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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 9v, page id 00068196:0018
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cangens curvae sit positione data, potest curva descirbi
ponond ex d Nempe si datur relatio inter A T et AB
sit AB, X et BC, y, fiet TB(s = ydx: dy es
AT= ydxidus -x
et AB = AT dy: dx
quod si ergo datur relatio inter ydx: dys = x et
du. x, hab erit tangens po recta curvam
tangens positione data. Si datur relatio inter yt xidus) X
acesi sit dy. dx
Xx +qu 2a et dy: dx habebitur
y(d X idyue) ( - X = ag dx: du. adeoque fret
dx: dy
 ylaX. e
Ergo X = y = dx. dy, dx: dy
sit aequatio dy: dx = extgy: aa seu aadu = Xx dx + gy Lx
seu X = aa  Y(aa (dy: dx) - yy) = y - dx: dy, du: dy
quae aequatio deberet esse identica, ita ut sublato y, haberetur
dx a dy quod in hoc casu non procedit. Itagus sem per possumus
haberi ex nosse in utrum in da in proposita curva differen
ect
tangentialiter vata sit dangens positione vala
.so sed quia habetur curva gansentialiter data, etiam
Cum Curvaarangeus est oedinatim positione datas
sit curva AF C(C) quam firmat concursus curvarum
AB, X, BC, y BT) V. fiat a
sit da  e.t = C: a = sit e constans sem constans, id est constans
TI
qualis +
in una curva transiens de curva ad carvam, et fiat
C f+ ge +hAeC HKA e + etc = 0, ponendo f, 9, h M, dari
utcunque ex  C et V, fiet 9de 9 + 2hC + 3ReC+ etc =0
quarum ope tollendo e, habetur relatio inter = et v, in Casa
concursus seu inter X et Y = AB,X, BC, y AF-E AF -f, Et - C
ad cu
sic A
12
tam ta
concurso
plunes
quan s
ixs+
EG= 9
qu EH = qu GH = qu EG.
fit FE - y = GH  et AF. X = Et
dependente
qu
quFE = , FG, L yu
qu
tandem
tale AF
et quia EG stinormalis ad culvam,
et
ubi pporeit
Ubi G∞C
unde
fiet, utrque
E-y, . AF- X
generaliter duae ad libenda aequationes una
Se
deamintad curbam G, (G), aliter alsera ad ejus fangentem
sarI
ut et
atroque modo resciendo ad axem ABB per AB et BG
eut
ubi variand, Et deinde odiendo, quod variando
atur curva centa lege opc harum duarum aequationum
prodibit aequatio diterentist una ex _ cuvae coefficientibus variantibus, sollebrur
Quod sinon
si anatus habeat, tollentur vacartese rabeaumr aeq uatio ad lurvaus quasit
ad curvam
da e
e
to
ejusque tangensialis
ey 05age
e rivi ducdue
tollandoes
V
sit aego
dut