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nydus/Philosophiae Naturalis Principia MathematicaPublic
Page 307 of 473
Table of Contents

SECT. V.

Figure for Corol.

Corol. Hinc si detur densitas Fluidi in duobus locis, puta A & E, colligi potest ejus densitas in alio quovis loco Q. Centro S, Asymptotis rectangulis SQ, SX describatur Hyperbola secans perpendicula AH, EM, QT in a, e, q, ut & perpendicula HX, MY, TZ ad asymptoton SX demissa in h, m, & t. Fiat area ZYmtZ ad aream datam YmhX ut area data EeqQ ad aream datam EeaA; & linea Zt producta abscindet lineam QT densitati proportionalem. Namque si lineæ SA, SE, SQ sunt continue proportionales, erunt Page 298 areæ EeqQ, EeaA æquales, & inde areæ his proportionales YmtZ, XhmY etiam æquales & lineæ SX, SY, SZ id est AH, EM, QT continue proportionales, ut oportet. Et si lineæ SA, SE, SQ obtinent alium quemvis ordinem in serie continue proportionalium, lineæ AH, EM, QT, ob proportionales areas Hyperbolicas, obtinebunt eundem ordinem in alia serie quantitatum continue proportionalium.

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