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# Title: LBr. 560 · L'Hospital
# Folio 37r, page id DE-611-HS-855907:0073
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dt = dx t dgu Ergo dxdax t Aydaus = 0
. 1693
jam alx= diu
atdx= diu ergo = a du adue = dus. Ergo addus = dx. Ergo at log du = xat
Rediucho-
Ergo at
dy
axedera xat
e
ay
seu AF. X = na: dy
xfad tus adu =) alx) daus
X I  a ddx = at - de
et elementum curvae
emus dc =
2
add a ddx = dys ex datis.
Jam E
eut
dx
log u, = X ax tctus = logdu: x
rax dy u.
Erggo X=
2
2
sit et constans
L
Ergo dx = addus
LL e2
dx dx dux = dus clax posua 
en
adux
dx + dy. X -c = aa: dy
Ce
(Ergo d ex dax + du ddus =0 jam quaeritur
2
linea in qua s posita at constante sit addx Z du pro ddx in aeg. 3
(4
etant
ponatur - dyadue: dx ex aeq. 2. et fiet = adyddus: dx = dus. seu dx =- addu: du
Dan h dB Kat=C loy ay a
ergo si ds1:  sint numeri, dy sint logarithmi
Rursus in aeq. 3 tolle du ope ag. 2. jam ex aeg. 2 est duax dax: dau
et ex 3 et 6fiet, a (ddx) = ax adx ddx: dau seu a daqe  x dax
9
aliter in 49. 3 tolla exdu _ semitollatur dus per aeg. 2. et sint dudir + adda ddy 78
de gendi et redit aeq. 4
I: X sint numeri.
superficos arancurva
circa langentem  e 1: X sint inueri
du sunt logarithmi
quoue guerle recedit ab A
addx = at - dx sit
a = 4 1: X
 sunt logarithmi
1:
ydy
vel X +a sunt numeri et
Fdt- dx sunt logarithmi
dt= dest sunt numeri
du + dt sunt
logarithmi.
X r+ u t F12B+ 13l+ 14F. sietque
dx = 10+ 1 + 4 12 ++ 13f + 14 f + 15t
dx = 11 + 24 t+ 3 +5 de +4. 14 t3 a
(+ dx = 10 + 2. 10. 11 F + 2. 10. 12 f + 2. 10. 13 (3 + 2. 10. 14 f) + 2. 10. 15+ et
o
de
= 1
Cx Eadem relatio ut in adZ =
q
+ 11. I1 +2. 11. 12 + 2. 11. 13 + 2. 1C
2
-4. 14
12. 12
-
15
3413
12. 13
eu
sit 10 = 0 fict 1 = = a et 12 =0 et 13 = l: 3a2 et 14 =0 et 15 =
14
n
addx = - 11a
2: 35a
 lX = 1 F + 2. 11. 13(4 + 2. 1115(6+ 2. 11. 17+8+ 2. 11. 191 +2. 11. 21 f4 211. 231+2. 1125l
p
2
dx - ut + 13 + 4 15 + + 17 t + 19t
+ 1B13 +2. (3. 15 42. 13,17 +2.1319 +2.13.21 +2.13.23
215. 21
2.
+ 13. 15 2. 15. 17
2. 15. 19
Aatu = -1a Za. B3 - 5a. 15 = 7a. 17 -9a. 19 = (1, a. 21 - (13 a 23 Guet 5
+ 1. 1
= 1 = =1
11= - lia et 13 = 1: 34 15 = 2. 195a 17 2
1. 1.352 3. 13. 54
16 er
(17) a 3
= a logdy: XtC
nmenta curvae
seu xc seu ASi
axis rebolulorum
sint ut pundri