Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 1: Opera mechanica
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HOROLOG. OSCILLATOR.
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mul ſuperficiei exhibeatur circulus æqualis. </
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<
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<
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<
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<
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<
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<
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.</
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in caſu uno cæteris ſimpliciore ſufficiet attuliſſe.</
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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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">Sit ſphæroides latum cujus axis S I, ſectio per axem el-
<
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/>
lipſis S T I K; </
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>
<
s
xml:id
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xml:space
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">cujus ellipſis centrum O, axis major T K.
<
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</
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<
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xml:space
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<
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xlink:label
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xml:space
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">TAB. XIV.
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Fig. 2.</
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ponatur autem ellipſis hæc ejusmodi, ut latus transverſum
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T K habeat ad latus rectum eam rationem, quam linea ſe-
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cundum extremam & </
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<
s
xml:id
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xml:space
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">mediam rationem ſecta, ad partem ſui
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majorem.</
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</
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<
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<
s
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xml:space
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">Sumatur B C potentia dupla ad S O, item B A potentia
<
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dupla ad O K. </
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<
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xml:space
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">& </
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<
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B C, B A, B F, B E, & </
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<
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<
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xml:space
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">In-
<
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telligatur jam conoides hyperbolicum Q F. </
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<
s
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xml:space
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">N, cujus axis
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F P; </
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<
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xml:space
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">axi adjecta, ſive {1/2} latus transverſum F B; </
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<
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xml:space
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<
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latus rectum æquale B C.</
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<
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</
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<
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<
s
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xml:space
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">Hujus conoidis ſuperficies curva, unà cum ſuperficie ſphæ-
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roidis S I, æquabitur circulo cujus datus erit radius M L,
<
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/>
qui nempe poſſit quadratum T K cum duplo quadrato S I.</
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style
="
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xml:space
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">Curvæ parabolicæ æqualem rectam lineam
<
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invenire.</
head
>
<
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>
<
s
xml:id
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xml:space
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">SIt parabolæ portio A B C, cujus axis B K, baſis A C
<
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<
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xlink:label
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xlink:href
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xml:space
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">TAB. XIV.
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Fig. 3.</
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>
axi ad angulos rectos; </
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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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">oporteat curvæ A B C rectam
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æqualem invenire.</
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</
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<
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<
s
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xml:space
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">Accipiatur baſi dimidiæ A K æqualis recta I E, quæ pro-
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ducatur ad H, ut ſit I H æqualis A G, quæ parabolam in
<
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/>
puncto baſis A contingens, cum axe producto convenit in G.
<
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</
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<
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xml:space
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">Sit jam portio hyperbolæ D E F, vertice E, centro I de-
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ſcriptæ, cujusque diameter ſit E H; </
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<
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dinatim ad diametrum applicata. </
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ſumi poteſt. </
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<
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xml:space
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lelogrammum conſtitutum D P Q F, quod portioni D E F
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æquale ſit; </
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<
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">ejus latus P Q ita ſecabit diametrum hyperbolæ
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in R, ut R I ſit æqualis curvæ parabolicæ A B, cujus du-
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pla eſt A B C.</
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</
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<
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<
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xml:space
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">Apparet igitur hinc quomodo à quadratura hyperbolæ
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pendeat curvæ parabolicæ menſura, & </
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>
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s
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">illa ab hac viciſſim.</
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