Full text: Volumen primum. Opera mechanica (1)

HOROLOG. OSCILLATOR. major erit ratio K B ad B N quam E F ad F G. Sed A B
major eſt quam K B, quoniam angulus K in triangulo A K B
eſt obtuſus, eſt enim major angulo H E F qui eſt obtuſus
ex conſtructione. Ergo ratio A B ad B N major erit ratio-
ne K B ad B N, ac proinde omnino major ratione E F ad
F G. Eodem modo & ratio B C ad C O, & C D ad D P,
major oſtendetur ratione E F ad F G. Itaque conſtat pro-
poſitum.

57.1.

Figure 1. Pag. 92.
TAB. XI
Fig. 1.
D C F E B L H I K A G
Figure 2. Fig. 2.
E D A B C
Figure 3. Fig. 3.
E H C A D F G B
De linea-
RUM CUR-
VARUM
EVOLUTIO-
NE.

58. PROPOSITIO III.

DUæ curvæ in unam partem inflexæ & in eas-
dem partes cavæ ex eodem puncto egredi ne-
queunt, ita ad ſe invicem comparatæ, ut recta
omnis quæ alteri earum ad angulos rectos occurrit,
ſimiliter occurrat & reliquæ.

Sint enim, ſi fieri poteſt, hujuſmodi lineæ curvæ A C E,
A G K, communem terminum habentes A, & ſumpto in ex-
teriore illarum puncto quolibet K, ſit inde educta K E recta,
curvæ A G K occurrens ad angulos rectos, ac proinde
etiam curvæ A C E.

58.1.

TAB. XII.
Fig. 3.

Poteſt jam recta quædam ſumi major curva K G A, quæ
ſit Q. Diviſa autem intelligatur ipſa K G A, ut in propo-
ſitione antecedenti dictum fuit, in tot partes punctis H G F,
ut ſubtenſæ ſingulæ K H, H G, G F, F A, ad perpen-
diculares curvæ ſibi contiguas H M, G N, F O, A P
majorem rationem habeant quam linea Q ad rectam K E. Itaque & omnes ſimul dictæ ſubtenſæ ad omnes dictas per-
pendiculares majorem habebunt rationem quam Q ad K E. Producantur autem perpendiculares eædem & occurrant cur-
væ A C E in D, C, B, nimirum ad angulos rectos ex
hypotheſi. Erit jam K E minor quam M D. Etenim, ducta
E L ipſi K E perpendiculari, quoniam K E occurrit lineæ
curvæ E C A ad angulos rectos, tanget E L curvam A C E,
occurretque neceſſario rectæ M D inter D & M. Unde

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