Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 1: Opera mechanica
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CHRISTIANI HUGENII
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O L ſuper regula L D; </
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<
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<
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<
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.</
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cumferentia figuræ O L ſumpto. </
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<
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xml:space
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væ A tangentem ducere. </
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<
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xml:space
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">Ducatur recta C A à puncto C,
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ubi figura regulam tangebat cum punctum deſcribens eſſet
<
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in A: </
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<
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xml:space
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">quod punctum contactus ſemper inveniri poteſt, ſiqui-
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dem eo reducitur problema ut duæ rectæ inter ſe parallelæ
<
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/>
ducendæ ſint, quarum altera tranſeat per punctum deſcri-
<
lb
/>
bens in figuræ ambitu datum, altera figuram tangat, quæ-
<
lb
/>
que inter ſe diſtent quantum diſtat punctum datum A ab re-
<
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gula L D: </
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<
s
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xml:space
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">dico ipſam C A occurrere curvæ ad angulos
<
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rectos, ſive circumferentiam M A F deſcriptam centro C
<
lb
/>
radio C A, tangere curvam in puncto A, unde perpendicula-
<
lb
/>
ris ad A C, per punctum A, ducta curvam ibidem continget.</
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</
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<
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<
s
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xml:space
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">Ducatur enim C B primum ad punctum curvæ B, quod
<
lb
/>
diſtet ultra punctum A ab regula L D, intelligaturque figu-
<
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/>
ræ poſitus in B E D, cum punctum deſcribens eſſet in B,
<
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contactus regulæ in D. </
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<
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">& </
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<
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xml:space
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">punctum curvæ quod erat in C,
<
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/>
cum punctum deſcribens eſſet in A, hìc jam ſublatum ſit in
<
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/>
E; </
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<
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xml:space
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">& </
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<
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xml:space
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">jungantur E C, E B, tangatque figuram in E recta
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K H, occurrens regulæ in H.</
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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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">Quia ergo recta C D æqualis eſt curvæ E D; </
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<
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xml:space
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">eâdem ve-
<
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ro curva major eſt utraque ſimul E H, H D; </
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>
<
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xml:space
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">erit E H ma-
<
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jor quam C H. </
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>
<
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xml:space
="
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">Unde angulus E C H major quam C E H,
<
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/>
& </
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>
<
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xml:space
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">proinde E C L minor quam C E K. </
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>
<
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xml:space
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">Atqui addendo an-
<
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/>
gulum K E B, qui æqualis eſt L C A, ad K E C, fit an-
<
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/>
gulus C E B: </
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>
<
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xml:space
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>
<
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xml:id
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xml:space
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">auferendo ab E C L angulum L C B, fit
<
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/>
E C B. </
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>
<
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xml:space
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">Ergo angulus C E B major omnino angulo E C B.
<
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/>
</
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>
<
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xml:space
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">Itaque in triangulo C E B, latus C B majus erit quam E B. </
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>
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<
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/>
ſed E B æquale patet eſſe C A, cum ſit idemmet ipſum unà
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/>
cum figura transpoſitum. </
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>
<
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xml:space
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">Ergo C B etiam major quam C A,
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hoc eſt, quam C F. </
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<
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xml:space
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">unde conſtat punctum B eſſe extra cir-
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cumferentiam M A F.</
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<
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xml:space
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">Sit rurſus punctum N in curva ſumptum inter regulam
<
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L D & </
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<
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">punctum A. </
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">Cumque punctum deſcribens eſſet in N,
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ponatur ſitus figuræ fuiſſe in V L, punctumque contactus L,
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punctum verò quod tangebat prius regulam in C, ſit </
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