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# Title: Leibniz-Handschriften zur Mathematik LH 35, 8, 7
# Folio 30v, page id 00068102:0016
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1
Htic in fine sublilis ac ns ent videtur invensa
reducenti plurimas quatratuta crrationales ar rationares.
 qvand lnciementaus incer X, y, dx dy.
ta Y
jam ax: dus:: Gp xt: 1 Data sa jam sit aequatio
a
relationem exprimens i ata jam aequationem incrementalis
++X
pro dx :dus sub stituamus  fiet aequus. inter t, X y, a
si Notatu dignum est quando curvae conflantur, tangentium
intersectione contrarium ejus fieri quod vulgo solet, ubi cor tangens una
est pro duabus curvae punctis. Hic bero duae langentes sint pro uno puncto
Curvae. Ponamus quaeri pL, ex AB quia via tangentium p duplices
AP et PL duglices, sed AB simplex. Hunc ad Ap et AL rem reducamus
Sit pF Xp: a C jam   Hoc jam accommodemus
sit verb. gr. A PL = AB. a
liunde autem yy +
AP = v pC = p AB, X, BL, y.
2
_ 9y + vN -ZVX + XX = pp sit jam p = XX: a. seu X=
 ubi sublato X ope aq. 2 ex aeg. c. sit gu ubi sublato p. siet
yy + vD =ZWX +XX= : X: aa. cujus quae rendo differentialem
+
et 20d∞ x 2 v = X quod tamen non licet. Quod si
et
my
Assumamus dam punctum P seu rectam Ap quam vocemus
data ponatur relatio inter AB et PL
deinde centro  P radio PL = p describamus circulum
indeque cursus centio (p) radio alio (P) L describumus
circulum, duoru Ex duorum circulorum intersectione communu
agatur perpendicularis LB in axcu, debet AB habere
ad pe mediam arithmelicam inter PL, et (P) L
(id est ad PL
altergtiam sec relitionem datam in inde finitum parvis
relatione,
sit circuli racius p, sit rudius pL sit p. ordinata
sinus rectus PB sit b sinus rectus BL sit y. sit bb + yy = pp
proposita
Et quia P) sit p(p) = db et PH = dp.
2
fiet bb + 2b ab +  +yy. - sp adp E
Ex ag. 1. et 2. sit differentialis ipsius 1 nemre bdb pap jam
A P  X AP = v . B = Xx. a + bY ret 6) sit seu b = paB. db et 1 = p Lusi
V, + vv EVX + XX  pp = bb (Fyy)
X +2XXb (B  - 2Xb A XY
fit
x
 et gy140 LX = p
jam AB =  X sit = Pp
b = v = X
Unde intro VV - 2∞x + xx + yy = pp. cuuus differentialis est
a
aa
unde AVdV - ∞ X dv = p dp et seu Vdu - pp dv: a = p d p
si letur relatio inter X et V res peduciur ad quadraturas si ob aeq. C sidetur delatio
celatio inter AP et B. sed non hac data detur illa
data relatione inter p et V dari relatio neem inter X et y patel ex aeq. 3
inte tp et V datitur et
cum ordinatae et ubscissa reguleri
sollant esse geminalae, et tangentes
simplices. Hic contras