Biancani, Giuseppe
,
Aristotelis loca mathematica
,
1615
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165
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009/01/165.jpg
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<
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PROPOSITIO SECVNDA.
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</
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type
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head
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<
s
id
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s.002811
">Si remi manubrium motu proprio, & nauigium, æqualia
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lb
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ſpatia pertranſierint, fieri non poterit, vt palmula mo
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ueatur: ſed veluti centrum immota manebit.</
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</
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type
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main
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<
s
id
="
s.002812
">Esto iterum remus A C, manubrium A, ſcalmus B: tantum autem ſpa
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lb
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tium conficiat nauigium; quantum motu proprio A. Dico, quod C,
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remi palmula immota manebit. </
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<
s
id
="
s.002813
">Nam ſi a loco ſuo dimota fuerit:
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lb
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ſpatium igitur permeet C D, ad poſteriora: quo quidem decurſo,
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lb
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remus A C, poſitionem rectitudinis habeat F D, ſcalmus
<
expan
abbr
="
itaq;
">itaque</
expan
>
B, tranſlatus
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lb
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erit in G. </
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>
<
s
id
="
s.002814
">Excitetur autem à puncto B, in
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abbr
="
vtramq;
">vtramque</
expan
>
partem linea E B R, ad
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id.009.01.165.1.jpg
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place
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text
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number
="
93
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rectos angulos ſuper B G, & à
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pũcto
">puncto</
expan
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A, recta A H,
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ſuper D F: itemque à puncto E, recta C E, ſuper
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E R; ipſarum verò rectarum linearum E R, &
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A H, ſectio ſit in K, ſed C F., & D F, ſit in Z, & quo
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niam A K, id ſpatium eſt, quod motu proprio re
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mi manubrium permeauit, curuilineo enim re
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ſpondeat A R, recta autem B G, id ſpatium eſt,
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quod nauigium confecit: ipſæ igitur rectæ lineæ
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H K, & B G, æquales erunt. </
s
>
<
s
id
="
s.002815
">Atqui in duobus æqui
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angulis triangulis E B C, & B A K, vel per 26.
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propoſitionem primi Euclidis, vel 4. 6. æquales
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eſſe concludes A K, & E C, rectas lineas: quapro
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pter æqualis erit E C, rectæ B G, per communem
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ſententiam: eidem autem B G, æqualis eſt E Z,
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in parallelogrammo, per 34. propoſitionem ip
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ſius primi libri: æqualis igitur erit recta E Z, re
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ctæ E C, pars toti, quod eſt impoſſibile. </
s
>
<
s
id
="
s.002816
">Et pro
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pterea immota manebit palmula C, quod erat à
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nobis oſtendendum.</
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>
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<
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type
="
head
">
<
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id
="
s.002817
">
<
emph
type
="
italics
"/>
PROPOSITIO TERTIA.
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emph.end
type
="
italics
"/>
</
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</
p
>
<
p
type
="
head
">
<
s
id
="
s.002818
">Si remi manubrium motu proprio duplum confecerit ſpa
<
lb
/>
tium, quàm nauigium, tantum prouehetur ea remiga
<
lb
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tione nauigium, quantum palmula retroceſſerit.</
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>
</
p
>
<
p
type
="
main
">
<
s
id
="
s.002819
">Remus enim incipiente motu poſitionem habeat A C, deſinente
<
lb
/>
verò rectitudinis ſitum F G. ſcalmus igitur B, propter nauigij
<
lb
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motum, ſpatium conficiet B D. </
s
>
<
s
id
="
s.002820
">Excitetur à puncto B, in
<
expan
abbr
="
vtramq;
">vtramque</
expan
>
<
lb
/>
partem perpendicularis E Z, in quam veniant a punctis A, & C,
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ad rectos angulos rectæ lineæ A E, & C Z: ſpatium autem A E, à manubrio </
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>
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</
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</
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