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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EPISTOL AE.
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379
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0379
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e
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<
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vnde angulus
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æqualis erit angulo
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portionis, cum duplus ſit angulo
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<
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medietati anguli ipſius portionis ex .19. tertij, ita quod angulus
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nobis
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cognitus erit, & ſimiliter arcus
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& conſequenter ar-
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cus
<
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>.p.g.</
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reſiduum medij circuli, & ſic
<
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eius ſinus re
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ctus, & etiam chorda
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vt dupla ſinus dimidij arcus
<
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>.
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p.g.</
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& ſic
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eius ſinus verſus, vel vt tertium latus trian
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guli orthogonij
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>.p.g.m.</
var
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vnde nobis cognita erit propor
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tio ipſius
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>.b.g.</
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(quæ dupla eſt ipſi
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>.m.g.</
var
>
) ad
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var
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& quia
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productum
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in
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æquale eſt ei, quod fit ex
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>.b.m.</
var
>
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/>
in
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var
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ex .34. tertij, quapropter nobis cognita erit pars
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<
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>q.m.</
var
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quæ cum
<
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>.p.m.</
var
>
complet totum diametrum
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>.q.p.</
var
>
vn
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lb
/>
de nobis cognita erit proportio ipſius
<
var
>.b.g.</
var
>
ad
<
var
>.q.p.</
var
>
qua
<
lb
/>
mediante cognoſcemus diametrum ſecundum partes il
<
lb
/>
las quibus propoſita ſuerit
<
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>.b.g</
var
>
.</
s
>
</
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<
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xml:space
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">Hoc autem problema non in numeris ſed in continuo ab Euclid. ponitur in .32
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.
<
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tertij.</
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">De inuentione alterius trianguli conditionati.</
head
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head
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<
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xml:space
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">QVotieſcunque etiam inuenire voluerimus triangulum aliquem, puta
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var
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æqualem triangulo
<
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>.t.</
var
>
(exempli gratia) propoſito, qui habeat angulum
<
var
>.n.</
var
>
æ-
<
lb
/>
qualem angalo
<
var
>.a.</
var
>
dato, latera vero continentia ipſum angulum
<
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>.n.</
var
>
ſint inuicem pro-
<
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/>
portionata vt
<
var
>.x.</
var
>
et
<
var
>.y.</
var
>
ita faciemus, accipiemus lineam
<
var
>.n.m.</
var
>
cuius volueris magnitu-
<
lb
/>
dinis, ſupra quam conſtituemus triangulum
<
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>.m.n.p.</
var
>
æqualem triangulo
<
var
>.t.</
var
>
hac metho-
<
lb
/>
do, hoc eſt prolungando latus
<
var
>.r.z.</
var
>
trianguli
<
var
>.t.</
var
>
quod ſit
<
var
>.r.e.</
var
>
ita vt duplum ſit ipſi
<
var
>.r.z.</
var
>
<
lb
/>
ducendo poſtea
<
var
>.c.e.</
var
>
habebimus ex .38. primi triangulum
<
var
>.t.</
var
>
eſſe dimidium totius
<
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/>
trianguli
<
var
>.r.c.e.</
var
>
deſignabimus deinde ex .44. dicti ſuperficiem
<
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var
>
parallelo
<
lb
/>
grammam
<
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norm
="
æqualemque
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type
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>
triangu
<
lb
/>
lo
<
var
>.r.c.e.</
var
>
habentem angulum
<
var
>.
<
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number
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xlink:href
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n.</
var
>
æqualem angulo
<
var
>.a.</
var
>
ducatur
<
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/>
poſtea
<
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>.p.m.</
var
>
& habebimus
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type
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<
lb
/>
gulum
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>.m.n.p.</
var
>
æqualem
<
var
>.t.</
var
>
cum
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/>
angulo
<
var
>.n.</
var
>
æquali angulo
<
var
>.a.</
var
>
pro
<
lb
/>
ducatur poſtea
<
var
>.n.p.</
var
>
ita vt
<
var
>.n.K.</
var
>
<
lb
/>
ſe habeat .ad
<
var
>.n.m.</
var
>
quemadmo
<
lb
/>
dum
<
var
>.x.</
var
>
ad
<
var
>.y.</
var
>
quod erit facilli-
<
lb
/>
mum producendo
<
var
>.n.m.</
var
>
et
<
var
>.n.
<
lb
/>
K.</
var
>
indeterminatè ſi oportuerit,
<
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</
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<
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xml:space
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">deinde eas ad æqualitatem ſe-
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can
<
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do ipſis
<
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>.x.</
var
>
et
<
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>.y.</
var
>
efficiendo
<
lb
/>
exempli gratia quod
<
var
>.n.i.</
var
>
ſit
<
lb
/>
æqualis ipſi
<
var
>.x.</
var
>
et
<
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>.n.u.</
var
>
ipſi
<
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>.y.</
var
>
du
<
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/>
cendo poſtea
<
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>.u.i.</
var
>
deinde à puncto
<
var
>.m.</
var
>
ducendo
<
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>.m.K.</
var
>
æquidiſtanter
<
var
>.u.i.</
var
>
ex .31.
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primi. </
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<
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xml:space
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">& ſic habebimus ex .4. ſexti proportionem
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>
ad
<
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>.y.</
var
>
eſſe inter
<
var
>.n.K.</
var
>
et
<
var
>.n.</
var
>
</
s
>
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