) uſ in 90. </
s
>
<
s
xml:id
="
echoid-s755
"
xml:space
="
preserve
">gra. </
s
>
<
s
xml:id
="
echoid-s756
"
xml:space
="
preserve
">ꝗ rurſus cadit ſup eclypticã, & </
s
>
<
s
xml:id
="
echoid-s757
"
xml:space
="
preserve
">quũ medius motus 8. </
s
>
<
s
xml:id
="
echoid-s758
"
xml:space
="
preserve
">ſphæræ habuerit
<
lb
/>
90. </
s
>
<
s
xml:id
="
echoid-s759
"
xml:space
="
preserve
">(hoceſt, ut prædixi, quãdo primũ punctũ Arietis 8. </
s
>
<
s
xml:id
="
echoid-s760
"
xml:space
="
preserve
">ſphæræ directe ſteterit ſub ecly-
<
lb
/>
ptica nonæ) ibi nimi℞ fit & </
s
>
<
s
xml:id
="
echoid-s761
"
xml:space
="
preserve
">eſt æquatio maxima, ea´ ex fundamẽto peritiſsimi doctiſsi
<
lb
/>
mi´ Aſtronomi Alfonſi Regis agno ſcitur eſſe nouẽ graduũ, at ideo æquatio illa ab
<
lb
/>
initio parui circuli uſ in 90. </
s
>
<
s
xml:id
="
echoid-s762
"
xml:space
="
preserve
">gra. </
s
>
<
s
xml:id
="
echoid-s763
"
xml:space
="
preserve
">ſemꝑ accreſcit, hinc rurſus à 90. </
s
>
<
s
xml:id
="
echoid-s764
"
xml:space
="
preserve
">gra. </
s
>
<
s
xml:id
="
echoid-s765
"
xml:space
="
preserve
">decreſcit, donec
<
lb
/>
trepidatio ꝑ
<
unsure
/>
ueniatad 180. </
s
>
<
s
xml:id
="
echoid-s766
"
xml:space
="
preserve
">parui circuli, ubi iterũ æquatio nulla eſt, ſicut in eius princi-
<
lb
/>
pio. </
s
>
<
s
xml:id
="
echoid-s767
"
xml:space
="
preserve
">Et inde à 180. </
s
>
<
s
xml:id
="
echoid-s768
"
xml:space
="
preserve
">gradibus rurſus augetur & </
s
>
<
s
xml:id
="
echoid-s769
"
xml:space
="
preserve
">creſcit uſ ad gra. </
s
>
<
s
xml:id
="
echoid-s770
"
xml:space
="
preserve
">270. </
s
>
<
s
xml:id
="
echoid-s771
"
xml:space
="
preserve
">at hinc rurſus in
<
lb
/>
cipit ſe octaua ſphæra ad initiũ parui circuli ſupradictæ trepidatiõis declinare & </
s
>
<
s
xml:id
="
echoid-s772
"
xml:space
="
preserve
">flectere
<
lb
/>
unde æquatio etiã ipſa eouſ decreſcit, dũ nulla omnino ſit reliqua, fit´ hoc ita in una
<
lb
/>
reuolutiõe (quæ ferè in ſeptẽ millibus annorũ cõficitur) bis, ut æquatio ſit nulla, in princi
<
lb
/>
pio parui circuli & </
s
>
<
s
xml:id
="
echoid-s773
"
xml:space
="
preserve
">in 180. </
s
>
<
s
xml:id
="
echoid-s774
"
xml:space
="
preserve
">gra. </
s
>
<
s
xml:id
="
echoid-s775
"
xml:space
="
preserve
">fimiliter & </
s
>
<
s
xml:id
="
echoid-s776
"
xml:space
="
preserve
">in 90. </
s
>
<
s
xml:id
="
echoid-s777
"
xml:space
="
preserve
">gra. </
s
>
<
s
xml:id
="
echoid-s778
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s779
"
xml:space
="
preserve
">280. </
s
>
<
s
xml:id
