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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2b
# Folio 88r, page id 00068198:0175
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invenio Quadraturam meam Geeralem Arithmeticam
Sectionis Conicae ex centro ic consignatam. ertor Genem
comprehensus areu sectiones (ontea à vertice
ad ejus extrema ductis aequatur rectangulo subsemi
et rectis ex centro
targentis in verbce, inter verticem e tangentem alterius extremi interceptam
et rectargulum sab dimnidus lateribus recto et trausverso seu quadratum asemi axe
conjunato, esse unitalem. Et + esse + in Hyperbola, sed- in circulo vel Ellipsi
= 444Ht- 49ttX
XX  - 4 gtt X
AC semitatus taus versum q
CV = a erit r latus aa = qr. postso
esse Y semitatus rectiuem SR, si ssit focus. AT, erit F,
fiet ACG A = 9t - 59l + 9t 9t
Baa Sat
q0 etc= 
differentia foret at - H dt + + - b 1 et c = dt 4a
aa
a
aa(at, quaeratur loguithnice 
aa+It
40
aa - (t1) a+ t. -1, ac LF -1
a- tf-1 a+ fY-1 D
2a,4-tr 2a, a111
= -2a tog. et (vat =  log (a - + f - 1) + log (a + t + -1), : 2a Y - 1
= a log (a - t r- 1) +28 log (a + F Y- 1) :3 - 1
rlog y = log y
Gaaloque (aa + H): 21 -1 = W = au lou aa  tE B S 
CB OFR+ R5 = 29 A5 = 2q FR = 29 -  = F5 + V IY-
Ergo 4g9 - 4qr(+ YV = FS( rr = 4 C5 ergo C5 = 94- qu
Ergo semidistantia focorum est media proportionalis inter semilatus et
differentiam semi lateris rectiX transversi vel pro gr, ponendo aa
fiet C5 = 9q - aa et CS i BG.. Est autem BG - y
cee quam operae pretium erit investigare ex t.
seu yy :, r - EX = BB seu 2YX - ZXX∞:, r- =X = BB. Et fiet
4 - 2
et AB: X = AY: y fiet 1 : + 2 = AT: y Deu AT - Y:, 1- X = +
 2rX GGXX, : 1- v + XP  H fiet CZ = 2X :, 1 
AT.F
N, 1:, 1-2
fit 2rgqx - rqxX = 44te - 2gX t+ + XX H sit . Y = = 4qu
1q:9
en -2 aaqX aa XX = 44 l1 2gX  + XA CA arK, GXx- 499 4qx + xi
XX (a+(  29 tt) - 29a) x + 49 = 49 . 9g H 99 aa (t gq. ut 4g H)
aatH
et fit X + q = ga: + aa + tt et X - 1 4
aa + H
Saane
et X = a  faa + E et y = t -  = + - ta Haartt tsa 1. ta
t Laa +H) ta (tsaa+tF: saa +tt =y
et CSG = L tgq -aa ta: Faa H = _Z
49912 +99ttaa + a99 Cujus numerus . Ergo
1
= 
499+ etc -gget 2d fit W +  = log (a + HF  3- 1) + log.
a gaau (+ Ergo  b
aat t
V, a+ +s. 1 + v, a -t f1 = 2a0 =  - + , seu v -
et (ataa
Saa +t+
BD - X = (3YX (ZXX = YX, + Y XY):
(aa + ltV
seat
exsoc
sanoit auistErx areo sectoris
(9+39ag eaq
49914
a
 yy = 2 rX - Z XX fit dus: dx -E_  r - ZX, :y  = (BG: BD = y: B
2AAGX = paXI
+XX Et seu
_ HE
1 aa +FF
et
verso, et recta
t +  (3+ = +E+  f etc posito t esse, urtionem resectam en portionem
2799X - Y9X =
499lf- 49Htx
+RX +F seu
a
aa + et
F-I
log. (aa + FF. 
28-1
2
vaatet
id sit nunus logaritham
20a) = cd
y - 2t - x)
4g. aa  2t = rx = 2GAat- 29t- 4a H + a, , sqqu. at
aa +tF
aa +H
dx- pa 1H) 8p + -  9 (Att vaa) 2F, dt - 8eaqt 39t. 
5
5-
aatt emet
aarr
fit dx = 6aa4t de
laaret
(5 + ga = 49
hoc patet
nam SV = CA = FV
y=  7
= aa.
quia qu  ac