Benedetti, Giovanni Battista de
,
Io. Baptistae Benedicti ... Diversarvm specvlationvm mathematicarum, et physicarum liber : quarum seriem sequens pagina indicabit ; [annotated and critiqued by Guidobaldo Del Monte]
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THEOREM. ARITH.
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23
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file
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0023
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xlink:href
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<
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diuidentibus numerum diuiſibilem per proueniens, oritur numerus diui-
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dens?</
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<
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xml:space
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numerus diuiſi
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fig-0023-01
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number
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="
0023-01
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0023-01
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>
bilis, qui producitur, tam ex
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>.a.o.</
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in
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quám ex
<
var
>.a.
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e.</
var
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in
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var
>.a.o</
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>
. </
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<
s
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xml:space
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">quare ſi
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diuidens fuerit
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proue-
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niens erit, ſi veró
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>.a.e.</
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>
diuidens extiterit,
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>a.o.</
var
>
pro-
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ueniens erit futurum.</
s
>
</
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</
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<
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type
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level
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n
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<
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xml:space
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">THEOREMA.
<
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value
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">XIIII</
num
>
.</
head
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<
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<
s
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xml:space
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">HOcipſum, alia
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quoque
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type
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uia licebit ſpeculari.</
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</
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<
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<
s
xml:id
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xml:space
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">Sit linea
<
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>.a.</
var
>
<
reg
norm
="
denotans
"
type
="
context
">denotãs</
reg
>
numerum diuiſibilem, et
<
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>.o.</
var
>
primi prouenientis linea
<
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>.e.</
var
>
pri
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mi diuidentis
<
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>.u.</
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>
ſecundi prouenientis ideſt cum
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>.o.</
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pro diuidente ſumetur. </
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>
<
s
xml:id
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xml:space
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">Iam ex
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indicata definitione diuiſionis nono theoremate huius libri, dabitur proportio
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ad
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>.o.</
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prout datur
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>.e.</
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>
ad vnitatem ſignificatam li-
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nea
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>.i.</
var
>
& permutatim
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var
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ad
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>.e.</
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>
ſicut
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>.o.</
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>
ad
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>.i.</
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>
ſed
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>.a.</
var
>
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<
figure
xlink:label
="
fig-0023-02
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xlink:href
="
fig-0023-02a
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number
="
21
">
<
image
file
="
0023-02
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0023-02
"/>
</
figure
>
ad
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>.u.</
var
>
ſic ſe habet prout
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ad
<
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>.i.</
var
>
ex eadem definitio-
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ne diuiſionis,
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ſic ſe habebit
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ad
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ſicut
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ad
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e.</
var
>
vnde
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>.u.</
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>
æqualis erit
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var
>
ex .9. quinti.</
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>
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n
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<
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xml:space
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<
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value
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15
">XV</
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<
s
xml:id
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xml:space
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preserve
">VNde prouenit, vt qui velit cognoſcere cuius numeri quatuor quintæ par-
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tes, ſint duæ tertię, aut quid ſimile,
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conſultiſſime
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type
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reg
>
faciat, ſi ad unam
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="
eandemque
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type
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">eandemq;</
reg
>
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denominationem reduxerit.</
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<
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<
s
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xml:space
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">Prout in propoſito exemplo,
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cum
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denominans
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type
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<
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communis
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type
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ſit quindecim, cuius duæ ter
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tiæ ſunt
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decem
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type
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">decẽ</
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, & quatuor quintæ duodecim,
<
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communis
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type
="
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">cõmunis</
reg
>
<
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norm
="
autem
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type
="
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">autẽ</
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>
denominans .15. multipli
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candus ſit per quatuor quintas, ſcilicet duodecim, & productum diuidendum per
<
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duas tertias, hoc eſt decem, ex quo oriantur decemocto quęſitus numerus?</
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<
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<
s
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xml:space
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">Quod ad
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<
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numeratorum
"
type
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">numeratorũ</
reg
>
ad vnam & eandem denominationem attinet,
<
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/>
ea de cauſa fit quo uti poſſimus regula de tribus, quæ tribus tantummodo notis ter-
<
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minis indiget, quo quartus à prędictis dependens, inueniri poſſit, quandoquidem
<
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bini illi reſpectus, tribus terminis comprehendi
<
reg
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poſsunt
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type
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. </
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<
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xml:space
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">At quod ad multiplicatio-
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nem ſpectat denominantis
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type
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reg
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<
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="
cum
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type
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reg
>
numerante denominantis in cogniti & diui-
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ſionem producti per numerantem
<
reg
norm
="
cognitum
"
type
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">cognitũ</
reg
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illę nihil aliud ſunt, quam
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quartum
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type
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<
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terminum
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type
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<
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inuenire, ita proportionatum tertio, vt ſecundus primo.</
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<
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<
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xml:space
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<
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denotans
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type
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nume-
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rantem denominantis cogniti, qui ſigni
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<
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xlink:label
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fig-0023-03
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xlink:href
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fig-0023-03a
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number
="
22
">
<
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file
="
0023-03
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xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0023-03
"/>
</
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>
ficetur linea
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et
<
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>.e.</
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>
ſit denominantis in-
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cogniti numerans, denotati linea
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>
imò
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verò & cogniti
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>
nempe quatuor
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quintæ, Iam ſi
<
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>.o.</
var
>
cum
<
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>.e.</
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>
multiplicemus, & productum per
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>.a.</
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>
diuidemus dabitur
<
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>.u.</
var
>
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ſic ſe habens ad
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>.e.</
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>
ſicut
<
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>.o.</
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>
ad
<
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>.a.</
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>
ex .20. ſeptimi.</
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