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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
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PRINOTPTA MATHEMATICA.
42)
cudo Aquae sub . quatore superet ejus altitudinem sub Polis men- L. IVet
tura pedtum Parisientium 85820; vis Solaris de qua egimus, cum Pearivo.
lic ad rim gravitatis ut F 2d 12668200, atque adeo ad vim illam
centrifusam ut 289 ad 12868200 Ccu 1 ad 44527 etticiee ut al-
cicudo aquae in regionibus sub Sole de Soli oppolicis, luperee alei-
cudinem ejus in locis qua 90 gradibus distane a Sole, menlura
tantum pedis unius Parisientis e digitorum undecim cum octara
parce disici. I.A enim hec mencura ad mensuram pedum 85820
uC I 2d 44,527.
PROPOSITIO ZXXVII. PROBLEMA XVIII.
Invenire vim Lunae ad Mare movendum.
Vis Lunx ad Mare movendum colligenda est ex ejus propor
tione ad vim Solis, de haec proporcio colliizenda eA ex prOpOr-
tione mocuum Maris, qui ab his viribus Oriuneur. Ance octium
Aurii Avonae ad lapidem cercium intra Bristoliam, tempore verno
e autumnali torus Aque ascensus in Conjunctione et Oppositione
Luminarium (observante samuele Sturmio) est pedum plus mi-
nus 45, in Ouadracuris aurem est pedum tancum 25. Alcicudo
prior ex summa virium, posterior ex carundem differentia Oritur.
Solis igitur e Lunae in Aquatore versantium et mediocriter a
Terra distantium sunto vires S e L, ec crit L. + S ad L =S ut
45 2d 25, Ccu 9 2d 5.
In Portu Plrmuthi A. Cus maris (ex obserratione samuelis C ole-
pressi) ad pedes plus minus sexdecim alcicudine medioeri artolli
tur, ac tempore verno sc aucumnali alcitudo F. Cus in Syryoiis su-
perare potest alcicudinem ejus in Ouadraturis, pedibus plus septem
vel octo. Si maxima harum alcicudinum ditterentia sic pedum no-
vem, erit L = S ad L = S ut 20: 2d 112 scu 4Y ad 23. Oux
proportio latis congruie cum priore. Ob magnicudinem A Aus in
Poriu Bistoliae, obserrationibus Scurmii magis Eidendum eNe vi-
detur, ideoque donec aliquid certius conttiterie, proportionem 9
ad 5 usurpabimus.
Caeterum ob aquarum reciprocos motus, Actus maximi non in-
cidune in ipsas Luminarium Sp2ygias, sed sunt tercii a Syzysiis
ut dictum fuie, scu proxime sequuntur tertium Lunx post Syzy
eias appulsum ad meridianum loci, vel Dorius (ue a Scurmio nO-
CaTUT) sune certii post diem norilunii vel pleniluniis seu post ho-
PaM