="
echoid-s780
"
xml:space
="
preserve
">gra. </
s
>
<
s
xml:id
="
echoid-s781
"
xml:space
="
preserve
">omniũ maxime. </
s
>
<
s
xml:id
="
echoid-s782
"
xml:space
="
preserve
">Aequa
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0031-02
"
xlink:href
="
note-0031-02a
"
xml:space
="
preserve
">
<
emph
style
="
it
">Quandoœ</
emph
>
<
lb
/>
<
emph
style
="
it
">quatio octa</
emph
>
<
lb
/>
<
emph
style
="
it
">uœ ſbhæræ</
emph
>
<
lb
/>
<
emph
style
="
it
">ſit addenda</
emph
>
<
lb
/>
<
emph
style
="
it
">aut ſubtra-</
emph
>
<
lb
/>
<
emph
style
="
it
">benda à mc</
emph
>
<
lb
/>
<
emph
style
="
it
">dio motu.</
emph
>
</
note
>
tio prima uſ in 180. </
s
>
<
s
xml:id
="
echoid-s783
"
xml:space
="
preserve
">gra. </
s
>
<
s
xml:id
="
echoid-s784
"
xml:space
="
preserve
">addẽda eſt medio motui nonæ ſphæræ, mot9 ille augiũ & </
s
>
<
s
xml:id
="
echoid-s785
"
xml:space
="
preserve
">ſtel
<
lb
/>
larũ fixarũ in tabulis dici ſolet. </
s
>
<
s
xml:id
="
echoid-s786
"
xml:space
="
preserve
">Secũda aũt æquatio, ſi à 180. </
s
>
<
s
xml:id
="
echoid-s787
"
xml:space
="
preserve
">gra. </
s
>
<
s
xml:id
="
echoid-s788
"
xml:space
="
preserve
">uſ in 270. </
s
>
<
s
xml:id
="
echoid-s789
"
xml:space
="
preserve
">ſubtrahitur
<
lb
/>
à medio motu augium & </
s
>
<
s
xml:id
="
echoid-s790
"
xml:space
="
preserve
">ſtellarũ fixarũ, ꝓueniet & </
s
>
<
s
xml:id
="
echoid-s791
"
xml:space
="
preserve
">remanebit uerus locus 8. </
s
>
<
s
xml:id
="
echoid-s792
"
xml:space
="
preserve
">ſphæræ in
<
lb
/>
nono orbe. </
s
>
<
s
xml:id
="
echoid-s793
"
xml:space
="
preserve
">Inuenturus ergo iam æquationẽ principio ex tabulis Aſtronomicis, quære
<
lb
/>
motũ octauæ ſphæræ, ꝗ cõiuſu & </
s
>
<
s
xml:id
="
echoid-s794
"
xml:space
="
preserve
">cõſuetudine motus acceſſus & </
s
>
<
s
xml:id
="
echoid-s795
"
xml:space
="
preserve
">receſſus appellat
<
unsure
/>
. </
s
>
<
s
xml:id
="
echoid-s796
"
xml:space
="
preserve
">mo-
<
lb
/>
tum illũ reſoluito primũ in gradus, dũmodo aliq̊t integra ſigna habuerit & </
s
>
<
s
xml:id
="
echoid-s797
"
xml:space
="
preserve
">ſi minor ſit ̈
<
lb
/>
90. </
s
>
<
s
xml:id
="
echoid-s798
"
xml:space
="
preserve
">ſubtrahito eũ â 90. </
s
>
<
s
xml:id
="
echoid-s799
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s800
"
xml:space
="
preserve
">erit operationi adcõmodus, ſin aũt maior ſit ̈ 90. </
s
>
<
s
xml:id
="
echoid-s801
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s802
"
xml:space
="
preserve
">tamen mi
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0031-03
