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# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 73v, page id 00068201:0146
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eundem calculum aliter perveniemus: si ex eodem puncto ducta perpendrentari
ad sectionem Conicam, ordinata non ad latus rectanguli nscrpti sed in axem condeae
sectionis demittatur qua ordinata appellata y, et ascista , ent aequatio:
rax +  X _=  H0 Et ob Tringulaum similia ert de 1y de Cay in y
Fa atqu
Esti cum sa  X. Uender da = pY + dax F C x7 1S) qutm aiu  ad
Unde ge AG D X p(t B y + de X + da
F) 
sive per borachplogiand n g yX + Hy 4 daX H ad
Ex puncto quaesito . H. ducntur ad Tangentem verticis AB ducata recta Z. sive A
ita udt angulus HNL sit obliquus, i rectu HL est perpendicularis in Recta erquZ vel supra
vel infra L. ocadere potest. Ponatur HL ad AZ ub  seu X ne 20 Erit ) ∞
et AZ V ciet A eni o t Z() ZL suive  (4) 2. Est autems
Erit ergo g v(+Si- Euso es  s (4) si DX  mdsirtana
sus valores aequationibus insoentu fiit tee
3p aZY + a x. . Z v
Et ex Aeq. 2. fiet Ay (1).
Drioris aequa tonis sepis militis
eam ita scribemus: 
e a emad rimuturs
e. 10l 26 1
(+)psu Z QSi Lnor
(1 (V
De. 9
Ende fiet Aequalio ad circulum:
ei
u 
ZV 2a093d. + V (+)2 Sn 2
Cao) a 1..
 x  ervit
edr 
squs
118.. + y P da
i. le 
ar a io ii mua et i nn  suans alai siner 
conferno cum facntia ad Cremlum:t
11+ Gr . nDZ = gr =ba Bo.  et
Et cnfeoie brmat YZ, e Habelinius Aequationes collatitias sequentes, quarum ope ante
invenietur e seu obliquivas anguli, per collationem terminorum vy, Unde.
21.  ri. (4 2 rut l 8 - im. 8. Unde jam patet putium signum (+) debere explicari
per +, alioquin 21. 3 destiuetur iutobique et  e fieret infiniti loaga, unde caeteraabsurda
sequentur quae supra. Quare fiet: 2 r in = 2S  + 19 - m  ive si mavis
eim- 20 . V. Ego m. A .  al  ma Est autem l p a. sive linitati. etm 1 +D a a.
G Ergo 4 4es.:  Va 4e sud e L m. sed = YB  S
Unde ae t am,  es.  Ergo 4d L im l- no. Jam um e + ) a3-a
et la l n et a +Va3-a. Ergo 4a + 3 a sinc Ae   Va
Ergo 4C sin da s B l = m. Ergo 4a + 4a e l = m, sive B a - m. Nam
a et lte aequivalet hoc loco a seu unitati. Mt-m r a Va - a. Ergo l- m ppl. V a- p
: Ergo- 4a  Pa4 + a, sive e ,V a + 4a2
Inventa ergo est e. sambego conflrendo termines Z. Erit -ge  P + aF- ut sive:
et
-2a + Y s. + dat, (a- n,) V s sue tag e 2a +e   4+ da,
1- a H 1 - =. Eno
+4 - 4. Erpo HI a Quoniam autem P   est quantit inexplieabus,
bilis hocid tolendum est signum radicale fiet: et primum ordinetur sic: _gcd +8a V + d CV  ea Y P
Uende gre du9 e tbaerSed G + 9a e  . In Ellipsi, uli + enter et a pa ibi
in opus est Ha quad ratione
landes t19 ones. p quo etta sidt a  
raen. prium G an A H 
l4ga. t  hit cGr fac
  9 ae
9 + 204
nate na die ead
Eet nen  1  sicet  a)  egeu 20   pdeet Poronus iam
sive eged  8a) + ea S   V. T enda irrulid nalitus, es emimi tali radx inexpica
c +4148..... 5.
gag L.  ⊓ +
Si Z. inderet ultra A. fiere AL , ZL A7.
1Z. constrnter erit
t it
2. 18∞ seu +12Z. F 1~L
 25p2S. -2. AS AZ- dZ)
sia ss vtu Ego 5+ V(VZ  (Cteq. (5.)
1Z51 Jam explicems aequalure
2. sclict eud upoplea 
ribit imutili celictis sigus  Aeq. (4)
( 9ra
et concilieturcu
t r
potes poni epe
Schemat sequentidia
a 505 Ada sid
sui lssto ea
 An. 
erite 416, et Woti 6+ 2
ponams Opo erit d et e
64 dn fiet X ∞ n. D
da - v Omittatur D
fiei a rn da p + mo.-
40 + 2O2 Erg
B X -da - YC+
vel da AYO -O2
- Va + b B X.
Ergo 7 N X 4 2bX +
Ecce exitum hinc duci pes
ubi problema alioqui
planum reddi potest
solidum hac  sola rave
quod asiogon eubo
ersa en li