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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tionatus .216. ad .156. vt .18. ad .13. maniteſtum eſt exijſdem, nam tam .18. quam
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13.</
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multiplicatus fuit per .12.</
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.</
head
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<
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<
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<
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xml:space
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">ſupponitur obſidio alicuius loci, vbi
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alimento ad nutriendos .10000. homines ſufficiunt pro quinque menſibus tan-
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tum, ſed quia eum locum obſidione non liberari putatur niſi .18. menſibus exactis,
<
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quæritur, quot homines eo tempore illis alimentis nutriri poſſint, hoc eſt .18.
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menſibus.</
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<
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<
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xml:space
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">Præcipitregula, vt multiplicetur primus numerus, hoc eſt hominum .10000. cum
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ſecundo, hoc eſt menſium quinque, productum verò diuidatur per .18. hoc eſt men-
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ſium, </
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<
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xml:space
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">tunc proueniet .2777. cum .7. nonis.</
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<
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<
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">Cuius operationis ratio eſt hæc, ſint exempli gratia duo hic ſubſcripta producta
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ſuperficialia
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et
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inuicem æqualia, ſed tal@ figura delineata, vt proportio
<
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>.u.
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x.</
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>
ad
<
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>.x.o.</
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ſit, vt .10000. ad quinque, & proportio
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>a.x.</
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ad
<
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>.x.o.</
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>
ſit vt .18. ad quinque,
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ct
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>.x.n.</
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>
ſit nobis ignota, quæ quidem eſt illa, quæ indagatur, ita
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norm
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quod
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type
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reg
>
vnumquodque
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iſtorum productorum ſignificabit alimentum, et
<
var
>.u.x.</
var
>
ſignificabit numerum homi-
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/>
num .10000. qui quidem homines comederent totum alimentum
<
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>.u.o.</
var
>
ſpacio tem-
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poris
<
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>.x.o.</
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>
quinque menſium, proptereà quòd
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>u.o.</
var
>
ſupponitur productum eſſe ab
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>.
<
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u.x.</
var
>
in
<
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>.x.o</
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>
. </
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tem
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pus eſſe .18. menſium, ergo
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>
ſignifi-
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cabit numerum hominum, qui eo tem-
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poris ſpacio ali poſſunt, hoc eſt
<
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>.x.a.</
var
>
ali-
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/>
mento
<
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>.n.a.</
var
>
eo quòd
<
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>.a.n.</
var
>
producitur ex
<
var
>.
<
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/>
n.x.</
var
>
in
<
var
>.a.x.</
var
>
vnde ex .15. ſexti, ſeu ex, 20.
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ſeptimi proportio
<
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>.x.u.</
var
>
ad
<
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>.x.n.</
var
>
<
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norm
="
eadem
"
type
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context
">eadẽ</
reg
>
erit,
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/>
quę
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>.a.x.</
var
>
ad
<
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>.x.o.</
var
>
quapropter rectè factum
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/>
erit accipere
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norm
="
productum
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type
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">productũ</
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>
<
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>.u.o.</
var
>
quodidem
<
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/>
eſt in quantitate, quod productum .2. n. & ipſum diuidere per
<
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>.a.x.</
var
>
vnde nobis
<
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/>
proueniat
<
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>.n.x</
var
>
.</
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>
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xml:space
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<
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value
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">CXXX</
num
>
.</
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<
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<
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xml:space
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">QVotieſcunque nobis propoſitum fuerit inuenire tertium terminum, trium ter
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minorum continuè proportionalium armonicæ proportionalitatis, quo-
<
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/>
tum duo nobis cogniti ſint, ita agemus.</
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<
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xml:space
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">Sint, exempli gratia, tres termini
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>
:
<
var
>a.g.</
var
>
et
<
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>.e.c.</
var
>
continuæ proportionalium at
<
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/>
monicæ proportionalitatis, quorum
<
var
>.q.p.</
var
>
maior et
<
var
>.a.g.</
var
>
medius ſint nobis cogniti,
<
lb
/>
cum ergo voluerimus tertium
<
var
>.e.
<
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/>
c.</
var
>
cognitum nobis eſſe: </
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hatur ex
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>.q.p.</
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>
differentia verò
<
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>.d.
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/>
p.</
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>
addatur
<
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>.q.p.</
var
>
quorum ſumma
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/>
erit
<
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>.q.o.</
var
>
cognita, qua mediante
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diuidatur productum, quod ex
<
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>.a.
<
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/>
g.</
var
>
in
<
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>.d.p.</
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>
exurgit, & proueniet no
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/>
bis
<
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>.n.g.</
var
>
hoc e@t minor differentia, eo quòd productum
<
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>.q.o.</
var
>
in
<
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>.n.g.</
var
>
æquale eſt pro- </
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>
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