Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica
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DE CIRCULI MAGNIT. INVENTA.
"/>
tem dodecagoni inſcripti facile invenitur, quia radius pe-
<
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ripheriæ ſextantem ſubtendit. </
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<
s
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xml:space
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">Eſtque hæc ratio accuratior
<
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quam ſi triplâ ſeſquiſeptimâ utamur. </
s
>
<
s
xml:id
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xml:space
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preserve
">Nam ſecundum eam
<
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excedetur {1/2} peripheriæ longitudo amplius quam {1/100} diame-
<
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tri.</
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</
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xml:space
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<
emph
style
="
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emph
>
.</
head
>
<
p
>
<
s
xml:id
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xml:space
="
preserve
">Eſto datus circulus cujus B C diameter. </
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>
<
s
xml:id
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xml:space
="
preserve
">Dividatur ſemi-
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<
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right
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xlink:label
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note-0079-01
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xlink:href
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note-0079-01a
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xml:space
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">TAB. XXXIX.
<
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Fig. 2.</
note
>
circumferentia B C bifariam in D. </
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<
s
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xml:space
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">reliqua vero trifariam
<
lb
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in E & </
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>
<
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xml:space
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">F. </
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>
<
s
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xml:space
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">Et jungantur D E, D F, quæ ſecent diametrum
<
lb
/>
in G & </
s
>
<
s
xml:id
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xml:space
="
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">H. </
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<
s
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xml:space
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preserve
">Erit trianguli G D H latus alterum una cum
<
lb
/>
baſi G H quadrante B D exiguo majus, neque enim exce-
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lb
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det {1/5000} diametri B C. </
s
>
<
s
xml:id
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xml:space
="
preserve
">Sciendum eſt enim fieri D G vel D H
<
lb
/>
duobus inſcripti dodecagoni lateribus æquales. </
s
>
<
s
xml:id
="
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xml:space
="
preserve
">G H autem
<
lb
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lateri dodecagoni circumſcripti. </
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>
<
s
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xml:space
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">Unde quidem junctas D G
<
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& </
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<
s
xml:id
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xml:space
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">G H majores eſſe conſtat quadrante B D. </
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>
<
s
xml:id
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xml:space
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">Nam quia per
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8. </
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<
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xml:id
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xml:space
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">huj. </
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<
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xml:space
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">octo latera dodecagoni circulo inſcripti cum quatuor
<
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lateribus circumſcripti majora ſunt peripheriâ totâ, ideo ſum-
<
lb
/>
ptâ omnium quartâ parte erunt quoque duo latera inſcripti
<
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/>
cum latere uno circumſcripti majora peripheriæ quadrante.
<
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</
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<
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xml:space
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">Porro quoniam latus inſcripti dodecagoni minus eſt quam
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partium 51764 qualium B C 200000: </
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<
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xml:space
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">erunt latera duo, hoc
<
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eſt, G D, minor quam 103528. </
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<
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xml:id
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xml:space
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">Circumſcripti autem dode-
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cagoni latus minus eſt partibus 53590, ipſa nimirum G H. </
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<
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<
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Itaque junctæ una D G, G H efficiunt minus quam 157118. </
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<
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<
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At quadrantem B D conſtat ex præcedentibus majorem
<
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eſſe quam 157079. </
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>
<
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xml:space
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preserve
">Ergo differentia minor eſt quam partium
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39, cum 40 demum efficiant {1/3000} diametri B C.</
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<
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style
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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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preserve
">Tribus ſemidiametris addatur {1/10} lateris inſcripti quadrati;
<
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</
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<
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xml:id
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xml:space
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">compoſita ſemicircumferentiæ æquabitur tam propè, ut
<
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non {1/18000} diametri brevior ſit. </
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>
<
s
xml:id
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xml:space
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">Latus quadrati eſt majus quam
<
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partium 141421 qualium radius 100000, unde quod dictum eſt
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facile demonſtratur.</
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