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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2a
# Folio 48r, page id 00068197:0095
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IriHusperbola et Ellipsi sit g latus transoeisum seu axis directus, e diestantia socorum
in ipso dec etemat sacriphcrae eut di t t r latus rectum h axis conjugatus.
fit Yg = hh et ee = q9 +hh. sit y ordinata ad axemdirectum, oidinata ad
uxem conjunatum, fiet gus = finh: 49) ZZ 4 +hh Et = in Hyp. est +, in Ellipsi est
sit dre elimentum artperppheriae fiet generaliter dic = dz - ee Z2,1:, L.9= 993Z) D
fiat 7Z = g17 fiet d = Zd7 = 2= qdv. 2 et dz = 4d0: 21qu. 2 et substitatione facta fit
dedo .  felv,.   (q 7 L qiu qer  (44 erq s., q 
seu 2d4 = dx +( 9 ees q - dv f(49 - eev, 4 4q - qub A,
eo
tlipsis cum foci inceretrum cocunt sit circulus. Hyperbolo cum foci intentium coeunt fit recta
fiet de = 9dp (49 ee q El et 2dn = do 1:
 qi
s
-.
Etqu.
P - quv
129 -eer des
V....
Fxaminemus valores ipsorum summas ipsorum dv 
119 - 99V
quae omnia possunt hiberi quadratura rationali. Compendii caussi pro =G ponamus 94)
dv s du s..
pB . B ....
aa 49f - eer = cded. fint ej qyf - eex  onscoto queoco et v = 45C af (9-co) , ee gco
4f - qqu 2 et fiet ggt eer = fcoco- veoco et fiet v = (9 ct) gu loco, f:, ee -coco
et dB = fico, 20 (es coco) trco (9q. colo) = faco, 2co (99. LDC)) et co dx = f deo, 1oco (99- ) sit 49 e gy
qu (e-10c0))
qu (ee=C0co) male
_ fiat (g cdco: gg (ee Coc1) - Y Y s a+ 1 = C Bocossus ec  iide
e
ee coco, ee loco
12e 
qu (2+c0) (e. C0)
qu (ee=Colo)
-, e- co + et co e = 4
1i2e e t
1.28 = 2e
qus e 1o) et Cmpo tunt
Et sandem s
est aut
...2
qu (et Co)
eto +e- ed
 ana
.
= 20
e 1.2
quse quterco)le co)
+ ee-c0co
= Tec qu e c0)
Coco
qu (e-co)(et C)
Hoc ex eo dumpoterat, quod
2Cold
Eon L +  qu (Ct) -coo
Qu (2. c0) qu (era) A, P- co
1
 + 4 eb - cocs
enco + et co = 4 qu (etuo)
qu... .)..
ee coco, ee o1  B, qu (- c0) L
Woeo, Lu +
28c0 = 
 et co, o ena erco
sit e co = , fiit 9929C + Q =W010)
e et et coto
= 8-28e +e 1 - 28. +2
qu (2. 10)
8)  = etco+l
qu( etco
1 = re log1  - ee = e+ 10 = 20 log (et c0) - ee
tco
sC
 +2e log (e - cv) + e
et erco = _ tit coco - eu- 24 (1 = 1 -  E +   jam lco = d et fiet
co
qu (et co) fcoco. S csto dus - (99 - 28C + ee -de = - 99 t y g + C9- log 5- sul. 1) re e . 1u. 
Je
coco deo
seocoduo = (e - e et ex A_ = L 1 1 - e  ec log  = 2 qu ( et ) -e (e+ ) + ex log (e+ C0)
gy9
etco
( -10
Ergosit 4ee coco - - et lo + 20 by se c0) reC
et 4440e 4q du 41, - = etu
Qu (eeci)
= L qu (C - 10) +  (e- c0) = ( log(e. c0)
 + e  (et co) -(e + C0) + e log (e+ co
+a
  logle ce)  by fet co)
et v= Z2. 9 = 4g. ed ita in casu ultimo fit co quantitis in finctae, sit
4 G eeV a.E
Ergo mutemus Hypothesu a ficiam (q P - eeto : a - pB) = 9: eo ita erit cd in ultimo inffinite parva
in casa ultono fit Z= 293 - cer
+4- 4
et fiet 995. ees = 42. et 49 feocd = eep coco = 99 syque - q u, et erit v = 9t - q9 g :, q recoco,
i enim loco = 24- qqe
49(- qq cocet  d ∞ =
qu (99 -co co)
44d
495 200 + ee 2 49f2 ( Be a) + ee 24 (15- 49) cro) du
ju
a ad _ b Ao + 2 PC495
Cuijo Eup debet summani 2
debelit summam
12
12
deo
99.
q- levo
qu (9 - ee coc0)
qu -coco
L
qu (q eCcto)
+ 99- coco, deo jam = ig
p egio) pusgerui)  gg alo quloguud 22 qusque
99. Wd
qu (99 Lolo
d
q. ee = 9d
I 129, 1. 2g
 g- a +9 +cd = g g.t 
9 -c0co
quao
+ 2C
 quege 18) gg- coro
1
( - XY
(1 - XX
qu (1 = XX
39 (L X X)