Huygens, Christiaan, Christiani Hugenii opera varia; Bd. 1: Opera mechanica

Table of figures

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[141] Fig. 3.a B c A C
Page: 355
[142] Fig. 7.D A C B E G
Page: 355
[143] Fig. 6.D A G B
Page: 355
[Figure 144]
Page: 359
[145] Pag. 262.TAB.XXIX.Fig. 1.P E O D C Q H M G N B S R T F
Page: 370
[146] Fig. 4.C A H N E P B L K I
Page: 370
[147] Fig. 3.N Q O P T
Page: 370
[148] Fig. 2.F D I C A B H K E R S G
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[149] Fig. 5.L M C M E H O D P I
Page: 370
[150] Pag. 268.TAB. XXX.a a I L K M g N l O c k P Q T S Q V T S R f f e n l d h g b
Page: 379
[151] Pag. 276.TAB.XXXI.Fig. 2.a a m f k b e @ b a g a f b b h
Page: 390
[152] Fig. 1.h g k h d a b c f e l
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[153] Pag. 286.TAB.XXXII.Fig. 1.A E C E E D B G
Page: 403
[154] Fig. 2.H N K M
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[155] Fig. 4.B A D C
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[156] Fig. 5.A E E C H D G B
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[157] Fig. 6.A C C C C H G K E F D D D D
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[158] Fig. 3.G F F B D D C D A F A E E H
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[159] Fig. 7.K L R Z Y H V N S P A C E B X T M G Q O
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[160] Pag. 308.TAB.XXXIII.Fig. 1.P F Q K H L R G B E C N O 3 A 2
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[161] Fig. 8.R G M K N D B V C A
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[162] Fig. 7.R d D G g B h H E V C u A c
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[163] Fig. 2.B F G C H A K D E
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[164] Fig. 4.A B G F E C D
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[165] Fig. 6.T G D H B E M L N C K I S P F V R Q O A
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[166] Fig. 3.A E G B D F C
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[167] Fig. 5.N K F E C B A H L V W R G
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[168] Fig. 9.Z R A X H C B D M K S Q G
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176110CHRISTIANI HUGENII æqualitatis; liquet rationem B G ad G M fore eandem quæ N H
11De linea-
RUM CUR-
VARUM
EVOLUTIO-
NE. ad H L; & dividendo, B M ad M G, eandem quæ N L
ad L H, ſive M K ad K H; nam L H, K H pro eadem
habentur, propter propinquitatem punctorum B, F. Data
autem eſt ratio M K ad K H, dato puncto B; quoniam
tam M K, quam K H dantur magnitudine; nam M K
æquatur dimidio lateri recto, K H vero duplæ K A. Dataque
etiam eſt poſitione & magnitudine recta B M. Ergo & M G
data erit, adeoque & punctum G, ſive D, in curva R D E;
quod nempe invenitur productâ B M uſque in G, ut ſit
B M ad M G ſicut {1/2} lateris recti ad duplam K A.
Et ſic quidem, adſumptis in parabola A B F aliis quotli-
bet punctis præter B, totidem quoque puncta lineæ R D E,
ſimili ratione, invenientur; atque hoc ipſo lineam R D E
geometricam eſſe conſtat, unáque proprietas ejus innoteſcit,
ex qua cæteræ deduci poſſunt. Ut ſi inquirere deinde veli-
mus, quanam æquatione exprimatur relatio punctorum
omnium curvæ C D E ad rectam A Q: ducta in hanc perpen-
diculari D Q, vocatoque latere recto parabolæ A B F, a;
A K, b; A Q, x; Q D, y. Quoniam ratio B M ad M D,
hoc eſt, K M ad M Q, eſt ea quæ {1/2} a ad 2 b, eſtque ipſa
K M = {1/2} a, erit & M Q æqualis 2 b. Eſt autem M A = {1/2}
a + b. ergo A Q ſive x æqualis 3 b + {1/2} a. Unde b = {1/3} x
-{1/6} a. Porro quoniam, ſicut quadratum M K, hoc eſt, {1/4} a a
ad quadratum K B, hoc eſt, a b, ita qu. M Q, hoc eſt,
4 b b ad qu. Q D; erit qu. Q D, ſive y y = {16b3/4}. Ubi, ſi in
locum b ſubſtituatur {1/3} x - {1/6}a, quod illi æquale inventum eſt,
fiet y y = 16. cub. {1/3} x - {1/6} a diviſis per a. Ac proinde {27/16} a y y
= cubo ab x - {1/2} a. Accipiatur A R in axe parabolæ = {1/2} a;
eritque R Q = x - {1/2} a. Curvam igitur C D ejus naturæ eſſe
liquet, ut ſemper cubus lineæ R Q æquetur parallelepipedo,
cujus baſis qu. Q D, altitudo {27/16} a; ac proinde ipſam para-
boloidem eſſe, cujus evolutione deſcribi parabolam A B ſu-
pra oſtendimus; cujus nimirum paraboloidis latus rectum æ-
quetur {27/16} lateris recti parabolæ A B. tunc enim hujus latus
rectum æquale fit {15/27} lateris recti paraboloidis, quemadmo-
dum ibi fuit deſinitum.

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