Newton, Isaac - Philosophia naturalis principia mathematica

LIBER
SECUNDUS.

PROPOSITIO XXII. THEOREMA XVII.

Sit Fluidi cujuſdam denſitas compreſſioni proportionalis, & partes
ejus a gravitate quadratis diſtantiarum ſuarum a centro reci
proce proportionali deorſum trabantur: dico quod, ſi diſtantiæ
ſumantur in progreſſione Muſica, denſitates Fluidi in bis di
ſtantiis erunt in progreſſione Geometrica.

Deſignet Scentrum, & SA, SB, SC, SD, SEdiſtantias in pro
greſſione Geometrica. Erigantur perpendicula AH, BI, CK,&c.
quæ ſint ut Fluidi denſitates in locis A, B, C, D, E,&c. & ipſius

172[Figure 172]
gravitates ſpecificæ in iiſdem locis erunt (AH/SAq), (BI/SBq), (CK/SCq),&c. Fin
ge has gravitates uniformiter continuari, primam ab Aad B,ſe
cundam a Bad C,tertiam a Cad D,&c. Et hæ ductæ in altitu
dines AB, BC, CD, DE,&c. vel, quod perinde eſt, in diſtantias
SA, SB, SC,&c. altitudinibus illis proportionales, conficient ex
ponentes preſſionum (AH/SA), (BI/SB), (CK/SC),&c. Quare cum denſitates
ſint ut harum preſſionum ſummæ, differentiæ denſitatum AH-BI,
BI-CK,&c. erunt ut ſummarum differentiæ (AH/SA), (BI/SB), (CK/SC),&c.

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