Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 1: Opera mechanica
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HOROLOG. OSCILLATOR.
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rum curvarum, hoc eſt, ſicut punctum D modo inventum
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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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fuit.</
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<
s
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xml:space
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">Denique, quæcunque fuerit ex paraboloidum genere cur-
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va S A B, ſemper æque facile curvam aliam, cujus evolu-
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tione ipſa deſcribatur, quæque propterea rectæ adæquari
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poſſit, per puncta inveniri comperimus. </
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<
s
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xml:space
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ſtructionem univerſalem ſequenti tabella exhibemus; </
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<
s
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xml:space
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quousque libuerit extendi poterit.</
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<
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# a x = y
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">2</
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>
# # B M + 2 B Z
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# a
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">2</
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>
x = y
<
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style
="
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">3</
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>
# # {1/2} B M + {3/2} B Z
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Si # a x
<
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style
="
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">2</
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>
= y
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">3</
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>
# Erit # 2 B M + 3 B Z # = # B D.
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/>
# a x
<
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style
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>
= y
<
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">4</
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>
# # 3 B M + 4 B Z
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# a
<
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style
="
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">3</
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>
x = y
<
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style
="
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">4</
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>
# # {1/3} B M + {4/3} B Z
<
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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 S B parabola, vel paraboloidum aliqua, cujus vertex
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xml:space
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">TAB XVII.
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Fig. 2.</
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S; </
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xml:space
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">recta S K vel axis, vel axi perpendicularis, ad quam re-
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feruntur æquatione puncta paraboloidis; </
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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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">ipſa quidem S K
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ſemper ad partem cavam ducta intelligitur; </
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<
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xml:space
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">cui perpendicu-
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laris S Z. </
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<
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xml:space
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">Ponendo jam S K = x; </
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<
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xml:space
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">B K = y, quæ à pun-
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cto quovis curvæ perpendicularis eſt ipſi S K; </
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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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">latere re-
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cto curvæ = a; </
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>
<
s
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xml:space
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">prior pars tabellæ, quæ ad ſiniſtram eſt,
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naturam ſingularum paraboloidum ſingulis æquationibus ex-
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plicat. </
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<
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xml:space
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">Quibus reſpondent in parte dextra quantitates lineæ
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B D, quæ ſi curvæ S B inſiſtat ad angulos rectos, exhibi-
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tura ſit punctum D in curva quæſita C D. </
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<
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xml:space
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">Exempli gratia,
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ſi S B eſt parabola quæ ex coni ſectione fit, ei ſcimus con-
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venire æquationem tabellæ primam, a x = y
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; </
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<
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xml:space
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">cui reſpon-
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det ab altera parte B M + 2 B Z = B D. </
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<
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xml:space
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">Unde longitudo
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lineæ B D cognoſcitur, adeoque inventio quotlibet puncto-
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rum curvæ C D. </
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<
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xml:space
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">Quam quidem, hoc caſu, paraboloidem
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eſſe ſupra demonſtratum fuit, eam nempe, cujus æquatio
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tertia eſt hujus tabellæ.</
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<
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<
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">Conſtruitur autem tabella hoc pacto, ut B M ſumatur
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multiplex ſecundum numerum qui eſt exponens poteſtatis x
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in æquatione; </
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<
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">B Z vero, multiplex ſecundum exponentem
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poteſtatis y; </
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<
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xml:space
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">ex his autem utrisque compoſitæ accipiatur
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pars denominata ab exponente poteſtatis a.</
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