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

Table of figures

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[61] Fig. 5.A D C G F E B H
Page: 166
[62] Pag. 106.TAB. XIV.Fig. 2.T B M S O I C A F K E L Q P N
Page: 171
[63] Fig. 1.E F K L A G H M C B D
Page: 171
[64] Fig. 3.I G E B P R Q A K C D H F
Page: 171
[65] Pag. 112.TAB. XV.Fig. 1.S D A B C E V
Page: 180
[66] Fig. 2.F A E B K G H N L D M O C
Page: 180
[67] Fig. 3.C D F A B K E G N H
Page: 180
[68] Fig. 5.S M A N B K X T P L F V O C Y D E G H
Page: 180
[69] Fig. 4.Y H A S B K T X F L V P O M N C D G E
Page: 180
[70] Pag. 114.TAB. XVI.Fig. 1.M F E A K G N H B D C
Page: 185
[71] Fig. 2.H A K B R P F L O M N D Q G E
Page: 185
[72] Fig. 3.Y H A S Z X T K B V L P F O C M N D G E
Page: 185
[Figure 73]
Page: 189
[74] Pag. 122TAB. XVII.Fig. 1.S A P B R M D I
Page: 196
[75] Fig. 2.H S Z K B C M D
Page: 196
[76] Fig. 3.P S Z M A B K D H
Page: 196
[77] Fig. 4.H C A E D F B G
Page: 196
[78] Pag. 128.TAB. XVIII.Fig. 1.A G C B D E H F K I M
Page: 205
[79] Fig. 2.A C G B E F D H M N O P
Page: 205
[80] Fig. 3.D L Q A G Q M R E P. Q B F N H Q C Q K Q
Page: 205
[81] Fig. 4.N Q K C Q D L R E P F A Q G M Q Q H B Q
Page: 205
[82] Pag. 136.TAB. XIX.Fig. 1.D C X B Y E R I Q L S N K P A TF G Y M H O
Page: 216
[83] Fig. 2.X C D A T E R I Q L S N K P B Y
Page: 216
[84] Fig. 3.F G K C D I E M A B D
Page: 216
[85] Fig. 4.D K E F L B A H G C E
Page: 216
[86] Fig. 5.D C K L F E A G H D B
Page: 216
[87] Fig. 6.C D K F L E H G A D B
Page: 216
[88] Pag. 142.TAB. XX.Fig. 1.D L F K A E G H C L K F D B
Page: 225
[89] Fig. 2.D F K L C H E G A K F L D B
Page: 225
[90] Fig. 3.L D C A E H G B L D
Page: 225
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175109HOROLOG. OSCILLATOR. ſtabit ab A; interſectio vero rectarum B D, F E, quæ eſt
11De linea-
RUM CUR-
VARUM
EVOLUTIO-
NE. G, cadet ultra punctum D in recta B D. Nam concurrere
ipſas B D, F E neceſſe eſt, cum curvæ B F ad partem ca-
vam inſiſtant rectis angulis.
Quanto autem punctum F ipſi B propinquius fuerit, tanto
propius quoque puncta D, G & E convenire apparet; ideo-
que, ſi interſtitium B F infinite parvum intelligatur, tria
dicta puncta pro uno eodemque erunt habenda; ac præterea,
ductâ rectâ B H, quæ curvam in B tangat, eadem quoque
pro tangente in F cenſebitur. Sit B O parallela K L, &
in hanc perpendiculares cadant B K, F L: ſecetque F L
rectam B O in P, & ſint puncta notata M, N, in quibus
rectæ, B D, F E, occurrant ipſi K L. Quia igitur ratio
B G ad G M eſt eadem quæ B O ad M N, data hac dabi-
tur & illa; & quia recta B M datur magnitudine ac po-
ſitione, dabitur & punctum G in producta B M, ſive D
in curva C D E, quia G & D in unum convenire diximus.
Datur autem ratio B O ad M N, ſimpliciter quidem in
Cycloide, ubi primùm omnium illam inveſtigavimus, inve-
nimuſque duplam; in aliis vero curvis, quas hactenus exa-
minavimus, per duarum datarum rationum compoſitionem.
Nam quia ratio B O ad M N componitur ex rationibus B O
ad B P, ſive N H ad L H, & ex B P ſive K L ad M N;
patet, ſi rationes hæ utræque dentur etiam ex iis compoſi-
tam rationem B O ad M N datum iri. Illas vero dari in o-
mnibus curvis geometricis, in ſequentibus patebit; ac proin-
de iis ſemper curvas adſignari poſſe, quarum evolutione de-
ſcribantur, quæque ideo ad rectas lineas ſint reducibiles.
Ponatur primò parabola eſſe A B F, cujus vertex A,
22TAB. XVI.
Fig. 2. axis A Q. Cum igitur lineæ B M, F N, ſint parabolæ ad
angulos rectos; ductæque ſint ad axem A Q perpendicula-
res B K, F L; erunt, ex proprietate parabolæ, ſingulæ
M K, N L dimidio lateri recto æquales; & ablata commu-
ni L M, æquales inter ſe K L, M N. Hinc, quum ratio
B G ad G M componatur ex rationibus N H ad H L, &
K L ad M N, uti dictum fuit, ſitque earum poſterior

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