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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 31v, page id 00068196:0062
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HZ
XY ejusque abscissas
Curva variari Yy refertur per ordinatas ad AXem AX. ducatur
alius AXis A per idem punctum originis A, et sint ordruatae
abscissam
novae YC. Ex  agatur normalis in L in A AX,
et normalis GM in ordinatam YX. sit AL: LG: AP =
Y M: MG: Y8 = b: C: C et eeL bb + cc
fiet suit AX, X et YX, y et A∞, 8 er YG, W
fiet ob  AX = AL +  M fint X = bG (1) + CW C M)
ob XZ = XM -9L fint y  wo (seu Y) - E  (sen PL)
fiat jam AG, g. parallela ipsi  Y8 et per G ducatur GH paralleta
ipsi AG e occurrens ipsi Y (si opis productae) in Z et sit
Z; et Y7 V erit P- 9 + Z et W AP = Gu +HZ seu G =  h +Z
similitens
N
+ v
N∞ = YZL AC, seu W
 FZ seu comperio K +E∞- EZ
etae sunt omnes varietates quarum capes unt ordinatae, quamdiu maneat
ch, :C
f+ k ist
normales: =h+ Z et Z. 8- h - et Ex 4 et 5 fil Z = (5) - 8 -h et
V = (11) =_ W - 9 ex 2 et 3 investigemns  et W, Nempe ex 2 fit
ex =  CW _,: B = 8 Et ex 3 fit bW = Cy3: C =9, quos duos
ralores equando fit cex - ccW = bb W F bey jam bb + cC = ee, fiet
CCX = eeW = bey seu Cx + by f: e= W, quem valorem ipsius W substi-
pendo in priore valore ipsius 8, fiatus, ee CCx = bcy, ibe =  seu bbx - bcy, : b =
sen ha ebs cbetincs; eu denique e bx = cy,: e=g. Hos valores 8 et o substituendo in b et 7
X - = y - h et vC5 Cx +by - g
Sit jam aequatio ad Conicam maxime variata, nempe
data
aa l aal a
amzu =-amh A ambx - amc y
+
(13)
u es
anv = -ang + ancx + anby l
ad dyus =2dEx + d+ xx
pZV = ph9 = Pb9X + P Ch y  p bb XyG + pbeXX - p bc yy
= pehX - p bu y q- p cC xy se
rata
rZZ = rhh -2rblx + Erchus- Erbexy + rbbxx +r ec yy
192
 cam une epehe
SWV = rgg = 2SCgX - 15b9y + 28bC xy + s ec XX + 5 bb yu
ee
Tollantur + primum X et y ope q et h.
et xy ope b: c
reliqua invenientur ope f, E, et q identificabuntur
sed calculus iste, etsi in potostate sit, non est hujus loci umenim honagitur decedeliore
aquedim adjauicam potius ex data ad conicam generaliscunte. ) S 2tX + + XX ducenda composita
Hinc
composilae datae ad simalicem
quautum fieci potest facendo assamendo valores ipsius ipsarum et es seu qualex
inventi supra aequ. 6,7,8, c. Nempe X = ft BZ + C∞ et y = K +  v- EZ
2F x = + 2tf + +Z + 2tcb
qee
 iuin
eer qee
gy = - KK + 2KC. Z - 2Kb∞ + 2bC vZ - 6b qqe = bb. v0
o
ee
identificanda seu per compendium
al + nZ + nV +Y 07 + = ZZ +s v0 = 0
ordinatas jam mutemus in obliquas, pro YZ _ et parallelis, su ad abscissas HZ seu Z
: ZH
YI-
ale
ad hibendo Y V et paralletas, _. ad abscissas H  seu . ita ut sit YZ
fiet v: co d: a et ZW siu V- Z: cd = d i: a
d: i:  a et dd +ii ac
seu v d co et X )  - 1 co, et fiet  beb7 fiat X = f + b. 1 - bi co+ cdc 
ea
et Y = K + bd c0 = C + Ci cd, et fiet x = + cd -bico + B ∞ et y + bd +cico - c V
quae aquationes servient sistatum velimus transfonuare  datam aequationem ad curvam nempe 19hoc loco.
posito  btrcqie
vi et - C9,: b = h
bg -ek: c 2h
ref - ccg = bbg - b et
seu cet = eeg - bek
seu 9 = cf + bk,: 
 bR + )
et B et Bek-
et = cf +bH ek:C
ien h= Cf- cbkrcet, 1B
et s-eef-as-cbr. dosciel y 11)
bbF - bCK,: bC
ergo ld demum hi- bf-ck; e)
0-
64
reducenda ad dyus Ltx