Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica
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ΕΞΕΤΑΣΙΣ CYCLOM.
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tro Π P. </
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<
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xml:space
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<
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xml:space
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">alio huic pa-
<
lb
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rallelo D Φ S ſecundum lineam Φ S, erit jam pars ungulæ
<
lb
/>
hiſce duobus planis terminata, æqualis ſolido quod fit ex du-
<
lb
/>
ctu plani S Φ Π P in ſe ipſum; </
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>
<
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xml:space
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">& </
s
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<
s
xml:id
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xml:space
="
preserve
">pars ungulæ E D S Φ, æ-
<
lb
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qualis ei ſolido quod fit ex ductu plani E Φ S in ſe ipſum.
<
lb
/>
</
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<
s
xml:id
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xml:space
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">Quare nunc demonſtrandum erit duntaxat, partem E D S Φ
<
lb
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eſſe ad partem Φ A P ut 53 ad 203, Sit Φ N parallela E P,
<
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& </
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<
s
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xml:space
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<
s
xml:id
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xml:space
="
preserve
">Ergo quoniam ex proprietate Para-
<
lb
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boles, P N eſt {3/4} Π P, erit quoque P C {3/4} A P. </
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<
s
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xml:space
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<
s
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xml:space
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<
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S D æquatur {3/4} A P, quum ſit huic parallela , ſitque
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xml:space
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Elem.</
note
>
rabola E A F: </
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<
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xml:space
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<
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xml:space
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">æqualis
<
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erit lineis P S, N Φ. </
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<
s
xml:id
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xml:space
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">Ducatur ſecundùm D C planum
<
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D B C parallelum baſi E Π F, fietque ſemiparabola B D C
<
lb
/>
æqualis & </
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>
<
s
xml:id
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xml:space
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">ſimilis ſemiparabolæ Π Φ N; </
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<
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xml:space
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">& </
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<
s
xml:id
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xml:space
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">erit Φ B N di-
<
lb
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midius cylindrus parabolicus: </
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<
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xml:space
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">D A C B verò dimidiata un-
<
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gula. </
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<
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xml:id
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xml:space
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">Hæc autem æquatur ſicut antea oſtendimus, duabus
<
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quintis cylindri dimidiati, baſin habentis D B C & </
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<
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xml:space
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<
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nem B A. </
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<
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xml:space
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">Ergo quum ſemicylindrus Φ B N habeat altitu-
<
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dinem B Π triplam ipſius B A, erit ungula dimid. </
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<
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xml:space
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<
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ad ſemicyl. </
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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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xml:space
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">Junctâ porro Φ Π, conſtat ſemiparabolam Π Φ N ad trian-
<
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gulum Π Φ N eſſe ut 4 ad@ 3; </
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<
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xml:space
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">ſed triangulus Π Φ N eſt ad
<
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rectangulum Φ P ut 1 ad 6, (eſt enim baſis Π N tertia pars
<
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ipſius N P) hoc eſt, ut 3 ad 18. </
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<
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xml:space
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">Ergo ex æquo erit ſemi-
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parab. </
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<
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xml:space
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<
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xml:space
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<
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xml:space
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">Itaque & </
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<
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cylindrus Φ B N eſt ad parallelepipedum ejuſdem altitudinis
<
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ſuper baſi Φ P, ut 4 ad 18. </
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>
<
s
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xml:space
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">Dictiautem parallelepipedi di-
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midium eſt priſma D N S; </
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<
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xml:space
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">ergo ſemicylindrus Φ B N eſt ad
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priſma D N S, ut 4 ad 9, hoc eſt, ut 60 ut 135. </
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<
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xml:space
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">Qua-
<
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lium igitur partium dimidiata ungula D A C B erat 8, ta-
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lium ſemicylindrus parab. </
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<
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xml:space
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">Φ B N erat 60, (ut ſuprà oſten-
<
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ſum eſt) taliumque priſma D N S erit 135. </
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<
s
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xml:space
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">Ac proinde ſo-
<
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lidum A Π S D, quod ex iſtis tribus componitur, erit 203.
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</
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>
<
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xml:space
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">Eſt autem ungula dimidiata A D C B ad dimidiatam un-
<
lb
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gulam E A P Π, ut 1 ad 32, ſicut Cl. </
s
>
<
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xml:space
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<
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xml:space
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">demonſtravit in
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prop. </
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<
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">95. </
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<
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">lib. </
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<
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">9. </
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<
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xml:space
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