"
xlink:href
="
note-0031-03a
"
xml:space
="
preserve
">
<
emph
style
="
it
">Illud perfi-</
emph
>
<
lb
/>
<
emph
style
="
it
">acs in qua-</
emph
>
<
lb
/>
<
emph
style
="
it
">drante ſi la</
emph
>
<
lb
/>
<
emph
style
="
it
">ter aliter in</
emph
>
<
lb
/>
<
emph
style
="
it
">grediaris.</
emph
>
</
note
>
nor ̈ 180. </
s
>
<
s
xml:id
="
echoid-s803
"
xml:space
="
preserve
">ſubducito ipſum rurſus ab 180. </
s
>
<
s
xml:id
="
echoid-s804
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s805
"
xml:space
="
preserve
">remanebit numerus graduũ iuſte paratus
<
lb
/>
ad operandũ. </
s
>
<
s
xml:id
="
echoid-s806
"
xml:space
="
preserve
">Quod ſi tñ medius motus maior ſit ̈ 180. </
s
>
<
s
xml:id
="
echoid-s807
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s808
"
xml:space
="
preserve
">minor adhuc ̈ 270. </
s
>
<
s
xml:id
="
echoid-s809
"
xml:space
="
preserve
">ſubtra-
<
lb
/>
he tũc 180. </
s
>
<
s
xml:id
="
echoid-s810
"
xml:space
="
preserve
">â 270. </
s
>
<
s
xml:id
="
echoid-s811
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s812
"
xml:space
="
preserve
">hic quo reliquũ tibi manebit, q̊d ad hũc uſum cõducet. </
s
>
<
s
xml:id
="
echoid-s813
"
xml:space
="
preserve
">Simili mo-
<
lb
/>
do ſi excedat gradus 270. </
s
>
<
s
xml:id
="
echoid-s814
"
xml:space
="
preserve
">reijciẽdo illos, & </
s
>
<
s
xml:id
="
echoid-s815
"
xml:space
="
preserve
">tũc remanebit numerus ꝑ quẽ inuenit̃ æqua-
<
lb
/>
tio. </
s
>
<
s
xml:id
="
echoid-s816
"
xml:space
="
preserve
">Numero illo ſic inuẽto & </
s
>
<
s
xml:id
="
echoid-s817
"
xml:space
="
preserve
">ad operationẽ cõpoſito, quære ſinũ illius rectũ, eũ multipli-
<
lb
/>
ca cũ ſinu recto 9. </
s
>
<
s
xml:id
="
echoid-s818
"
xml:space
="
preserve
">graduũ, ꝓductũ partire in ſinũ totũ, quotientis arcũ quære, mox ꝓpo-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0031-04
"
xlink:href
="
note-0031-04a
"
xml:space
="
preserve
">
<
emph
style
="
it
">Per arealẽ</
emph
>
<
lb
/>
<
emph
style
="
it
">ingreſſum</
emph
>
<
lb
/>
<
emph
style
="
it
">in quadrãte</
emph
>
<
lb
/>
<
emph
style
="
it
">ſimile aſſe</
emph
>
<
lb
/>
<
emph
style
="
it
">queris.</
emph
>
</
note
>
ne tibi ſinũ cõ plementi huius inuẽti, ſimiliter & </
s
>
<
s
xml:id
="
echoid-s819
"
xml:space
="
preserve
">ſinũ cõplemẽti 9. </
s
>
<
s
xml:id
="
echoid-s820
"
xml:space
="
preserve
">graduũ(ſiquidem ſe-
<
lb
/>
midiameter circuli trepidatiõis ex ſuppoſitione eſt 9. </
s
>
<
s
xml:id
="
echoid-s821
"
xml:space
="
preserve
">graduũ.) </
s
>
