Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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79
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&
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LD.
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Seca autem pro lubitu vel inter puncta
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K
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&
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H,
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I
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&
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L,
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vel extra eadem: dein age
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RS
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ſecantem tangentes in
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A
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&
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P,
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& erunt
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A
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&
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P
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puncta contactuum. </
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<
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>Nam ſi
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A
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&
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P
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<
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ſupponantur eſſe puncta contactuum alicubi in tangentibus ſi
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ta; & per punctorum
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H, I, K, L
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quodvis
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I,
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in tangente al
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terutra
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HI
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ſitum, agatur recta
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IY
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tangenti alteri
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KL
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paral
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lela, quæ occurrat curvæ in
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X
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&
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Y,
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& in ea ſumatur
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IZ
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me
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dia proportionalis inter
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IX
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&
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IY:
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erit, ex Conicis, rectangulum
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XIY
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ſeu
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IZ quad.
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ad
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LP quad.
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ut rectangulum
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CID
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ad rectan
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gulum
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type
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CLD,
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id eſt (per conſtructionem) ut
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SI quad.
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ad
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SL quad:
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atque adeo
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IZ
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ad
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LP
<
emph.end
type
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ut
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SI
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emph.end
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ad
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SL.
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Jacent ergo punc
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ta
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S, P, Z
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in una recta. </
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>
<
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>Porro tangentibus concurrentibus in
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G,
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e
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rit (ex Conicis) rectangulum
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XIY
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ſeu
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IZ quad.
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ad
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IA quad.
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ut
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GP quad
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ad
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GA quad:
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adeoque
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IZ
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&
<
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type
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IA
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ut
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GP
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ad
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GA.
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Jacent
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ergo puncta
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P, Z
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&
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A
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in una recta, adeoque puncta
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S, P
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&
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A
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ſunt in una recta. </
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<
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>Et eodem argumento probabitur quod puncta
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<
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R, P
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&
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A
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ſunt in una recta. </
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<
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>Jacent igitur puncta contactuum
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A
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&
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P
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in recta
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RS.
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Hiſce autem inventis, Trajectoria deſeribetur
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ut in caſu primo Problematis ſuperioris.
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q.E.F.
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</
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LIBER
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PRIMUS.</
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LEMMA XXII.
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Figuras in alias ejuſdem generis figur as mutare.
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<
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>Tranſmutanda ſit figura quævis
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HGI.
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Ducantur pro lubitu
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rectæ duæ parallelæ
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AO, BL
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tertiam quamvis poſitione datam
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<
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AB
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ſecantes in
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A
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&
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type
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B,
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<
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/>
<
figure
id
="
id.039.01.107.1.jpg
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xlink:href
="
039/01/107/1.jpg
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number
="
54
"/>
<
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/>
& a figuræ puncto quo
<
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/>
vis
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type
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G,
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emph.end
type
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ad rectam
<
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type
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AB
<
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type
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<
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/>
ducatur quævis
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type
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GD,
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<
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ipſi
<
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OA
<
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parallela. </
s
>
<
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>De
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/>
inde a puncto aliquo
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O,
<
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<
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/>
in linea
<
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type
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OA
<
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"/>
dato, ad
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/>
punctum
<
emph
type
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D
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ducatur
<
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/>
recta
<
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type
="
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"/>
OD,
<
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type
="
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"/>
ipſi
<
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type
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"/>
BL
<
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oc
<
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currens in
<
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type
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d,
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& a puncto
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/>
occurſus erigatur recta
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/>
<
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dg
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datum quemvis angulum cum recta
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BL
<
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continens, atque eam
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/>
habens rationem ad
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Od
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"/>
quam habet
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type
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DG
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ad
<
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type
="
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"/>
OD
<
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; & erit
<
emph
type
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g
<
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"/>
punc
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/>
tum in figura nova
<
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type
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"/>
hgi
<
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puncto
<
emph
type
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G
<
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reſpondens. </
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>
<
s
>Eadem ratione
<
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puncta ſingula figuræ primæ dabunt puncta totidem figura novæ. </
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</
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</
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