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# Title: Leibniz-Handschriften zur Mathematik LH 35, 9, 2
# Folio 66r, page id 00068126:0131
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FQ = ye. 99- 84+ 2CX: b9 599- pp. cujus quadratum crferatur a quanato ipsius 2MF seu q. p
residuument quadratum ipsius 3AQ. jam FZ = gy ex FI 99- eq+ EFX: bbg9 49 pp
interatur a 49 +pp - 29p. fit 3MF = 49 + xp- 29p bb99 49 pp = ax - 2: 9 XX CC  49. c9, ∞
omnia divis. per bb99. 99. pp. cujus ratio ad FZ. hinc ita habetur.
3MF ad F2:: 49 + pp - 29p bb 99. 99 pp = ax = a : qXX eC F99 C9+ 2X
2X = a: qXX eC 12) 99- e9+ 2Cx. sene qqe
jm yy = ee - px b: 4eC ergo yyee = ec- pp_bb: 4
seu
qV qp. bbg9e. 9+ p. q P
3y ee (2119. 59u
So
1 = SM
FE
rursus quin X = 9. 28 C= p ergo 2Cx = 9 C- p, et 99 - eg + 2Cx = 49 (= e9 + eg - 9p = 9. qp
Ergo 2ME=
yy
ee
gr  bb 49- 4)p + ee-pp
yyec
proba 29: 2e . q.e = bb: vore 499+ ee. Ergo erior in calculo. Resumamus:
FR2 C. 24 9 multiplicetur per y dabit y. C. 29 q- p = Y3M in FA = 3MR.  F9. jam 3M A=
b: 29 199 - pp. Ergo FQ = y. C: 29. 9- p: b: 29. 199 pp. _por 1F4: seu
= de: b g- p. g7B FQ:  3MF seu F9: = P:: ye .  49 - pp et F9: 3MF:: yyec.: bb 49- pp
Ergo 1- 3yeC ibb 4q. pp = seu bb 49 - pp - yyee, 4bb 99- pp = 3ng: 3MF. Ergo fiet.
3A9: F9V.
-
L.: 2bb. 19. pp  - yyee,: gy ee _:: bbgu bbpp cebl. 4 + bbpp. 4, ce H
. 46894  4bbpp - = bb ee (+ = bbpD), : 4 bb ee -  bbpp
2d3M: 2md
1 ut alocalculo inveneram.
seu 3Mg: F0V.
2:: 99 ee seu bb: ee-pp et 3MZ: FQ:: b: Lee -pp. 3Mod.
2
et quia y = Vee - pp b: 2e fiet Vec - pp: b,: _ 2Cy: bb
n
veloclatumc
rationes qum impetus  si planelarum porcienti esse
Hinc patet
corum ad velicitates circulandi esse ordinalis seu distantris alinea obsieum proportio naler
Et si circulationes _ planelic fingantur nformes aequales temporum ellmentis inaequalibus assumtis
sore impetus paracentcss ordinatis proportionales.
Ex valore etiam ipsius patet eimen
tadiorum fore elementis abscissarum proportonati. Hix cudetum spositis circulationibus
aequalibus erunt ardiant summae impetuum Elementa reulem radiorum sunt ipsae velocilotes para
cntricae. Hinc eo caso Ccrculavim aequalium) sunt ordinatae proportionales abscissam
elementis ergo arearum Ellipseos ex ordinatis elementa, ut smamas absissum quadrata
elementorum ab abscissaerum. Si ponantur velocitates rtu paracentricae aequales erunt
velocitates circulandi ordinatis reciproce proportionales. Ergo summa velocitatum circulandi
labebitur ductu oidinatarum in Elementa paratentrica, seu nomentis elementorum paracentricom
Ex axee
No quod examinandum ad meditatione meam de via centr gravitatis cum
mobile partem sui retporsum continuo quiescentem relinquit Nota: cum circulationes
ecomentau
sint in cposita ratione angulorum en radiorum. Ergo cum circulationes aequales anguli sunt reci
anguli elementulos sunt reciproce ut radii ergoub ord et differentia un. Cum tempore
aequalia circulares sunt reciprore ut radis, ergo recipioce ut abscesae data quantante aucto
vel minute.
Gandratorum
Tempo in Elm ente sunt in rade, posito ratione angulorum elementalium et rdiorum