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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 425r, page id 00068196:0845
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CA usum
anta
FA qu= f. L qu.  jam l Lqu
CX, x. XTy CB - db y = bb: X
dy = -bb dx: XX Y(d Xdx + dylus) = dx SCx  + b+): XX
Datur summ SXdx Y(X +b) seu cur  AY momentum
ex Hsymplota CE, posito enim exX = BZ fiet  2X dx-
seu Xdx = LbdZ et SXdx SCx L64 = B sdZ ((22+66). b
quae summatio pendet ex quadratura Hyperbolae
Eodem modo datur momentum arcus AY ex asum
ptota CB Est enim D X = bb: y et dx = ubbayu: y
et ( ydy + dxdx) = dy Cyt +64) :yy sit gy = bv
seu ydy - de et t curvae momentum ex CB, seu syduy ( ( + 62) dabit
LbSd) S(ov +bb): V quae misus pendet exquadiatura Hyperbilae
itaque inventa ratione ipsius  (aZ S( + bb) ad abs L (OB +bb 3.v ex supposit
hyperbolae quadratura, habetur rc positione recta  Csi quae
Ducatur jam Hyplibolae Axis CAW, inquem ex. Y agatur dormalis 
sen  et qu - 24 t 2 oa ot compleatur rectingulum C  Ctr Et CW0 vocetur  W, et c8
mursi FL 4u + Ctqua CB qu  BE qu
saocetur D. ipsa 8Y secet ex in H. C8 = GH XY = HX CH (9Y2
et su eA +  CD4KBtq 
3B qli , BF quam 2BA. bt etsit
et sed hoc hoco BA= CB
etsia Cqu + DCt 2BA. BE.
aaquet pt Aeotm oAv
qunesiqu AeAt quBqu
HY = XYI2 CX = C912 + XY
X Y : CG CX XY 2
en D CW C:, CX XY seu fret
:C8 - CW -C8,  CfZ XF = XYF2 = (W = CG. seu
Au. BF. q
AV. Cx - C1- ():, i2 Ergo CX = (72 + C. W (1. 12) - C9 (1. 12) jam est
est antem CxBA = CA. (2
 seu H = W - G, in 2 et X = c + CW.  8 + Wd, : 12
et esigu  i BCtEgo x  bb (= X9) = _ W1 = 89. : 2. seu   A 2bb +. 
siet CA+ ABs CL
otiract
ct CAa B CA BF
r sit 2bb = aa = quadrato BE et fiet _∞ L aa = WoW. jam fd =  dn
aqu. F2CBBF(2 + + BEqu. + Gfiet d = - W dW: P et des dc + do du = W diodu, Wd t 8G,:,
iodu _; doW + o 54,: 9 du dwo, WoWd aa WoWo
 + qFCqu ( 4BCqu+ 1BF)
et fitt
codd, 1 + son:99) duare, Aa
it ergo seudi - - dys g.: d (d W dW = dGd es = dedes, 1 + (89: 110) = de dis 1010 + 9.: cas
CA. B( Y2+ 2BFqu
IE: L
seu denique e  d9 d d∞, 288+ aa :, P + aa, vel (dode + duo d 10)=
seu n  = CAXBFs2
CAt BFA
momente
H de Y(aa t 289,: aa +95). Et etenrentum curvae AY ex
xe AW, erit ( de + (aa =+ 288, : aa +8). sit 88 = a V)
n Bet = 3. BC+ O:  et cd = L a  diV et saet Elementum curvas AY momenta ex Axe AW
est autem BC - CB. ∞ :C
averia
ecBC C
BFs = D. CA: 0. ciri erit L a f dip VCa a + 2a, :, aa + a2) quod ex quadraturo senica
sed BCs2 = CA. ergo fit
Rursus al   quia 52en haberi potest. Quaeratur rursus, momentum curvae AY ex ax e
denique n - O-
ne A verticem curvae ducatur ngt Conjugato CH
retento de tolatur d relento tollatur G, et ex de dis + duvato
fiet et du du c. + (Wol:8) du du, 88 ui: 8 seu fiert
ce diodus,  ac +290 eut dudu, 1 + ols 4 (ion: 98) X 
(C ) = dudio, 8G + WW, : 4 = duodi, Wt- ia t WW,: Wwu-na, seu denique
 Elementi curvae est duo, s(2c1 = da i oW = aa) et momentum Carvae A)
50+5) = 9(0 D)) ex une Conjugnto a, ent sudWo t(ruto -aaq:, vn - aa) sit Wo1 =aa
esse quantitates fiet Wdi = =a dβ et habemus Momentum curvae AY ex ae conjugato CE,
AP hyperbolae aequilatera
ipla atta producta transit per Gcentrum gravitatis curvae AY
tucta .L
=2Cst qu + a BF qui
seu FL = C1
FL: et
eo in Hyperbutia
n  putosu ducatur et per lentrum C, apis conjugatas, C angulo ad CE semirecto
equale Za ( aβ 1 (23- a, i, B- a) quod pendet ex quad aura Hyplitio  (onica
Dacatu AF tangens Hyperbolan in vertice A, ert monentum curvae AY ex
C, tagente verticis = La (d β+ (2β- a3: , B- a)
Ad Cora AY suct. rectam (A duct.
eid (CB. BF CBi sideque ((bba ZI): Z), in S(dv ACbbave) V) EtG f i ste
sdide at trari  parate),
ao AY - 5: Q sit   cno
Stpi 6. q  Dubi, 917 o i neidiem tris p mi 426
psumbus
hoc loco, quid
rattimo eva
rectus cuvani si ponit, 
Ct_ CA+BFVZ,:
FL = CA -BFSC,: 2
CQ eet M
FL2CF = l. eZ
BA A i 2a )50
BF C
Rat saaes
tic 
CF = 1Bq +BFqu
L= teAqu
Sxdxtuxne et QA = n B: 5 et GA - M-
seu m - a. siet M= a F. n
ergo denique fiet
= 82, a8+nE
vel  nS. O+D = nO-
sd
ia fine huius pa
sa
su cu
situs
a explicatus
Arexax t
pts ivedam per
5eCO
 uo cion et b2. 4
D Xt Sid s ma