Full text: Volumen primum. Opera mechanica (1)

HOROLOG. OSCILLATOR. traque parte centri Z, & ſit G H, earum quæ ſunt à parte
B, centro proxima, vel per ipſum centrum tranſeat. Itaque
tangentes omnes inter G H & B O comprehenſæ, ut H K,
L M, N O, ſingulæ ſuis arcubus minores ſunt . Porro autem & tangens G F, arcu ſequente F D minor eſt , & ſimiliter tangens E D arcu D A. Itaque tangentes omnes
inter B O & C D interjectæ, minores ſunt arcubus B H & F A, ac proinde omnino minores arcubus B H, H A, ſive
arcu B A, quod erat primo oſtendendum.

43.1.

De motu
IN Cy-
CLOIDE .
Prop. 16.
huj.
Prop. 17.
huj.

Porro jam demonſtrabimus tangentes omnes inter B O & A
majores eſſe arcu A N. Enimvero parallela G H, vel pro-
pius centrum Z tranſit quam parallela E F, quam pono
proximam eſſe earum quæ à parte A tranſeunt, vel erit re-
motior, vel æque diſtabit.

Quod ſi E F longius à centro vel æque remota eſt ac G H,
erit tangens F G major arcu ſuo F H, & reliquæ tangen-
tes verſus A, nimirum E D, C A majores ſingulæ arcubus
ſuis ; adeo ut omnes ſimul G F, E D, C A majores ſint arcu H A. ſed & arcu H L major erit tangens L M , & arcu L N tangens N O; itaque tangentes omnes, præter
H K, majores ſimul erunt arcu A N; multoque magis, ac-
cedente ipſa H K, tangentes omnes inter A & B compre-
henſæ arcu eodem A N majores erunt.

43.1.

Prop. 15.
huj.
Prop. 19.
huj.

Si vero G H à centro longius diſtat quam E F, erit tan-
gens K H major arcu H F , & tangens M L ut ante ma- jor arcu L H, & tangens O N major arcu N L, & omnes
proinde tangentes O N, M L, K H majores arcu N F. Sed & tangens E D major eſt arcu ſuo F D , & tangens C A major ſimiliter arcu ſuo D A. Itaque tangentes omnes
inter B O & A, præter G F, majores erunt arcu N A; multoque magis tangentes eædem, accedente G F, hoc eſt,
omnes quæ inter B O & A interjiciuntur, eodem arcu N A
majores erunt.

43.1.

Prop. 19.
huj.
Prop. 11.
huj.

Ex his vero etiam demonſtratio manifeſta eſt in caſibus
aliis, qualiscunque ſemicircumferentiæ arcus accipiatur,
quippe cum vel eadem ſit ubique, vel pars tantum præce-
dentis demonſtrationis.

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