<
s
xml:id
="
echoid-s822
"
xml:space
="
preserve
">Minorẽ ex ijs duobus nu
<
lb
/>
merũ cũ toto ſeu perfecto ſinu multiplica, productũ diuide in ſinũ maiorẽ, numeri quoti
<
lb
/>
entis arcũ quære, eo ſubtra cto à 90. </
s
>
<
s
xml:id
="
echoid-s823
"
xml:space
="
preserve
">gra. </
s
>
<
s
xml:id
="
echoid-s824
"
xml:space
="
preserve
">remanebit tibi æquatio 8. </
s
>
<
s
xml:id
="
echoid-s825
"
xml:space
="
preserve
">ſphæræ quæſita, & </
s
>
<
s
xml:id
="
echoid-s826
"
xml:space
="
preserve
">il-
<
lb
/>
la quidem addi aut ſubtrahi debet à medio motu augiũ & </
s
>
<
s
xml:id
="
echoid-s827
"
xml:space
="
preserve
">ſtellarũ fixarũ, ſecundũ quod
<
lb
/>
arguit medius mot9 acceſtus & </
s
>
<
s
xml:id
="
echoid-s828
"
xml:space
="
preserve
">receſſus 8 ſphæræ, ꝗ ſi fuerit minor gradibus 180. </
s
>
<
s
xml:id
="
echoid-s829
"
xml:space
="
preserve
">æqua
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0031-05
"
xlink:href
="
note-0031-05a
"
xml:space
="
preserve
">EXEM
<
lb
/>
PLVM</
note
>
tio addẽda eſt, ſi maior, ſubtrahẽda. </
s
>
<
s
xml:id
="
echoid-s830
"
xml:space
="
preserve
">?</
s
>
<
s
xml:id
="
echoid-s831
"
xml:space
="
preserve
">? At obſcura hæc tibi forte uidẽtur, ꝓinde lucẽ ad
<
lb
/>
demus exemplo, q̊ deinceps ſemper ſumus uſuri, at proponimus hic diem 14. </
s
>
<
s
xml:id
="
echoid-s832
"
xml:space
="
preserve
">Maij, an-
<
lb
/>
ni 1517. </
s
>
<
s
xml:id
="
echoid-s833
"
xml:space
="
preserve
">id´ in honorẽ Reuerendiſsimi patris & </
s
>
<
s
xml:id
="
echoid-s834
"
xml:space
="
preserve
">D. </
s
>
<
s
xml:id
="
echoid-s835
"
xml:space
="
preserve
">D. </
s
>
<
s
xml:id
="
echoid-s836
"
xml:space
="
preserve
">Chriſtophori à Stadio Epiſcopi
<
lb
/>
Auguſtẽſis, ꝗ eo die ad Epiſcopatũ intronizatus eſt. </
s
>
<
s
xml:id
="
echoid-s837
"
xml:space
="
preserve
">nolumus enim hic à cõi loquẽdi cõ
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0031-06
"
xlink:href
="
note-0031-06a
"
xml:space
="
preserve
">
<
emph
style
="
it
">Quo anno</
emph
>
<
lb
/>
<
emph
style
="
it
">& die R@-</
emph
>
<
lb
/>
<
emph
style
="
it
">uerẽdißim9</
emph
>
<
lb
/>
<
emph
style
="
it
">Dñs D.</
emph
>
<
lb
/>
<
emph
style
="
it
">Chriſtopho</
emph
>
<
lb
/>
<
emph
style
="
it
">rus epiſoo
<
unsure
/>
-</
emph
>
<
lb
/>
<
emph
style
="
it
">pus Augu-</
emph
>
<
lb
/>
<
emph
style
="
it
">ſtenſis & c.</
emph
>
<
lb
/>
<
emph
style
="
it
">introniza-</
emph
>
<
lb
/>
<
emph
style
="
it
">ius ſit, ad</
emph
>
<
lb
/>
<
emph
style
="
it
">qd’ tpis mo</
emph
>
<
lb
/>
<
emph
