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# Title: Leibniz-Handschriften zur Mechanik: Dynamika LH 37, 5
# Folio 114r, page id 00068534:0223
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 115v); this page is its right half.
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(1) planeta circa solem A, fertur in Ellipsi D PEXI, ita
ut areae PACA PACp sint temporibus proportionales.
irca ejus axen
(2)Centro B allipseos, diametro ejus majoro vel Ax, pX describatur
circulus pdXF. Et LC ordinata
Ellipseo) ad axem, producatur dum circudo occurrat in K
erunt areae circulares PAKP temporibus proportionales
Nam LC ad LH, ut BE ad Bd. Ergo PL CP ad PLKp
ut BE ad Bd. Rursus AL C ad ALK ut LC ad LK seu ut BE ad BC
ergo PLCP + ALC id est PACP, ad PLKP + A ALK id est ad PAL p
ut B ad BE ad Bd
(3)at (3) dato tempore quaritur locus planetae, seu data area PACp, quaeritur
angulus pAC, vel aliud quiddam determinans sit radius circuli BP, sit Y. BC, C
BEsit C, AB sit f decter locus planetae C ponatur datus, adeoque BL, X et By et L, LC, y. est
autem LK = fr - XX et y = eFrr. x: Y et PBKP s sit BK = a 
fiet sector PAF  PBK P = ra : 2 et triangulum ABK = LK, AB: 2 =
Vrr = XX. f: 2 ergo Area PAKp = ra + fYYr XX, : 2 = ZY
Somex
et fiet Yysdx + f Vir = 2YZ seu rdx  - Xdx = 2rdz
X
srrxx
seu rix  dx = 2r errx dZ unde rVX -ZnX = 2Y (srr. dX dq. sint PX vel 27
sinus frr-XX et PF vrlX Q sint tempora  erit PTZ = prrxx dque = 2rX (XX, : 2+
quia dx r-x a,: 2Y = dque hinc quaeratur  per seriem ex X,  valo multi-
Ver - xx =  fit do = - 2X x  sir x
plicetur per r-X. jedies prodiens summetur. fiet secies = e dq 2rZ seu tempori.
Trrx
est hac aequatione doncatur radix per seriem, ut habeatur X per L
 (e at v = a + e a v + C. e1 a V  + C. p. 116. 2 13 17 +  al e. 2. 3 B. 4 4
ax YI = 2r dZ
vn
. 2. 3
seu q =  x + p
Vir n
1,23. 4
 set rr- XE 2 rE X - C r xx + C. C 1 p. 4 - P. E. 1. 8- 2. pre 67 6 exr vr a3, pe 8, 
2.3
+ 12.3. +.
Sit exai folse) rruxx = = = + +    +  Z.  5 H + 2. 2E arr 2
er
F.1.2
Er
2
inna Dro cu.