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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IO. BAPT. BENED.
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88
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0088
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0088
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Taurino Patauium .220. quæ quiſque confecerit.</
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<
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xml:space
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lixior. </
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eſt eiuſmodi. </
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Accipiatur
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medietas minoris numeri
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,
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nempe
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.4.
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dimi
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dio, & per .400. multiplicetur,
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per
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numerum diuidemus ſcilicet
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11. ex quo dabuntur .163. cum .7. vndecimis, quo proueniente è dimidio
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riorũ</
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itineris .200. detracto, &
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.36.
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.4. vndecimis multiplicato pro
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diuiſo
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per
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type
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dimidij itineris .200.
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primo
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.163. et .7. vndecimis
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.363. ct .7. vndecimas partes
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.16.
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cum
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.4. vndecimis, quo
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type
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pri
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mo
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type
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">ꝓueniẽti</
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, primus .180. milliaria
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type
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, quæ è .400. detracta ſupererunt .220.
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pro itinere ſecundi, qui .9. diebus iter abſoluit. </
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xml:space
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eius, qui .11. diebus appellit, multiplicabimus .11. cum .180.
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type
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per .400.
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partiemur,
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type
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paulominus, quam quinque dies, nempe .4. cum .22. horis
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et .48. minutis, quod tempus vtrique viatori inſeruiet, quandoquidem idipſum pro
<
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uenit multiplicato .220. per .9.
<
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productoque
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type
="
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">productoq́;</
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>
per .400. diuiſo.</
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</
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<
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<
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xml:space
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">Huius autem, qui à me pręſcribitur modi, ſpeculatio talis eſt. </
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>
<
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xml:space
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">Duo termini duabus
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rectis lineis æqualibus, & parallelis inter ſe
<
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>.b.p.</
var
>
et
<
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>.d.q.</
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>
ſignificentur, quæ alijs dua-
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bus
<
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>.b.d.</
var
>
et
<
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>.q.p.</
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>
<
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norm
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coniungantur
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type
="
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">coniungant̃</
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>
, quę parallelæ & æquales erunt ex .33. primi, quibus ſigni
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ficentur duo itinera. </
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<
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xml:space
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">Viator primus quidem lentior à. b in
<
var
>.d.</
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velocior à
<
var
>.q.</
var
>
in
<
var
>.p</
var
>
. </
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>
<
s
xml:id
="
echoid-s1015
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xml:space
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">Iam
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ſumatur
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punctum
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type
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">punctũ</
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medium
<
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>.q.p.</
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>
<
reg
norm
="
ſitque
"
type
="
simple
">ſitq́;</
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>
<
var
>.k.</
var
>
& ab ipſo ad
<
var
>.b.d.</
var
>
ducatur
<
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>.k.i.</
var
>
parallela
<
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>.d.q.</
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>
aut
<
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<
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>b.p.</
var
>
quod idem eſt, ex quo
<
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>.b.i.</
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>
æqualis erit
<
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>.p.k.</
var
>
ex .34. primi, hoc eſt
<
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>.q.k.</
var
>
<
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norm
="
certique
"
type
="
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">certiq́;</
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>
eri-
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mus primum viatorem
<
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>.q.p.</
var
>
in dimidio itineris
<
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>.q.k.</
var
>
occurrere non potuiſſe viatori ip
<
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ſius
<
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>.b.i.</
var
>
quandoquidem eo tempore, quo is, qui ipſius
<
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>.q.p.</
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>
mouetur per
<
var
>.q.k.</
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>
(cum ſit
<
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/>
altero velocior) qui per
<
var
>.b.d.</
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>
nondum peruenerit ad .i: Sit itaque punctum
<
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>.c.</
var
>
in quo
<
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/>
lentior reperitur, dum velocior eſt in
<
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>.k.</
var
>
ex quo certi erimus eos inter
<
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>.c.</
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>
et
<
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>.i.</
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>
ſibi in-
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uicem obuiaturos eſſe. </
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<
s
xml:id
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xml:space
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">Cogito deinde rectam lineam ductam
<
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>.k.c.</
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>
& ut ſe habet
<
var
>.i.
