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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2b
# Folio 142r, page id 00068198:0283
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in circulo sitAR AH a, ABX, BC, y et 2aX - XX -gy
AH sit y, et
in circulo sit AH radius a ordinata nommalis  mum seu deametrum _, absussa
abscissa AB sit X, erit vap XX = gy, hoc est re jam rectangulum ABH = quadrato
CBE, et fit ron ra aX - XX = y
sit alias sabe sitli recta in circulontrinque termeta FG, ad quam a perpendiculariter
ducta CE, secans ipsam in L. constat esse c rectamtum FLG aequale rectangulo CLE
sit x
 vet LB sit b Dimidia FG sit f
sit FG, B et BL, b et FL Z, et CL, V
FM sit m, pG sit g t Ad FG sit normalis FM, ccur us colculo in M, diamcetro in d.. ja
ADH = FDM = sd et AD- AH - FG, 2 et DH = FG4 AII FBytL AH+ FG, : 2 erigo
ADH = AH aFG: = pD = YM. 4. Ergo A AN. F = FB, on bien FM F FG = AH, quod
et ex figuaa per se patebat dimidia pC sit jam FG214 + PDa
sit FM hormalis ad FG occurrens diametro in D, et circulo in M, cum  ergo GM sit
d -y
diameter, patet fore FM + FG = aa sit CL in CL  Fd Ct  B
A vg FD Z0X AD, et fic L
+= y = v+ Fd X = Z+ AD et fiat aZ + a. Ad - ZZ- Z AD. ZAV = v0 + 2Fd. ∞+ Fd
Y+D et sit v et FL sit Z
sed 2FD est FM et a - 2Ad est FG et fiet v ZZ + vV + FM B = FGZ = a Ad - FD = AD
sed Ab A FG,. 2 et Ad si sid a Ad F D ABC sid A a Ad - AD = FD = 0. ergo
fiet ZZ + vV + FM. D - FG.Z = 0 ubi FM FG= AB2
Veniamus ad ordinatas i obliquas ducatur recta crculum secans Nque ai occ in 
diametio decurrens in O, et ex N ad diamelium sit noom alis rp. darique ponamus AO, et AP,
quibus mnia determinatur NG. jum NRAsit pt sit T et CR sit cd
jam NRsit H, et CR sit co NF Nq sit n fit N. n - H = co. Cs - W
(s = CR 2N + D2AB RB: Np = H ONFN,: ON sed NP: ex datur et sit Y
fietus RB = ON+F, P et Cs = 2 + v (OXFN) 2p et nA -X N = 2Co + 25ON es t EsEN
seu Hn+ coco + 2∞COH + 25. ON. co = 0
n HI
sed prestat  generalius rem definire etsi recta oR sit extralitutum
applicare ad sectionem Conicam in genere
sit sectio conica AC, cujus Axii AB, cui occurrat in H recta
indefinita e, cui angulo dato _AN, occurrat d CR ordina
ta ad ipsam EA ex sectione Conica sit AB, x BC, y. 
et semi latus rectum a fit 2ax + ax = gy
qu
ER sit Z et CR sit v
norinalis TA
cupenstati
jam
AEsit C. Ex N ad AE agatum
occurrat ipsi ER in F, et
per  agatur  paraliosa AE, occurpem ipsi AN in G.
et AB, f et  et BC producatur dum
occurrat ipsi CR in A. EB est  etx et BH_ = etX, f: C LCCA +y
sit AE, e
CR: CH se CH = C + R, f. C y
C CRa =CH, An: f, adeoque siet
CR - etX H etX. B: C - xy:f CH: e = RH EH seu (C +X) 5. e y
sec et xfe(e X, f. 1) - y i (etX, frC) = EH ER; CH seu y: (ern s. B) = E
BC BH = ER. EH seu (C+X, f. 1. 9 - Z. C
 Z: ((C+X) H(sfreC): C
EH (: EB = EF, A seu EH = etQ CFX, se C+ s): C. jam ER. EH = BC: BH
et fit ER seu Z = (e +X, Rec + S): e), y : (et X, f. C) seu _
BH = CH + y sit CH = (etX, f: C) - y et CR = (et X, f: C)  =y, n: C = v
Rursus RH = V, NF: f s
sit Et EH = EB. EF; EA= etX, 1 et H): C eritque EK
ER = EH = RH = (e+ X) ABCtH): e = VNF: F = Z
NF = 9 ee+ H):C
NG sit q AGsit g et fiet
GK et EG = C-g et GN = eg, f: e et A N seu An = 99 + e g: C
seu nn= egee +ec ff + ggf  2eg9ff; ee
et x - v9: f, Hec + s): e = Z. Ergo C+ X = ZC:  lee+ ) + vg. f = yn: f  + ve: f
et  A Zef. Aece+ B) - yn, i e-g et y = ZCf. X(cet B) + v (9- C),: n
Geroraliter sit curva quaecunque cC cujus axis ABB sit AB, X BC et recta quocunque ER
et X = ZC: ((ec +H) + vg: f - e
occurrens axi AB in E, ad qu siet ad ondinalae ad axem normales CB, y. ABX ordinatae ad ipsam
AEsut e, AF sit f
titque ER Z et CR, ~
ER obliquae CR