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# Title: Leibniz-Handschriften zur Optik und Dioptrik LH 37, 2
# Folio 78v, page id 00068531:0156
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problema: Datu ( cumatua vitiii monnee una superficie tentis invenire, aliam,
ila ut ratii paralleli in prisem incidentes in unum punctum cogantiu
Ergo 43 
au t  rer o
 Ergo B3 3
n. pC Leg
n
sergo sed C et Gon hPa B3, P+ 8
np
e vel G3B n p _p C+8C n p + 
G3aGA13A. GR AG. AAp  -2. fiet
A3R_ h - X + Z m. ab a
AG, X. FG,B. AR Z. eR, v. . F p. g
GP, p
L5 Nb)
BA, l. FMpEM, ZCp 25+ f. 32
LH: MN :: C∞ : ST:: d b. C. (Ft 5 n
Triangula FLH, PEF similia. Ergo 8b
PF, G: FGy:: FH, f 2 LH, yF
Erg Mrex, 3tC et FN IXFC+ 
costi sye sier FN,  sn  f196:
quGq in g. quaerentum ergo punctum concursui
L. quod fiet dum quaeritur ordinati communis
tum ad rectam FMQ quae ordinata debet
esse RG parallela ipsi GF Quaeratur aliqua
odniata ad ipsi FGnacllela ab ax e ad AG
ad Fq producta, quae sit data, seu a puncto
quodam dato, ut educta quae erit 2 p.
Ertus RQ simul opdirata et a curva Z2 et a
recta F93 unde ejus valor habebitur bis
Nimirum Fg producitur dum axi occurrat in 3
invenlaturque primum punctum 3
taquo fiet  ex puncto P in DF 23 demittendo
perpendicularem P2. eit Triangulum F2p
cnsiderandum ad inveniri intersectione rectarum F 9
B. itaque quaerenda recta ad quam am ab his duabus
rectis didinatae haberi possint talis autem est
recta F ex puncto 3 in Fp perpend. est 34 ex
puncto Gui FP perpen est G6. jam FN. N NMa F4. 4
dus qualores ipsius 43. ut inveniamus Pa. set prius considerab
pi posse s et tunc quia g, peay. fore 19b. s bp.
8p E+ Y  seu P4Y ~P bp 13A 
cun addatur  GPad sit G3
+5 p paX
=p AE
8+bpas yal
hyos bu
Ergo 3 RY, S lp X + 2B jam db trimus sin BA q 3GF fier.
3+bP X+Z ex v+bt y Habetur ergo RG seu V
ob iriangula similia 3AQ eF 3GF fit: 3R: R8:: 3C5s eadem habebitur ad huc semel seu labitur ejus recetro ad
eu h- X+Z: v:: h. y, seu fiei: vhrmy
vnyh - Xy + Zy seu  yh. vh  Zy- Xy
seu h: y:: 2X: y- v iis. V. Est autem
s8 rpiptve on ponendo
 b - qup
rk p+ vyeC R yn p t CB - n xy Xpexy
+ n2gy - peZY. fiet?
ny vyC + pcZV - C - pexy s9b- y
yp-vp = Xy Y27
tabetur ergo R9, seu V ex datis X. y. Z.
eadem habebitur sd huc somel quia datur ejus
relatio ad Z. ex natura curvae 29. a
seu L. ex natura curvae et
Superest ut jam inveniamus punctum B. Quia dat
intelligatur
duci poten
ab auer GA A perpendicitaris  est perpendicularis ad curvam
jam in productafque S sumatur 2S aequ. FM et centro Q. radio
et describatur circuli se expundtu S. demittatur perpendicularis,
in in slg7 et  ex Z. ad partes. educatur 27 paralleta
S. quae sit ad TS ut b ad C. sive sut L H ad MN. et ex 7.
demissa perpendicularis eductus perralleta ipsu QT ad partes S. ocentret
circulo in C juncta qt eproducta erit ratius ref secundo refractus qui
occurret avi in B
quaeritur recta AB. punctum B
est intersectio rectarum G A est GF quae ambae referuntur ad
ipsam AqT. ad quam ipsarum ordinata perpendat communiserit ad AQC perper
dicularis BT. B8. quae invenietur inventa puncto prius punctus C
seu recta C∞ vel g20. qu sed hoec invenientur inventa intersectione
circuli se et recta 7C. unde opus puncto 7. seu longitudine rectae 27.
im pGs ergo lonosent Yse Fa ys P
rgo (13 eut GF, P seu 43 parit v. (4
P47 + 2 quad Eug P
G3GRH 3R. GRHIG-
b- p
obssi rest aguse
b-
simile striangulo FNM. Ergo FM: NM: : F P: 2P, NM EY
8 seu 2p erit 
sed ut puncum inveriamus, sic agendum erit,
Rursue P43 miang. sim. XC
et fiet.
et p
b
b
roducatur JFM dones occarrat urvarf
et ex ducati
son ses qit
p  Iherit
aequando hupus aequa
fiet P+H
P3n (G laquad tce3 quad Ergo fiet:
n
ex
s
ando
in
i
c 2
et H