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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 109r, page id 00068196:0215
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N
(M
AB e Data tangensium proprietate datur GD; DL
ex AB, BG, F. si jam  hinc inveniri posset
punctum C tale, ut junctis CG, CL et ex L
n ge der acta normali LA daretur
Ga: AL ex GC et F. Tun problema tangentium
rectitoum esset ad quadraturas.
(2)
GD: DE ABF AB. BG. F G (D + DL = G4+ AL
et
Datis punctis G et C quaeramus pcu rectam GC; ea secat
CG in
GL, L(G)
Data Tangentium prosprietate datur curvae G(G) datur Gd. DL
ex AB, BG, F. jam ex G secundum certam quandam legem educatur
GN, ita ut ut datis AB, ee BG, F, detur GN; et ex () secundum eandem Legem
educatur (L(N) et concursus rectarum GN, (S) (V) sit C. Debet lex
educendi sic assumi, ut ex (G) in GC de acta normali (GD. detur
GD: D(G) ex GC et F. itaque datur eGte: 1G) etB. B et tursus
Hoc enim obtento dabitur reductio problematis Tangentium, inversi
ad quadraturas.
datur GL: L(G) = AB; BG; F datur
et NB: BG = AB, BG;F seu N
AB; BG: F
(6
CE: EN = BG: NB
NE E AE = AB - BN Ergo, CE: AE - AB - BN = BG: NB. Et ex 6 per 2
ex 4 per 5 fit
fit AE = AB - BN, : CE == AB; BG; F seu AE = AB - BG. AB; BG; F = CE. AB, B5, F
utge creperi quae est aequatio ad rectam GC; cumque eadem sit et ad rectam
(G) C, variatis G et B, retentis C et E, hinc ex methodo a me praescripta
habetur intersectio rectarum GC et (G) C, habetur differentiando 
aequationem 8 cum autem  dAB sit GL, et dBG sit 28) (G) L. (Cssi
itaque ex aequ. 8 fiet - GL - BG. d AB; BG; F GL = BG d AB: BGiF. (G) L = AB; BG; F (5) L
+
CE d AB; DG, F GL + CE = AB; BG;F (5) L ser compendium AB BGiF
sit AB; BG; F  Z. et AB; BG; F = v feGL  fiet
+ (12)
GL: (C,) L + B, =Z GL: (G)L + BG Z + Z + (E+ Z. GL: (G) L + C2 dZ0
seu ex 12 per 1 et 11 fit v + BG = D+ BG d Z + Z + CE Z. v + CE Z =0, in qua
aisse
non aliae sunt quantitates quam AB, BG, F, CE. Pate autem Z non esse constantem
Eesse et fore alioqui evanescentibus omnibus fieret v + Z=0. ergo non foret Z constans
(nisi et v constans seu nisi linea G(G) recta) contra hypothesius. Possumus
jam  iterum differentiare equ. 13, considerando jam CE, ut constantem
S +
+  pore
et ex aeq. B fiet: d v. G- + d ∞ (G) L + vd d Z + DG B. a dZ. + eZd Gt
bic
+ 6)L
+ dZ. v (5)L + eq B + BG + Z GL + BG  (5) + que (9) 2t 1d 
e
5)L+5D,
Ex ge, unde datur d EE seu Gd per et,  ex aeg.  quemadmodum ipse
ex aeq. 14 per AB, BG dAB aBG; quemadmodum ipsa CE datur ex  AB, BG.
(4)
Praeterea est 
jam c jam C9 = BE + BGHCE seu CG = AE- AB + BG+ CE, ex qua aequatione
ob aeq. 13
tolli possunt AE, et CE, ope a49. 8 et 13. et fiet aequ (15) in qua extabunt CG, AB, BGF
panter
Hujus aequationis quaeratur differentialis aeq. (16) in qua eibunt C5, AB, BG, F,
et Hujus quoratur diein qua praeterG, AB, BG, F, es extalunt  dec, + AB, d05
datus praeterea exaegi. datu, D d AB; dBG per AB, BG, F et postremo GL + (G) L = GD A (G)
seu d + dBG=  De dcy + (G) D Habemus ergo aequ. 15 1b, 1, 17. Et ex aeq. 16
 et 17 tollendo dBG ope aeg. 1. fi aeq  fient ae9q. (18) et (19) a quibus erunt erit solum
junctis collendo dAB sit aequ. 20) in qua erunt CG, AB, BG, F et G aCG, (5) D. sed inde per aeg. 15
ipsa, non possumus tollere, e AB, et BG simul nisi ad eam rem ante assumta sit Z
id
si velimus
Sane (verte
eE) nsq concurrere ose uvitum non enum indoemus puncto