style
="
it
">mẽtũ oẽs il</
emph
>
<
lb
/>
<
emph
style
="
it
">læ propoſi</
emph
>
<
lb
/>
<
emph
style
="
it
">tiões dire-</
emph
>
<
lb
/>
<
emph
style
="
it
">ctœ ſunt.</
emph
>
</
note
>
ſuetudine diſcedere, eò maxime ꝙ nõ ſtyli elegantiã, ſed illuſtrãdæ aperiendæ´ rei ueri-
<
lb
/>
tatem ſectamur. </
s
>
<
s
xml:id
="
echoid-s838
"
xml:space
="
preserve
">Illo ipſo die inuenio mediũ motũ augiũ & </
s
>
<
s
xml:id
="
echoid-s839
"
xml:space
="
preserve
">ſtellarũ fixarũ Signũ o. </
s
>
<
s
xml:id
="
echoid-s840
"
xml:space
="
preserve
">gra.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s841
"
xml:space
="
preserve
">11. </
s
>
<
s
xml:id
="
echoid-s842
"
xml:space
="
preserve
">mi. </
s
>
<
s
xml:id
="
echoid-s843
"
xml:space
="
preserve
">11. </
s
>
<
s
xml:id
="
echoid-s844
"
xml:space
="
preserve
">ſec. </
s
>
<
s
xml:id
="
echoid-s845
"
xml:space
="
preserve
">26. </
s
>
<
s
xml:id
="
echoid-s846
"
xml:space
="
preserve
">tert. </
s
>
<
s
xml:id
="
echoid-s847
"
xml:space
="
preserve
">21. </
s
>
<
s
xml:id
="
echoid-s848
"
xml:space
="
preserve
">Et mediũ motũ 8. </
s
>
<
s
xml:id
="
echoid-s849
"
xml:space
="
preserve
">ſphæræ 1. </
s
>
<
s
xml:id
="
echoid-s850
"
xml:space
="
preserve
">ſignũ, 17. </
s
>
<
s
xml:id
="
echoid-s851
"
xml:space
="
preserve
">gra. </
s
>
<
s
xml:id
="
echoid-s852
"
xml:space
="
preserve
">11. </
s
>
<
s
xml:id
="
echoid-s853
"
xml:space
="
preserve
">mi. </
s
>
<
s
xml:id
="
echoid-s854
"
xml:space
="
preserve
">38, ſec. </
s
>
<
s
xml:id
="
echoid-s855
"
xml:space
="
preserve
">28. </
s
>
<
s
xml:id
="
echoid-s856
"
xml:space
="
preserve
">ter. </
s
>
<
s
xml:id
="
echoid-s857
"
xml:space
="
preserve
">
<
lb
/>
Inuenire iam uolens æquationẽ, primũ oĩm reſoluere debes ſignũ in 60. </
s
>
<
s
xml:id
="
echoid-s858
"
xml:space
="
preserve
">gradus (quãdo
<
lb
/>
ſignũ illud phyſicum eſt, deinde addere gra. </
s
>
<
s
xml:id
="
echoid-s859
"
xml:space
="
preserve
">17. </
s
>
<
s
xml:id
="
echoid-s860
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s861
"
xml:space
="
preserve
">erũt gra. </
s
>
<
s
xml:id
="
echoid-s862
"
xml:space
="
preserve
">77. </
s
>
<
s
xml:id
="
echoid-s863
"
xml:space
="
preserve
">ijs ſubtractis à 90. </
s
>
<
s
xml:id
="
echoid-s864
"
xml:space
="
preserve
">mane
<
lb
/>
bunt 12. </
s
>
<
s
xml:id
="
echoid-s865
"
xml:space
="
preserve
">gra. </
s
>
<
s
xml:id
="
echoid-s866
"
xml:space
="
preserve
">48. </
s
>
<
s
xml:id
="
echoid-s867
"
xml:space
="
preserve
">mi. </
s
>
<
s
xml:id
="
echoid-s868
"
xml:space
