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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 127, page id 1041163592:0161
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PRWNCIDLA MAEEIEMAELCA
nitum diminutam, rationes ultimx CrUnE R C C ad T cub. UF -F F
EIDEK
ad = 3TY seu CC ad TT uE F F ad 3P Y et viciltim GC 2d PRIMOS.
EF UE FF ad 3 TF id cA, ut 1 ad 3; adeoque C ad l.
hoc est angulus V C p ad angulum VC P, UE I ad v 3. EF
30 cum corpus in Ellipsi immobili, ab Apside summa ad AP-
sidem imam descendendo conticiat angulum V C F (ut ita di-
Cam) sradum 180; corpus aliud in Ellips mobilis atque adeo in
Orbe immobili de quo asimus, ab apside summa ad ApSidem
imam descendendo conticiet angulum V C p gradum: id
adeo ob similitudinem Orbis hujus, quem corpus agente uniformi
vi centripeta describie, ec Orbis illius quem corpus in EllipA re-
volvente erros perasens describie in plano quiescente. Per su-
Periorem terminorum collationem similes redduntur hi Orbes, non
universaliter, sed runc cum ad Formam circularem quam maxime
appropinguane. Corpus igitur unitormi cum vi centriveta in
Orbe propemodum circulari revolvens, inter Apsidem summam
ee Apsidem imam consiciet semper angulum =8e graduum, seu
103er. 55M. 23 sec. ad centrum; perveniens ab apside summa ad
Apsidem imam ubi semel contecit hunc angulum, ec inde ad APSi-
dem Cummam rediens ubi icerum contecie cundem angulum; et
sic deinceps in infinitum.
Exempl. 2. Ponamus rim centripetam esse ue alcirudinis A dig.
nicas quaelibet A = 3 scu =: ubi n - 3 et n signiticane digni-
cacum indices quoscunque inteoros rel Fractos, rationales vel irracio.
nales, aftirmatiros vel negatiros. Numerator ille A (Cu Y - X 
in seriem indeterminatam per Mechodum nostram Serierum conver-
sentium reducta, cradie F, - n X 72 - 1 , nn - n y Y fn -.
eC.
FE collatis hujus cerminis cum terminis Numeratoris alcerius
RC G = R FF L FFF = F F XE, GIER C C =RFF + FF Fact F.
UE = F F ad - n Jn - 1 + n B = n ∞  n - 2 _C. EF sumendo eatjo-
nes ultimas ubi Orbes ad Formam circularem accedunE, st RCC
ad Fr UE = P F ad - n Fn = 1, Teu C, C ad Fn = 1 UE F F ad p F n - 
id est nE F ad n3
ec vicissim C C 2d F F uE Tn - ad n T n -
adeoque C ad F, id est angulus VC P ad angulum VC F