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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 1
# Folio 29v, page id 00068194:0058
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 (: paro 1676. pro h.. n conta sene rationalis quaerenqu 13.  suo pinem
0
+
pro  poneno ahae x PaB  p 3a  a
intiquf
a VH BZ et VZY
V2
+p
VcaF Y 2 
VE unde hic rationalis figua
19e utius habe potest summa
nan + sit Xp y + D fei ray + rab A a y +. a yb + = D. et hay pabrid
Ergo Q ve 4 9 er 2ri y + quier ran +ane (a y) + 2aqu. + 29 49  1 +  + ag
et fiet 4.  a9: y et fier
et y C
+ a9Z + aq Ergo dindende per aq 9 debet + Z Y a
 + a + 42
sulficii = a + ad 42 aequ van quandcato, seu: + a + 2
2 + a
a2
100
+3. + a
+ a nom quadrato
atsano adcrum coincum a(dr aq - aY y ,  V
(aquay)
2= Da. Ergo gu. Da, qu y () guadunto qui
Z+ Sda
quan
+ a + at pz0 A (+ 1 f20 quod
ostis
+1 - =. 1) 2 aequalio ipsarum sinquae honogeneae sunt curvae Conicae. 91 + 2.
a
qu+ queayt,  - y
et 4a
qugu F
a
fingamus si 9+g  c0d
a H 2) aequatio cnvelonicae
2 +D Z
aequatio ad carvum Conitam generalis figurae quae curvae conirae homogenta est 
et fiet y   - 4 et q y p, 29 -
7+ Ba
5
et prs Z Da C q 7 5 4 . fiet. Zasta (29 a  9a
a2
2
deuminudo ad tanigentes: N 2at + 2 t + 2a + +2at xt p 1Z at paxtz  4z at parir
1 +202 f24 r2ax
V
B
tage dy
compendit
se
rocurtiorpeir
+1 + a  E. seu a +2a +a+qX, rax + a t  EZ aX
cuique tH 4Z ax + 2a5 qu
11 2 2a8 f 24 X 720 f2a7
per C p
unde
216a
ZaBa
c0a
Z+ sta, Z. IBa, 4+g, q y r qa. qui ponatu 9+ N2, 18a Z. id a
fici ac q- y p 9a et q 3 p
29 ( 42, Z +ba. Z. iea no2e
e
.Ergo 29 qu 4 co ar
2+ Y8a. Z. 1Ba
sei ( e 4u Z qada + co a p 2 geoz -. a D
2+ sFa, Z. 1Fa ponatur AZB 5C + d V + fa et cor det hr rla
q+ tad ev + 2cLe, + dv= 1d fiv + fa- gaba + se tgnev + glaea ter  hlavrVa
B igec gder isa , ege +2cdge +2cfa+ dN e + 2d sagve +faege + d v ohsat
1 fa3l
d+paetdr
+2dflae
- 296, +hv + ta
+eh + la a +2cdh
+ 2 cfah
+Ela cd  aecf.
Ubi habemus. v2. C3. ve. Cv. e. V. v. c..
tollendi ergo termini e3. ev. et.
pro e3 tollenda: Cg 10. pro e Y, tollenda erit d D+ 4h 170 2Cd9 +eh 0.
1ad.
quorum utrumque non potest praestari rectius quarum ponendo c10. sed et.  video hac eadem
methodo non posse colli simus enim cer 9 ferent ( et evanesceret e, nec nisi una
incogni indeterminata v, utaret aequationem
1a aq. list qu pone aZ B ce + d v + fa. et ay r ge+hvela. erit:
qu  C + 2cde v + efae + dV + 2d fav+ fa, -Da, age + 2ghe v+ Egla e+h V + Ehlaverae
est
viceo potuisse etiam si denominatorem nis dari ipsis az, et ayc. in queue intrassent ipsae
O. et v, nec ideo ad altiores terminos ascendissemus, habuissemus alterum tantum arbitrariam
adeoque libertatem destruendi magnam, at in aequatione D potnissemus quidem etiam majorem habere
numerum arbitrariarum licet altius non ascendendo, onem sed ea cantione, ut ut idem sit de-
minator ipsaruma Z. et saco. . Nimiram aequatio gaZ ( + co a + 29B a C0 p 29coz  qab
pro Z ponatur a8. pro s act, unde fiet: aN 29Ba AV p 24 a GY gaeD 173
1 6
alri cetd0+ fa ac ge +hv + la. at metnorar
nuspiam ascendetur ultra, v. C3. ve. Ex. v. e., ve. v. e. 0. quod si ergo desideramus, e puram. (nam par
est ratio, cum eodem modo formetur ex C, quaen V. et si unum impossibile, erit et altrum). tollenda e3, etv, et
x Ut excerpamus P3 fi: explicando saltem animo terminos quibus opus: quin eaMe +24 nCC C
ergo aqg m +a C m +29Om C ∞ 249 9C + qB m3. Bt pro ev, fiet apntio tollenda fiet aequatiorusue negrgtent aen taectu a
+248 md = 440 mnc 14g d + 493tc x 34d m n. Denique eroe tollenda siet: 4ga rqua quglac t q a cararcsam
Lratnisa 24admare A 299fa +  gglac + 4d3n e ar. ponendo maot Cn o. ratis fiot aequ. unde pro aegpr: 99 2 N299d
n n
2d. et ex aeq. 3 9glapggza, seu la 2ta
caerne artinunae et focr poperr ha et ea
et s dot
dvita s
13
mmnuce
fici