12779HOROLOG. OSCILLATOR.
A D, erunt anguli ad circumferentiam ipſis inſiſtentes,
11De motu
IN Cy-
CLOIDE. E D A, A B D æquales. Itaque in triangulis A B D,
A D F, æquales anguli A B D, A D F. Communis au-
tem utrique eſt angulus ad A. Ergo dicti trianguli ſimiles
erunt, ideoque B A ad A D ut A D ad A F.
11De motu
IN Cy-
CLOIDE. E D A, A B D æquales. Itaque in triangulis A B D,
A D F, æquales anguli A B D, A D F. Communis au-
tem utrique eſt angulus ad A. Ergo dicti trianguli ſimiles
erunt, ideoque B A ad A D ut A D ad A F.
PROPOSITIO XXIII.
SIt Cyclois A B C, cujus vertex A deorſum con-
22TAB. IX.
Fig. 5. verſus ſit, axe A D ad perpendiculum erecto;
ſumptoque in ea quolibet puncto B, ducatur inde
deorſum recta B I quæ Cycloidem tangat, terminetur-
que recta horizontali A I. recta vero B F ad axem
perpendicularis agatur, & diviſa bifariam F A in
X, ſuper ea deſcribatur ſemicirculus F H A. Du-
ctâ deinde per punctum quodlibet G in curva B A
ſumptum, rectâ Σ G parallelâ B F, quæ circum-
ferentiæ F H A occurrat in H, axi A D in Σ, in-
telligantur per puncta G & H rectæ tangentes u-
triusque curvæ, earumque tangentium partes iis-
dem duabus horizontalibus M S, N T interceptæ
ſint M N, S T. Iisdemque rectis M S, N T in-
cludantur tangentis B I pars O P, & axis D A
pars Q R.
22TAB. IX.
Fig. 5. verſus ſit, axe A D ad perpendiculum erecto;
ſumptoque in ea quolibet puncto B, ducatur inde
deorſum recta B I quæ Cycloidem tangat, terminetur-
que recta horizontali A I. recta vero B F ad axem
perpendicularis agatur, & diviſa bifariam F A in
X, ſuper ea deſcribatur ſemicirculus F H A. Du-
ctâ deinde per punctum quodlibet G in curva B A
ſumptum, rectâ Σ G parallelâ B F, quæ circum-
ferentiæ F H A occurrat in H, axi A D in Σ, in-
telligantur per puncta G & H rectæ tangentes u-
triusque curvæ, earumque tangentium partes iis-
dem duabus horizontalibus M S, N T interceptæ
ſint M N, S T. Iisdemque rectis M S, N T in-
cludantur tangentis B I pars O P, & axis D A
pars Q R.