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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 2
# Folio 178r, page id 00068195:0355
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inter
si problema aliquod Geometricum construi potest persectionem duaru
locate
nearum, potert necesse est ut ad binas aequationes educi possit  una sit
ad unam lineam, altera ad alteram, et ambae habeant coordinatas
uter se nonnales.
AVY
sit recta positione data, relata ad aliam rectam positione datam
AX X per
eX normales ad
Tt AXIXY a ratio iata. sumatur
alia recta positione data BZZ secans ipsam AX X in B et
ipsam AYY in C et ex Y. in  BZZ agntur rormalis YZ
 jum relation inter AX et XY, quaevitur relatio inter BZ AVZ
Habita
voce c A3, b CAC 1B48. AX, x. XFy. ABZ Z t 2Y∞
inci
Profbema est celebre mipimam m
vel maxima
 puna
Conicam AY ducere minimam (CY Ex in Axem Conicae AX
gngatur normalis YX, sit vertex A, ta semilatus rectum Y
semitares transversum
AX vocetur X, et XY vocetur y. Erit 2YX +X XX = yy
Ex centro in axem agutur normalis CB, et ABsit b, et BC sit C
minima producta axi occurrat in p. Erit dx: dus G= y: XP
seu xP = ydy: dx Ex natura autem conicae
differata ejus aequatione fit 2rax + F 2xdx = rydus, seu
dy: dx = Y + YX, :y seu y dy: dx = Y + 7x = X s.
jam XP: y = YE: EC = x+b,:, y-c. Habemus
r
Y (X + rX, : y = X +b, :, , seu . b + xy = 
seu by + xy = rC f Xx = ry = s y seu a(bersus + (1+ Z Xy - rc + 2 x
si punctum ladat in axem S
 quae est aequatio ad Hyperbolam, itaque commode solvitur, problema
fisk
bxr+
inter sectione Conicae data, et Hyperbolae si mocum Ccadat imnaxems sitm tomud
eriorem secans in Y.
Ycujus overtex L. Axis Ln
in eod em plano
sit eadem sectio sanica alita
1
t et Y ad L M normalis 5B
naspriorem AAs in M. sit
Z Ht Z et ZY sit veis am, En
 aigatur in RX pormalis L, quae vocatur  n, et N M vocetu
jungatur YL _ Er YCq = Rt ~ X qu + (XY  N1) qu. habetur ergo
cgu intoloratio s YL centro Y radio YL describatur arcus circuli secans ipsam LZ inp
quaeritur LB. punctum Z est intersectio rectae per Lm, et circuli
as ex YR qu + ZRau = YL qu. ob
rectam LZ est MT: 79 =mn
Sed 79 = Ns Ee ZA et
MY =  pM SY + YR NM = AN A AX + YR  AN - AM fit
nH = X + YR AM. Ergo fiet AX+ _R = AM, :, NS - QR = AM+AN. LN
habemus ergo duas aequationes secund YA et AQ fint exs et
seu LN. AK + LNYR-  LN AM = NS. AM ZR. AN et fiet utique
YR = (NS. AM + LN. AM L N AX AN. ZR,
Z secet AX in L. triangula MZZ, MNL sunt similim, rursus MNL et  sunt
simibia fit ut LZ LM - LM seu sed Z M = LM - LZ
39 = ZY -Y
MZ: Z2 seu LM- Z,:, ZY - Y Z = MN: LN lon a Y = YX B ML: MN, fiet
LM = L7,:,: Z (M L. XX: M N) YX - v. hs ursus X Q = XV. LN: NM et similitem
YM -F A(Z n =). LMF LZ, C LM: VN
jam AX + X q + qm = A M
et fiat AXF XY(L N: NM) + (M - LZ) (M: NN) = AM. sit ZM, l, MN m. NL, n
LZ, Z et ZY, v. fiet l = Z, :, v - (L: m) y, =, m: H, _ X + y(n: M) +(l: m) l - _: 12
= p seu l. 7 = pen: l) B X (m: 1I = y(n: () = vim: 1 - l al st v r t (pxsm: 1)
et set  xp X + Hl.m) Htnd et Z-  l +X p: 1) n +. ye: )
vetene te d tete  u se e u t. esitet  riti
t ny.m
a om
ta
potest punctum
inde quataor
perpendiculares C1 Y, (+Y
(3Y, C4.Y ad Gonicam
duci possint. sit cit
minima, sit erm ea
cressat usque ed CEY. Quodsi
Jam perpendi colaris pips
potest ad
nessetist reviss
nde urus decrepere, upque ad NY
rurtus ex
ou
nns luu 3
teste
Aeit
a
ut
AM, P
AA, qu.