="
preserve
">ſinus horũ graduũ & </
s
>
<
s
xml:id
="
echoid-s869
"
xml:space
="
preserve
">minutorũ eſt 22154. </
s
>
<
s
xml:id
="
echoid-s870
"
xml:space
="
preserve
">hunc ſinum ſi duxero in ſi
<
lb
/>
num 9. </
s
>
<
s
xml:id
="
echoid-s871
"
xml:space
="
preserve
">graduũ, ſcilicet 15643. </
s
>
<
s
xml:id
="
echoid-s872
"
xml:space
="
preserve
">reſultabunt inde 346555022. </
s
>
<
s
xml:id
="
echoid-s873
"
xml:space
="
preserve
">producto illo diuiſo in ſinũ
<
lb
/>
totum, qui eſt 100000. </
s
>
<
s
xml:id
="
echoid-s874
"
xml:space
="
preserve
">ex ea diuiſione prouenient. </
s
>
<
s
xml:id
="
echoid-s875
"
xml:space
="
preserve
">3466. </
s
>
<
s
xml:id
="
echoid-s876
"
xml:space
="
preserve
">arcus illius eſt 2. </
s
>
<
s
xml:id
="
echoid-s877
"
xml:space
="
preserve
">gra. </
s
>
<
s
xml:id
="
echoid-s878
"
xml:space
="
preserve
">Poſtea ad
<
lb
/>
ſume cõplementũ eius, hoc eſt, reſiduũ ad 90. </
s
>
<
s
xml:id
="
echoid-s879
"
xml:space
="
preserve
">gra. </
s
>
<
s
xml:id
="
echoid-s880
"
xml:space
="
preserve
">ſ. </
s
>
<
s
xml:id
="
echoid-s881
"
xml:space
="
preserve
">88. </
s
>
<
s
xml:id
="
echoid-s882
"
xml:space
="
preserve
">ſinus ip ſius erit 99939. </
s
>
<
s
xml:id
="
echoid-s883
"
xml:space
="
preserve
">hinc adhuc
<
lb
/>
propone ſinũ cõplementi 9. </
s
>
<
s
xml:id
="
echoid-s884
"
xml:space
="
preserve
">graduum. </
s
>
<
s
xml:id
="
echoid-s885
"
xml:space
="
preserve
">ſ. </
s
>
<
s
xml:id
="
echoid-s886
"
xml:space
="
preserve
">81. </
s
>
<
s
xml:id
="
echoid-s887
"
xml:space
="
preserve
">gra. </
s
>
<
s
xml:id
="
echoid-s888
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s889
"
xml:space
="
preserve
">erit 98768. </
s
>
<
s
xml:id
="
echoid-s890
"
xml:space
="
preserve
">ex ijs duobus ſinum adſu-
<
lb
/>
me minorem, eũ ducin ſinum perfectũ, ꝓductũ diuide in maiorẽ, qui eſt 99939. </
s
>
<
s
xml:id
="
echoid-s891
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s892
"
xml:space
="
preserve
">proue
<
lb
/>
nient in quotiente 98828. </
s
>
<
s
xml:id
="
echoid-s893
"
xml:space
="
preserve
">arcus illius erit 81. </
s
>
<
s
xml:id
="
echoid-s894
"
xml:space
="
preserve
">gra. </
s
>
<
s
xml:id
="
echoid-s895
"
xml:space
="
preserve
">13. </
s
>
<
s
xml:id
="
echoid-s896
"
xml:space
="
preserve
">mi. </
s
>
<
s
xml:id
="
echoid-s897
"
xml:space
="
preserve
">Complementum eius 8. </
s
>
<
s
xml:id
="
echoid-s898
"
xml:space
="
preserve
">gra.</
s
>
<
s
xml:id
="
echoid-s899
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
</
text
>
</
echo
>