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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 1
# Folio 82r, page id 00068194:0163
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De translatione coordinatarum. Normalium
ad unum axem, in coordinatas normales
ad alium axes
ii ie
e nna
AB, X BL, y 
itr
AMZ ML, Pr: 
 LM: MK seu 
YFGILF-
tun
ot G.16  et 1G.FG it 
ABx. B x= W GF
Utseu X = R GF K LG: h. LG = _AMsenZ, - 5d
GD = Ad seu ML, s Vp Ergo X = - i1
J: SI+Y
Eodem modo s LB sin y  LNDEr et L
= Z+ ad a xd= Nd OAd ih Ergo
Lase
Zearem
si ntstria autuli Rectidtatera aa Hbb = cc
pbn
aa +bbec
ut aa a+  pst
saat bb
aabb quosis data
fiet FL FG. LF-: b. a tam r.  et siet
aa + bb, seu aa + bb = ee auq H a a rbb + 2 ab.
bs
seu _ 1r ceat 1 rec Y + een seu rra e, Y +1
seu r  et (N et ec-
LB: LN:: VI dLL. F + DG _ FG: GL.
jam GL = FG + FL. Ergo LB. LN:: FG: SFG2+ FF
seu LB: LX :: F1: f1 + 1: rY. seu LN=
si   Et y (seu LB) = LN: Si+ 1: rr. jam
LN = AM seu Z + DN. et DN: AD seu v:: LF: FG. 1: Y
Ergo DN =  T:r V. Ergo denique fiet:
_ y (seu LB) = Z + T: r V: E YI + I. rY
sit jam aequatio ad circulum Xxagu = aa, fiet
Z2 - 2 2Y ZV + Y N + Z + 2F. r ZV + l. r VV = aa
+rr
1. = 1: rr
ubi debet evanescere ZV, quod an verum, experiamur, fit scilicet:
-2r = 2Y + 2Y F 2Y3.  nempe _Y = L 1.Y
Itrr
1 + J: 
seu TArr ad 1+ J: rY. ut Y ad 1:
iaque non potest obtineri aequatio ad circulum coordinatarum rectam
gularium, in qua extet rectangulum indetemmuntarum
seu coordinatarum;
haus formioebus cum
in ca
linililis minime pro cognosisnd pro invemendo modo desidetatam ut
ectignem
Conicam obtinendi nihil ad rem facit angmentum aut dimiantio
radicis, utqueni tasuam quadratis invellitum tum quaquam tat
as sol B, 82