DelMonte, Guidubaldo
,
In duos Archimedis aequeponderantium libros Paraphrasis : scholijs illustrata
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archimedes
>
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text
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id
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N10019
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type
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main
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N14F79
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<
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="
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pagenum
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133
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tur KN FL IM, quæ diametrum BD ſecent in punctis
<
lb
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STV. oſtendendum eſt, lineas KN FL IM baſi AC ęqui
<
lb
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diſtantes eſſe. </
s
>
<
s
id
="
N14F87
">deinde diametrum BD lineas KN FL IM
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bifariam in punctis STV diuidere poſtremo lineas KN F
<
gap
/>
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lb
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IM ita diametrum BD diſpeſcere, vt poſito vno BS, linea ST
<
lb
/>
ſit tria, TV quin〈que〉; & VD ſeptem. </
s
>
<
s
id
="
N14F90
">Producantur FE KH
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lb
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ad RX. quoniam enim FR eſt æquid
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gap
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tans BD, erit AE
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arrow.to.target
n
="
marg211
"/>
<
lb
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EB, vt AR ad RD; eſt〈que〉 AE ipſi EB æqualis ergo AR i
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lb
/>
pſi RD æqualis exiſtit. </
s
>
<
s
id
="
N14F9D
">eodem què modo oſtendetur FX æ
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lb
/>
qualem eſſe XT. quandoquidem eſt FX ad XT, vt FH ad
<
lb
/>
HB. ſimiliterquè ad alteram partem, exiſtentibus LO NP i
<
lb
/>
pſi BD æquidiſtantibus, erit DO ipſi OC æqualis, & TP
<
lb
/>
ipſi PL. quod quidem eodem prorſus modo demonſtrabi
<
lb
/>
tur. </
s
>
<
s
id
="
N14FA9
">Quoniam autem AC bifariam à diametro diuiditur in
<
lb
/>
puncto D, erit DR ipſi DO æqualis, cùm vnaquæ〈que〉 ſit
<
lb
/>
dimidia ipſarum AD DC æqualium. </
s
>
<
s
id
="
N14FAF
">eſt igitur RD dimidia
<
lb
/>
ipſius AD, quæ dimidia eſt baſis AC. quod idem euenit ipſi
<
lb
/>
DO. quare BD ſeſquitertia eſt ipſius FR, & ipſius LO, ex de
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lb
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cimanona Archimedis de quadratura paraboles. </
s
>
<
s
id
="
N14FB7
">ac propterea
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eandem habet proportionem BD ad FR, quam ad LO.
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n
="
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"/>
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ſequitur FR æqualem eſſe ipſi LO. & obid FL ipſi AC
<
expan
abbr
="
æ-quidiſtantẽ
">æ
<
lb
/>
quidiſtantem</
expan
>
eſſe. </
s
>
<
s
id
="
N14FC6
">& FT ipſi RD, & TL ipſi DO ęqualem.
<
lb
/>
vnde FT ipſi TL ęqualis exiſtit. </
s
>
<
s
id
="
N14FCA
">eadem quèratione prorſus in
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lb
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portione FBL oſtendetur KN ipſi FL, ac per conſe〈que〉ns i
<
lb
/>
pſi AC ęquidiſtantem eſſe. </
s
>
<
s
id
="
N14FD0
">& KS ipſi SN æqualem exiſte
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lb
/>
re. </
s
>
<
s
id
="
N14FD4
">Producatur IG ad Z, quæ ipſam AB ſecet in 9. linea ve
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lb
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rò LO ſecet BC in
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expan
abbr
="
q;
">〈que〉</
expan
>
ductaquè MY ipſi BD æquidiſtans
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lb
/>
ipſam ſecet BC in
<
foreign
lang
="
grc
">α</
foreign
>
. & quoniam IZ eſt æquidiſtans FR, e
<
lb
/>
rit AG ad GF, ut A9 ad 9E, & AZ ad ZR. & eſt AG
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arrow.to.target
n
="
marg213
"/>
<
lb
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GF æqualis, erit igitur A9 ipſi 9E, & AZ ipſi ZR æquaiis.
<
lb
/>
Eodemquè modo oſtendetur C
<
foreign
lang
="
grc
">α</
foreign
>
ipſi
<
foreign
lang
="
grc
">α</
foreign
>
Q, & CY ipſi YO ę
<
lb
/>
qualem eſſe. </
s
>
<
s
id
="
N14FF5
">quo niam autem in portione AFB a dimidia baſi
<
lb
/>
ducta eſt LF, à puncto autem 9, hoc eſt à dimidia dimidię ba
<
lb
/>
ſis AB (eſt enim E9 dimidia ipſius AE, quæ dimidia eſt baſis
<
lb
/>
AB) ducta eſt 9I diametro æquidiſtans, erit EF ſeſquitertiai
<
lb
/>
pſius I9 pari〈que〉 ratione oſtendetur QL ſeſquitereiam eſſe i
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lb
/>
pſius M
<
foreign
lang
="
grc
">α</
foreign
>
quare vt FE ad I9, ita LQ ad M
<
foreign
lang
="
grc
">α</
foreign
>
. obſimilitudinem </
s
>
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</
archimedes
>