Newton, Isaac Philosophia naturalis principia mathematica 1713
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266
tatem BIut summa omnium AH+BI+CK+DL,in infiNI­
tum, ad summam omnium BI+CK+DL,&c. Et BIden­
sitas secundæ B,est ad CKdensitatem tertiæ C,ut summa om­
nium BI+CK+DL,&c. ad summam omnium CK+DL,&c.
Sunt igitur summæ illæ differentiis suis AH, BI, CK,&c. pro­
portionales, atque adeo continue proportionales, per hujus Lem. I.
proindeQ.E.D.fferentiæ AH, BI, CK,&c. summis proportionales,
sunt etiam continue proportionales. Quare cum densitates in locis A,
B, C,&c. sint ut AH, BI, CK,&c. erunt etiam hæ continue propor­
tionales. Pergatur per saltum, & (ex æquo) in distantiis SA, SC,
SEcontinue proportionalibus, erunt densitates AH, CK, EM
continue proportionales. Et eodem argumento, in distantiis qui­
busvis continue proportionalibus SA, SD, SG,densitates AH, DL,
GOerunt continue proportionales. Coeant jam puncta A, B, C,
D, E,&c. eo ut progressio gravitatum specificarum a fundo Aad
summitatem Fluidi continua reddatur, & in distantiis quibusvis con­
tinue proportionalibus SA, SD, SG,densitates AH, DL, GO,
semper existentes continue proportionales, manebunt etiamnum
continue proportionales. que E. D.

DE MOTU
CORPORUM

Corol.Hinc si detur densitas Fluidi in duobus locis, puta A&
E,colligi potest ejus densitas
figure
in alio quovis loco queCentro
S,Asymptotis rectangulis SQ,
SX,describatur Hyperbola se­
cans perpendicula AH, EM,
QTin a, e, q,ut & perpendicu­
la HX, MY, TZ,ad Asymp­
toton SXdemissa, in h, m& t.
Fiat area ZYmtZad aream da­
tam YmhXut area data EeqQ
ad aream datam EeaA; & li­
nea Ztproducta abscindet li­
neam QTdensitati proportio­
nalem. Namque si lineæ SA, SE, SQsunt continue proportiona­
les, erunt areæ EeqQ, EeaAæquales, & inde areæ his propor­
tionales YmtZ, XhmYetiam æquales, & lineæ SX, SY, SZ,id est
AH, EM, QTcontinue proportionales, ut oportet. Et si lineæ
SA, SE, SQobtinent alium quemvis ordinem in serie continue
proportionalium, lineæ AH, EM, QT,ob proportionales areas
Hyperbolicas, obtinebunt eundem ordinem in alia serie quantita­
tum continue proportionalium.