Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 1: Opera mechanica
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145
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HOROLOG. OSCILLATOR.
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C D & </
s
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<
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xml:space
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">ipſa D G. </
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<
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xml:space
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<
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<
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<
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<
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">EVOLUTIO-</
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<
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.</
note
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que ſimul, rectæ C D, & </
s
>
<
s
xml:id
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echoid-s2008
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xml:space
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">lineæ D G, æquari rectam H G.
<
lb
/>
</
s
>
<
s
xml:id
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echoid-s2009
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xml:space
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">Ergo duæ ſimul C F, F G majores quoque erunt recta H G.</
s
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<
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xml:id
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echoid-s2010
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xml:space
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<
unsure
/>
<
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& </
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>
<
s
xml:id
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echoid-s2011
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xml:space
="
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">ablata communi F G, erit C F major quam H F. </
s
>
<
s
xml:id
="
echoid-s2012
"
xml:space
="
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">Sed
<
lb
/>
F E major eſt quam F C, quia angulus C trianguli F C E
<
lb
/>
eſt rectus. </
s
>
<
s
xml:id
="
echoid-s2013
"
xml:space
="
preserve
">Ergo F E omnino major quam F H. </
s
>
<
s
xml:id
="
echoid-s2014
"
xml:space
="
preserve
">Unde ap-
<
lb
/>
paret, ab hac quidem parte puncti C, fili extremitatem non
<
lb
/>
pertingere ad rectam C E.</
s
>
<
s
xml:id
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xml:space
="
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"/>
</
p
>
<
p
>
<
s
xml:id
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echoid-s2016
"
xml:space
="
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">Sit jam punctum H propinquius principio evolutionis A
<
lb
/>
<
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position
="
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xlink:label
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xlink:href
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xml:space
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">TAB. XII.
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Fig. 1.</
note
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quam punctum C, ſitque fili poſitio H G, tunc cum ejus
<
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/>
extremitas eſſet in H, & </
s
>
<
s
xml:id
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echoid-s2017
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xml:space
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">ducantur rectæ D G, D H, qua-
<
lb
/>
rum hæc occurrat rectæ C E in E: </
s
>
<
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xml:id
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echoid-s2018
"
xml:space
="
preserve
">apparet autem D G re-
<
lb
/>
ctam non poſſe eſſe in directum ipſi H G, adeoque H G D
<
lb
/>
fore triangulum. </
s
>
<
s
xml:id
="
echoid-s2019
"
xml:space
="
preserve
">Jam quia recta D G vel minor eſt quam
<
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/>
D K G, vel eadem, ſi nempe evolutæ pars D G recta ſit;
<
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/>
</
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>
<
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xml:id
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xml:space
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">additâ utrique G H, erunt rectæ D G, G H ſimul mino-
<
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/>
res vel æquales duabus iſtis, ſcilicet D K G & </
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>
<
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xml:id
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xml:space
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">G H, ſive
<
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/>
his æquali rectæ D C. </
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>
<
s
xml:id
="
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xml:space
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">Duabus autem rectis D G, G H mi-
<
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nor eſt recta D H. </
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>
<
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xml:id
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xml:space
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">Ergo hæc minor utique erit rectâ D C. </
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<
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<
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Sed D E major eſt quam D C, quia in triangulo D C E
<
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/>
angulus C eſt rectus. </
s
>
<
s
xml:id
="
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xml:space
="
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">Ergo D H multo minor quam D E. </
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<
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xml:space
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<
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Situm eſt ergo punctum H, hoc eſt extremitas fili G H, in-
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tra angulum D C E. </
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>
<
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xml:space
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">Unde apparet neque inter A & </
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<
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xml:space
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quam illam pertingere ad rectam C E. </
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>
<
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xml:space
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">Ergo C E tangit
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curvam A C in C; </
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<
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">ac proinde D C, cui C E ducta eſt
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perpendicularis, occurrit curvæ ad angulos rectos. </
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<
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erat demonſtrandum.</
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</
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<
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<
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xml:space
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">Hinc etiam manifeſtum eſt curvam A H C in partem u-
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nam inflexam eſſe, & </
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>
<
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xml:space
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">in eandem partem cavam ac ipſa A G B,
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cujus evolutione deſcripta eſt. </
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<
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xml:space
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">Omnes enim tangentes lineæ
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A H C, cadunt extra ſpatium D G A H C: </
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<
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tangentes lineæ A G D, intra dictum ſpatium. </
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<
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<
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cavitatem A H C reſpicere convexitatem A G D.</
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