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# Title: Leibniz-Handschriften zur Mathematik LH 35, 10, 7
# Folio 16v, page id 00068160:0032
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imo non suni eementa destepsus absolut rested en soluju
Y et progressuu circularium ergo. seu elementa descensus ECG. nantulit ddO = a daf + nt fdd +2a f
At eadem 2CG sunt in composita ratione velocitatum,  2 adioro ad
sunt in ratione differentio differentiarum ab ordinatis, et radisrm
progressuum circulariam; ergo demtis utrobique radiis velocitates
erunt in ratione differentio. differentiarum ab odinatis directa
sit jam curva sectio conica, cujus axis AB (an foill et diameter)
Ho fet vertex A, fiet cu latus rectum a transversum b, fiet
Paf+ = ff = eC. et B X~ + eC. et AP = h. fint PC seu
X = L+  eeth - f + ec sin quod si AB sit auis et B
sit curvae umbilicus prit a latus rectum primatium, b latus trensver sum primartum
ger axis curapplicantur ordinata inter verticae interceptus, sit c distantia socorum
12) tape si AB sit agis primarius erit a latus rectum, b tatus t primarium, et
aX ux
blatus transversum primarium seu axis primari pars inter vertices intercepta
nempae ASt =b. sit ju p e et sunt foci p eeentium curae sit +, et erit
sin
am g = Y bb - ab et  bb -99: b = a seu a = b449. b jam
ut inveniatur pB, de AP, de seu h debet, a dimidio axe b: 2 detrahi dimidia
l
qu2
indissi ti elgo his substitaris
distantm umbilicorum q.2 ergo h = b74.V
fiet B  - B9q. b f + l - 49: b6 fs = e,
e
sed ante explicatioaeu tollamus f
ex aequalionibus 1 et 2, fiet ff + bf +. bb = + ee + bb, et adeo
b: 2 +9. 2 - f + ee
X = 1
fiet f = bb + ee 4b:2. rursus ob  ag. 2. fiet 1XX - ee = h -f
seu f = h - Sxx - ee. Ergo bbb + ee + b.: = h - (xX - ee- ja
H: jam a SO = seu d 92 = 1: 2 3 ad. Ergo aequationis D differentiali
erit Fede: s1bb tee = -  X dX A ede: Sxx - ee
seu ee de. XX - ee = X dx + 2Xedx de + Cde. = bb + ee
sed ex e, investigam aequo t. anvestigemus de fint _ ads trafas= de
de  Lads +4fds: 1af + aff, et dde. Od3 - 3dco: D.
seu ade seu Za+ f4fd5 . de = e. = a daf + a fads + 4 d5,: e
seu d adt +gfd5
ut enveriome
I.2 = 
ddeseu d d (9) 2 = 1: 2,, C
1: 2C
- l: 2
do et
I: 2 sdC + d C
2
1: 2 dC
dd
i2
jam d O
T: 2, dC
1: 2
132
= - 7:2C
.3:2  si jam -
Ergo ad O1. 2 = 1: 23, C ddC  - 5: 2 C
= tas e = (af + a4 fs fiet 6
a
denque
 = et O = a5 + 4f et dC = adf + 24f af et d0
si jam C 1: Z
1
et dO = +f. a + 4 a f + 49 s seu df. a + 2485
directa. ordinatauum autem inversa; at eadem per superiora
sunt i coproposita ratione radi velocitatum, et ratiorum et
et ordinatarum ac progressuum circularium inversa.
d
es