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c.</
var
>
ad
<
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>.c.b.</
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>
ita cogito ſe habere. u
<
unsure
/>
<
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>.k.</
var
>
ad
<
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>.k.q.</
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>
& à puncto
<
var
>.u.</
var
>
ad
<
var
>.i.</
var
>
duco
<
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>.u.i.</
var
>
quæ, vt manife
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ſtum eſt, lineam
<
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>.k.c.</
var
>
in puncto
<
var
>.e.</
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>
interſecabit, à quo cum fuerit ducta
<
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>.e.o.n.</
var
>
parallela
<
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<
var
>k.i.</
var
>
habebimus
<
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>.o.n.</
var
>
ea ſcilicet puncta, quibus occurrunt ſibijpſis, nam cum ſic ſe ha
<
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beat
<
var
>.q.k.</
var
>
ad
<
var
>.k.u.</
var
>
vt
<
var
>.b.c.</
var
>
ad
<
var
>.c.i.</
var
>
et
<
var
>.k.u.</
var
>
ad
<
var
>.k.n.</
var
>
vt
<
var
>.c.i.</
var
>
ad
<
var
>.c.o.</
var
>
ex ſimilitudine manifeſta
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triangulorum, ex æqualitate proportionum ſic ſe habebit
<
var
>.q.k.</
var
>
ad
<
var
>.k.n.</
var
>
vt
<
var
>.b.c.</
var
>
ad
<
var
>.c.o.</
var
>
<
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/>
& permutando ita
<
var
>.k.q.</
var
>
ad
<
var
>.b.c.</
var
>
vt
<
var
>.k.n.</
var
>
ad
<
var
>.c.o.</
var
>
& cum
<
var
>.q.k.</
var
>
et
<
var
>.b.c.</
var
>
ſpatia ſint tempori-
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/>
bus æqualibus confecta, itaque ſpatia
<
var
>.k.n.</
var
>
et
<
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>.c.o.</
var
>
ex communi ſcientia temporibus
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æqualibus conficientur.</
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>
</
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<
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xml:space
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preserve
">Quare rectè dicimus, ſi tot diebus à
<
var
>.b.</
var
>
in
<
var
>.d.</
var
>
aliquis peruenit, quot milliaria in di
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/>
midio temporis alterius viatoris idem conficiet? </
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>
<
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xml:id
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"
xml:space
="
preserve
">ex quo ex regula de tribus quam
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/>
primum iter
<
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>.b.c.</
var
>
cognoſcitur, quo ex dimidio itineris detracto, remanet
<
var
>.c.i.</
var
>
cogni
<
lb
/>
tus, ſed cum probauerimus
<
var
>.q.k.</
var
>
ad
<
var
>.k.n.</
var
>
hoc eſt
<
var
>.i.o.</
var
>
(cum ſint æquales inter ſe, ex .34
<
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/>
primi) ita ſe habere. vt
<
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>.b.c.</
var
>
ad
<
var
>.c.o.</
var
>
permutando ſic ſe habebit
<
var
>.q.k.</
var
>
ad
<
var
>.b.c.</
var
>
vt
<
var
>.i.o.</
var
>
ad
<
var
>.
<
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o.c.</
var
>
&
<
reg
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componendo
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type
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>
<
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>.q.k.</
var
>
et
<
var
>.b.c.</
var
>
ad
<
var
>.b.c.</
var
>
vt
<
var
>.i.c.</
var
>
ad
<
var
>.c.o.</
var
>
</
s
>
<
s
xml:id
="
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"
xml:space
="
preserve
">quare rectè dicimus ſi ſumma
<
var
>.q.
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/>
k.</
var
>
cum
<
var
>.b.c.</
var
>
dat
<
var
>.b.c.</
var
>
quid dabit
<
var
>.i.c</
var
>
? </
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>
<
s
xml:id
="
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xml:space
="
preserve
">nempe dabit
<
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>.c.o.</
var
>
quo coniuncto cum
<
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>.b.c.</
var
>
cogno-
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ſcitur
<
var
>.b.o.</
var
>
quo
<
var
>.b.o.</
var
>
detracto ex
<
var
>.b.d.</
var
>
remanet cognitus
<
var
>.o.d.</
var
>
nempe
<
var
>.q.n.</
var
>
illi æqualis
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/>
ex .34. prædicta. </
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>
<
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xml:space
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">Gratia verò
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>
patet nos rectè dicere ſi
<
var
>.b.d.</
var
>
tot diebus abſolui
<
lb
/>
tur, aut etiam
<
var
>.q.p</
var
>
: quo
<
var
>.b.o.</
var
>
aut
<
var
>.q.n.</
var
>
abſoluetur.</
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>
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<
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<
s
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xml:space
="
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">Vt autem ad ſpeculationem regulæ antiquorum deueniamus, cogitemus pri-
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mum viatorem ipſius
<
var
>.q.p.</
var
>
velociorem eo, qui per
<
var
>.b.d.</
var
>
iter agit, tanto tempore præ
<
lb
/>
tergredi
<
var
>.p.</
var
>
quanto alter
<
var
>.b.d.</
var
>
abſoluit. </
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>
<
s
xml:id
="
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xml:space
="
preserve
">Is autem ad
<
var
>.g.</
var
>
pertingat, ex quo eadem pro-
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lb
/>
portio ſpacij
<
var
>.q.g.</
var
>
ad
<
var
>.q.p.</
var
>
hoc eſt
<
var
>.b.d.</
var
>
dabitur, quæ temporis quo
<
var
>.b.d.</
var
>
abſoluitur ab </
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>
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