Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 1: Opera mechanica
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CHRISTIANI HUGENII
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<
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">IV.</
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.</
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<
s
xml:id
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echoid-s1986
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xml:space
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">Illa vero cui filum circumplicatum erat, dicatur
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Evoluta. </
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<
s
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echoid-s1987
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xml:space
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">In figura ſuperiori, A B C eſt evoluta,
<
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note-0134-02
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note-0134-02a
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xml:space
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">TAB. XI.
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Fig. 2.</
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A D E deſcripta ex evolutione A B C, ut nempe
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cum extremitas fili ex A venit in D, pars fili ex-
<
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tenſa ſit D B recta, reliqua parte B C adhuc ap-
<
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plicata curvæ A B C. </
s
>
<
s
xml:id
="
echoid-s1988
"
xml:space
="
preserve
">Manifeſtum eſt autem D B
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tangere evolutam in B.</
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<
s
xml:id
="
echoid-s1989
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"/>
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<
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echoid-head80
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">PROPOSITIOI.</
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<
s
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echoid-s1990
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">R Ecta omnis, quæ evolutam tangit, occurret li-
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@eæ ex evolutione deſcriptæ ad angulos rectos.</
s
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<
s
xml:id
="
echoid-s1991
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"/>
</
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<
s
xml:id
="
echoid-s1992
"
xml:space
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">Sit A B evoluta, A H vero quæ ex evolutione illius de-
<
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<
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left
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xlink:label
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note-0134-03
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xlink:href
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note-0134-03a
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">TAB. XI.
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Fig. 3.</
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ſcripta eſt. </
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<
s
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="
echoid-s1993
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xml:space
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preserve
">Recta autem F D C, tangens curvam A D in D,
<
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occurrat in C curvæ A C H. </
s
>
<
s
xml:id
="
echoid-s1994
"
xml:space
="
preserve
">Dico ei occurrere ad angulos
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rectos: </
s
>
<
s
xml:id
="
echoid-s1995
"
xml:space
="
preserve
">hoc eſt, ſi ducatur C E recta perpendicularis C D,
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dico eam in C tangere curvam A C H. </
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<
s
xml:id
="
echoid-s1996
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xml:space
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preserve
">Quia enim D C
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tangit evolutam in D, apparet ipſam referre poſitionem fili
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tunc cum ejus extremitas pervenit in C. </
s
>
<
s
xml:id
="
echoid-s1997
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xml:space
="
preserve
">Quod ſi igitur o-
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ſtenderimus filum, in tota reliqua deſcriptione curvæ A C H,
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nusquam pertingere ad rectam C E præterquam in C pun-
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cto, manifeſtum erit rectam C E ibidem curvam A C H
<
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contingere.</
s
>
<
s
xml:id
="
echoid-s1998
"
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="
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"/>
</
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<
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<
s
xml:id
="
echoid-s1999
"
xml:space
="
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">Sumatur punctum aliquod in A C præter C, quod ſit H,
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ſitque primo remotius à principio evolutionis A quam pun-
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ctum C, & </
s
>
<
s
xml:id
="
echoid-s2000
"
xml:space
="
preserve
">intelligatur pars libera eſſe H G, cum extremi-
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tate ſua ad H pervenit. </
s
>
<
s
xml:id
="
echoid-s2001
"
xml:space
="
preserve
">Tangit ergo H G lineam A B in G.
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</
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<
s
xml:id
="
echoid-s2002
"
xml:space
="
preserve
">Cumque interea dum deſcribitur pars curvæ C H, evolu-
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tus ſit arcus D G, occurret C D à parte D producta ipſi
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H G, ut in F. </
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>
<
s
xml:id
="
echoid-s2003
"
xml:space
="
preserve
">Ponatur autem G H occurrere rectæ C E
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in E. </
s
>
<
s
xml:id
="
echoid-s2004
"
xml:space
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">Quia igitur duæ ſimul D F, F G, majores ſunt quam
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D G, ſive curva ea fuerit ſive recta: </
s
>
<
s
xml:id
="
echoid-s2005
"
xml:space
="
preserve
">fiet addendo utrinque
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rectam D C, ut rectæ C F, F G ſimul majores ſint </
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