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# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 2
# Folio 61r, page id 00068202:0121
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068202&page=121
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ato puncto curvae, datoque puncto in ipsum radiante, hruic respondens punctum
ut
corradiationus eus catacausticum invenire
AMFVFsC LNF. Ergo AFaEF AM D eN. Rurtus triangulum AEF
ad triangulum FK ut  AMad XN (ob bas tanquam altitudine
ad eandem basit) ergo ergo erit triangulum AFK ad tuangulur
∞FK, ut AF ad aF. Ergo AF in K p ad a F in RZ ut AF ad aF,
ergo L
= K
G
Haec vera sunt, ubicunque sumatur Kin recta
AM in MG in F(F) bisA F ()  et NCC in ) bis _ F(F)
relproFH vel
pursus bis AFF) A Aeq ex F in A(F) et ex (F) in aF agantur normales FB, (F) B. Patat
A ese BIF) esse differentiam inter AF et AF) et βF differentiam inter 46) et ne
sed hae differentiae sunt aequales. Ergo B()  βF. ergo similiter et. BF = β1F) b angulos 
la curvae IFF, 3F, indefinite vicina, et ex puncto fixo A, ducantur rectae
ad B, et β rectos
AF A2F, A3F, et ex ducatur 1FIO, 2F2d, angulis ad id, 2d, rectis, seu ita ut id2F 2d3F sint
antere
concurrente
differentiae radiorum ex sitit KIF, K2F normales ad curvam, seu ejus elementa 1F2F, 2F3F, o1
R.  Ex A ducantur normales ad K. C, et ad H2F, nempe A.B, et A2B
it emque q
erunt prangula similia A. B. A et 2 FIDIF. Rurfu
curiem
LG2
Itk, et 2FA se secent in H et ex rect  1F)
posito A1B nt AIF esse
A1B: AIF 2F1D seu Ar. 2F1F seu dc. seu A.B = YdV: dC
puncto utcuna sumto ut iL agatur nornalis in IFA, quae sit iL Mporro AB porro  iHt M. MiL
e
 F MIL AM vocetur Z et P. LA vocetur V, erit 1FM = r- Z jam  ,FM: MiL
= 1F1D: 1d2F et siet r -g.: v = (dcde - drdr): dr. sed ita non vide tur commode
ad com calculum sic ergo procedendum puto
Ex buncto quocunque rectae IFK agatur in ipsam AK recta ILIM
parallela
ipsi A. F sumatur punctum R, ut jam cognitum, per A ducatur recta AM angulo
ad A, F, quocunque N ita ut ratio tala terum Trianguli rectanguli 1FNAsit assumta F AFY, AN, p EA
sit AK = K AN = x rs  rqa rp: a et FN = a et NX.
1L. M, V AIM, Z
K- r et A
1L M, B, AM sit Z
et ATNE LM: MK = IFN: NK fiet 1L M = qia) M K = Y (9. a) R A. MM). sit
dikrpia
poncursus
y - r9. a) (R Z): X- rp. a, pro fiet v = _ 9, K-Z.: R P ubi in vaso F
fiet
punctoum IL et 2L, siet
∞ = d9 (R. Z (k - B) - Gu p =, qu. k. P = dq R . Z. X. p - 4 ap (1Z
1.
iensCNFK et A2F in 1H, et 2F2K et Ay3F vin 
aopricrem similitudo
las
 in it
D
p