Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica
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CHRISTIANI HUGENII
"/>
ad B H, ita K G ad C H. </
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<
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xml:space
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">Ergo major erit ratio E G ad
<
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C H, quam duplicata ejus, quam habet K G ad C H. </
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<
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xml:id
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echoid-s1372
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xml:space
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">Qua-
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re major ratio E G ad K G, quam K G ad C H. </
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>
<
s
xml:id
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echoid-s1373
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xml:space
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">Ideoque
<
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duæ ſimul E G, C H omnino majores duplâ K G. </
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>
<
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xml:space
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">Et ſumptis
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omnium trientibus, erunt trientes utriuſque E G & </
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<
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xml:space
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mul majores duabus tertiis K G. </
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>
<
s
xml:id
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xml:space
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">Quamobrem addito utrim-
<
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que ipſius C H triente, erit triens E G cum duabus tertiis
<
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C H, major duabus tertiis K G cum triente C H. </
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>
<
s
xml:id
="
echoid-s1377
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xml:space
="
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">Hiſce
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vero minor etiam eſt arcus C G . </
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>
<
s
xml:id
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xml:space
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">Igitur duæ tertiæ C
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xml:space
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">per pra
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ced.</
note
>
ſimul cum triente ipſius E G majores omnino ſunt eodem ar-
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cu C G. </
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>
<
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xml:space
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">Unde ſumptis omnibus toties quoties arcus C G
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circumferentiâ totâ continetur, erunt quoque duæ tertiæ pe-
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rimetri polygoni C D, cum triente perimetri polygoni E F,
<
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majores circuli totius circumferentiâ. </
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>
<
s
xml:id
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echoid-s1380
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xml:space
="
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">Quod fuerat oſtenden-
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dum.</
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>
<
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xml:space
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</
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<
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<
s
xml:id
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xml:space
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">Omnis igitur circumferentiæ arcus quadrante minor, mi-
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nor eſt ſinus ſui beſſe & </
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>
<
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xml:id
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xml:space
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">tangentis triente.</
s
>
<
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xml:space
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"/>
</
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</
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<
emph
style
="
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emph
>
I.
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style
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emph
>
. X.</
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>
<
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xml:id
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style
="
it
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xml:space
="
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">Peripheriæ ad diametrum rationem invenire
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quamlibet veræ propinquam.</
head
>
<
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>
<
s
xml:id
="
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xml:space
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">MInorem eſſe peripheriæ ad diametrum rationem quam tri-
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plam ſeſquiſeptimam: </
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>
<
s
xml:id
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xml:space
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">majorem vero quam 3 {10/71}, Archi-
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medes oſtendit inſcripto circumſcriptoque 96 laterum po-
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lygono. </
s
>
<
s
xml:id
="
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xml:space
="
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">Idem verò hic per dodecagona demonſtrabimus.</
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>
<
s
xml:id
="
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xml:space
="
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"/>
</
p
>
<
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>
<
s
xml:id
="
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xml:space
="
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">Quia enim latus inſcripti circulo dodecagoni majus eſt par-
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tibus 5176 {3/8}, qualium radius continet 10000: </
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>
<
s
xml:id
="
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"
xml:space
="
preserve
">duodecim la-
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tera proinde, hoc eſt, perimeter inſcripti dodecagoni major
<
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/>
erit quam 62116 {1/2}: </
s
>
<
s
xml:id
="
echoid-s1391
"
xml:space
="
preserve
">perimeter autem hexagoni inſcripti eſt
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radii ſextupla, ideoque partium 60000. </
s
>
<
s
xml:id
="
echoid-s1392
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xml:space
="
preserve
">Igitur dodecagoni
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perimeter perimetrum hexagoni excedit amplius quam par-
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tibus 2116 {1/2}. </
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>
<
s
xml:id
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echoid-s1393
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xml:space
="
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">Quare triens exceſſus major erit quam 705 {1/2}. </
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>
<
s
xml:id
="
echoid-s1394
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xml:space
="
preserve
">Igi-
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tur dodecagoni perimeter unà cum triente exceſſus, quo pe-
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rimetrum hexagoni ſuperat, major erit aggregato </
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