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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 419, page id 1041163592:0453
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III
DRTNCTPTA MAACEMTEMATICA.
+19
C Anus Inclinationis quae lIEX.
AIBD + HEq = BIIg = AIBD + BFg = 2BIIX BH=
duplicatam dictantiam Nodorum a Juadraturis post datum ali-
quod momentum temporis completum, ec arcus (5, ob datum
LK
Duadraturis, e ad AD celacur pepenuculum GH: crie
PEKFIOE.
Nam GF. g aequale eA G TIg + TIFg =- BIID + HF. 9
BF9 + 2L. CXD1L = EVCKAD + 2BCXBII = 2Ven
Idcoque cum 2 F. C decur, cA G F g ut AFI. Designet jam ALE
angulum G F C, erie ut distantia GF. FA autem FIB ad C
uE GTI ad GC, _ PropterCa LTB CA ut contentum G TIX G e.
SCu G HLZ G. F., id CA, uE EL
FXGFq seu
II
F XAII, id cA,
ut AI e sinus anguli AF. C conjunctim. Igitur A AFI in
casu aliquo sc sinus Inclinarionis, augebitur ea iildem incremen-
eis cum sinu Inclinationis, per Corol. 3. Propolitionis superioris,
ex propterea linui illi aequalis semper manebit. Scd E ubi
punctum C incidic in punctum alterutrum B vel D huic sinui
aequalis est, e propterca eidem semper aequalis manet. . P. D.
In hac demonstratione suppotui angulum BF. C, qui est du
plicara distantia Nodorum a Ouadracuris, uniformiter augeri.
Nam omnes inxequalicatum minutias expendere non vacat. Con-
cipe jam angulum BF. C rectum esse, de in hoc casu G8 ete
auementum horarium duplae dictantix Nodorum et Solis ab invi-
cem; ee Inclinationis Variacio horaria in eodem casu (per C Orol.
3. PrOp. nOvisImX) erit ad 33. 10. 33. ut concentum sub In-
clinationis sinu AF ec linu anguli recti BP. C, qui est dupli-
caca distantia Nodorum a Solc, ad quadruplum quadratum radii;
id eAt, ut medioeris Inclinationis sinus AEY ad radium quadru-
plicatum; hoc est (cum Inclinatio illa medioeris sic quasI 5er. 8=)
uc ejus sinus 896 ad radium quadruplicatum 40000, sive ut 224
ad 10003. FA aucem Variacio toca, linuum disferentie BD
respondens, ad Variacionem illam horariam ue diameter B D ad
Ahn 2
arcum