Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica
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371
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DE CIRCULI MAGNIT. INVENTA.
"/>
jor quam 5176 {3/8}. </
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<
s
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xml:space
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">cujus dupla F H major quam 10352 {3/4}. </
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<
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xml:space
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">unde
<
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G H major quam 352 {3/4}; </
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<
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xml:id
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xml:space
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">& </
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<
s
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xml:space
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">H I major quam 117 {7/12}. </
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<
s
xml:id
="
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xml:space
="
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">Tota igi-
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tur F I major quam 10470 {1/3}. </
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<
s
xml:id
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echoid-s1517
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xml:space
="
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">Arcus autem C D, ſextans pe-
<
lb
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ripheriæ, minor eſt quam 10472. </
s
>
<
s
xml:id
="
echoid-s1518
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xml:space
="
preserve
">Ergo deficiunt lineæ F I
<
lb
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partium earundem pauciores quam 1 {2/3}. </
s
>
<
s
xml:id
="
echoid-s1519
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xml:space
="
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">Quæ non æquant {1/6000}
<
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F I. </
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>
<
s
xml:id
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xml:space
="
preserve
">Porro cum arcus quadrante major datus erit, dividen-
<
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dus eſt in partes æquales 4 vel 6 vel plures, prout accura-
<
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tiori dimenſione uti voluerimus; </
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>
<
s
xml:id
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xml:space
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">ſed numero pares: </
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>
<
s
xml:id
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xml:space
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">Earum-
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que partium ſubtenſis ſimul ſumptis adjungendus eſt triens
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exceſſus quo ipſæ ſuperant aggregatum earum quæ arcubus
<
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duplis ſubtenduntur. </
s
>
<
s
xml:id
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echoid-s1523
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xml:space
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">Ita namque componetur longitudo ar-
<
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cus totius. </
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<
s
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xml:space
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">Vel hac etiam ratione eadem habebitur, ſi arcus
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reliqui ad ſemicircumferentiam longitudo inveniatur aut ſu-
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pra eandem exceſſus, aut reliqui ad circumferentiam totam,
<
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ſi dodrante major fuerit datus; </
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>
<
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xml:space
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">eaque longitudo adjungatur
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vel auferatur à dimidiæ vel totius circumferentiæ longitudi-
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ne, quam antea invenire docuimus.</
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</
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<
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emph
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. X.
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. XIII.</
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<
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Atus Polygoni æquilateri circulo inſcripti, pro-
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portione medium eſt inter latus polygoni ſimi-
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lis circumſcripti, & </
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">dimidium latus polygoni in-
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ſcriptiſub duplo laterum numero.</
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<
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xml:space
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">IN circulo cujus centrum A, radius A B, ſit latus inſcri-
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">TAB. XXXIX.
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Fig. 4.</
note
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pti polygoni æquilateri B C; </
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<
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xml:space
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">latus circumſcripti ſimilis
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polygoni D E ipſi B C parallelum. </
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<
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xml:space
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">Ergo producta A B trans-
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ibit per D, & </
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xml:space
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">Et ſi ducatur C F ipſi A B ad
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angulos rectos, ea erit dimidium latus polygoni inſcripti ſub-
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duplo numero laterum. </
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xml:space
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">Itaque oſtendendum eſt, B C me-
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diam eſſe proportione inter E D & </
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dividat E D bifariam, itaque erit ipſa quoque circuli ſemi-
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diameter & </
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<
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">æqualis A B. </
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xml:space
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">Et quoniam eſt ut E D ad C B,
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ſic D A ad A B, hoc eſt, D A ad A G; </
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