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# Title: Leibniz-Handschriften zur Mathematik LH 35, 10, 7
# Folio 39v, page id 00068160:0078
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in Ellipsi
et PRt RF = dataeFP
FG+GP = datae AV FG: GP:: FR: RB
Ergo erit
PG+ GF: FG  PR+ RF: RF. seu ipsa FG sunt
ipsis  FR proportionate
tam (FR in GB = esp in
tmo GB ipsis RN proportionales)
pohas ongulis  et Z recta
s
i Gp
sit F= p= P et BS pH = h. sit angulus ad E rectus erut
timam. Trianguta sit sit pG = p, et pH-  C fiet
et PG+ GF  seu A
esse PC
s
et
et PR+ RF seu PF=  pertel
R  jam  et PG+ GF = b et PR + AF = f
jam b : p:: f: PR. Ergo PR = f p: b et FR = f - fp: b et
FG= b - p. jam sit PH = e. posito angulo ad H recto. pat et
esse FG. eii (obtriangula RQF et PHR similia) jore se
FG: B:: FR. RP:: FG: PG:: b - p: p. sergo F9= eb p p cujus quad retum
detructum ab FG dabit data dabit A23, et idem FG detractum, ab
FD dato, dabit qR datu autem ZR habebitur YH ei proportio
habetur ergo tota GH cuisi detratas sed eadem habebitur. Quadrati
Hs detrahas a quadrato GP. habetur ergo aequatio, pro invenienda
quod exequemur: b2 2 bp + p - e b - p - C b- p: pt = Gq
Ergo GQ = b- p Y Sp CV: p est autem Sp= C2 = GH
ergo fiet GQ: GH:: FG: GP Porro RQ - E FR = F et, e
=  b- p: B = C b- p: p. Ergo RZ: FG a C: bx
.:
Sf p = bC: bp. seu Rg =  b - p S5p - b0: bp
tam AR: RQ::  p: bip Ergo HR = 52p - b C:  b
Seu LH
itaque tandem fiet: G b - p Ip C: p 4 (seu G2 + b. p Ss p - 6: bp
+
Ysp = b e: b (seu RH) = p  p- C seu GH
quam aequationem ordinando fiet 
2p - b Sp. e :p = (5p - b0: p seu  2p 6 p apet
seu  ip -b p - ape + +bpe (He b = fp (b18
et denique firt e = f p - 2p- b p 3: b - p.
et: f- 2p. b :: p: b. p
seu quadratum ipsius. HP est ad quadcatum Epconstans, multatum quadrat
dquadrato differentiae inter AV et duplam BG axem, et duplum
ipsius pseu radii PGse ut radius P ad radium ex foco opposito b= p.
Jam triangula jam quia ML parallela tangenti PH, et angulus ad D rectus
erunt triangula L et HP similia, fiebque jum et erunt
jam LD=aN: p in casu motus at areas aegeales aequalibus lem
poribus abscindentis. Ergo et MD= dp et fiet:
ap e ap: a : p + dp:: c:
to
Ergo dp ex-d et= a n: p seu du
p(12
a
PH: pt
aen: p GH
Ca p: prpp. ee =aa GH
est autem GH = Ap bp - si paA + 2p. b
ap - f p - 2p - b
estante 
3: V - p
p P- sY + 2p.
bp bup p
si sint n ut temporum
inciementa