Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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1ITXPGXAZad ATcub,erit angulus GPg(ſeu Inclinationis
horaria Variatio) ad angulum 33″.
10′. 33iv, ut ITXAZXTG
X(Pp/PG)ad ATcub. q.EI.
LIBER
TERTIUS.
Hæc ita ſe habent ex Hypotheſi quod Luna in Orbe Circulari
uniformiter gyratur.
Quod ſi Orbis ille Ellipticus ſit, motus me­
diocris Nodorum minuetur in ratione axis minoris ad axem majo­
rem; uti ſupra expoſitum eſt.
Et in eadem ratione minuetur
etiam Inclinationis Variatio.
Corol.1. Si ad Nnerigatur perpendiculum TF,ſitque pM
motus horarius Lunæ in plano Eclipticæ; & perpendicula pK, Mk
in QTdemiſſa & utrinque producta occurrant TFin H& h:
erit ITad ATut Kkad Mp,& TGad Hput TZad AT;
ideoque ITXTGæquale (KkXHpXTZ/Mp), hoc eſt, æquale areæ
HpMhductæ in rationem (TZ/Mp): & propterea Inclinationis Varia­
tio horaria ad 33″.
10′. 33iv, ut HpMhducta in AZX(TZ/Mp)X(Pp/PG)
ad AT cub.
Corol.2. Ideoque ſi Terra & Nodi ſingulis horis completis re­
traherentur à locis ſuis novis, & in loca priora in inſtanti ſemper
reducerentur, ut ſitus eorum, per menſem integrum periodicum,
datus maneret; tota Inclinationis Variatio tempore menſis illius
foret ad 33″.
10′. 33iv, ut aggregatum omnium arearum Hp Mh,
in revolutione puncti pgenitarum, & ſub ſignis propriis + & ­
conjunctarum, ductum in AZXTZX(Pp/PG)ad MpXAT cub.id
eſt, ut circulus totus QAqaductus in AZXTZX(Pp/PG)ad MpX
ATcub.hoc eſt, ut circumferentia QAqaducta in AZXTZX(Pp/PG)
ad 2 MpXAT quad.
Corol.3. Proinde in dato Nodorum ſitu, Variatio mediocris
horaria, ex qua per menſem uniformiter continuata Variatio illa
menſtrua generari poſſet, eſt ad 33″.
10′. 33iv, ut AZXTZ
X(Pp/PG)ad 2 ATq,ſive ut PpX(AZXTZ/1/2AT)ad PGX4AT,id

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