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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 51r, page id 00068196:0101
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sit Logarithmicar
erm
A occure
65
c
d
a
s
Hyperbolae primariae linea
sit vinla Cupsts smnit dui
set te
es
intet se hormae
BCV. ju Asym potae AB, AII. vertent
tirum Ai.
quad ratum prim potentia AHVI)
dpnnillmea tangent l
all
oudens Hkc eses l
as
n
polica VC
vapithaic quadratrix rigurae Hyperbolis
icentrun Ai
 et c
A
artens illins tantient, 1
e
et u thuie
hui
intraita Asymptota AN, tanguas ink let
recta
senst
. logarithmicam tangens in K
A sit AH, a; et AB, X et BC, y, et BK,
u X, logarithmus issius X, talis, ut
ex sit = Zona VB
V
loco unitatis _e eNa jam Zdna = fex
ugxis
1.
xax:x posito X incipere ab a. Ergo simili sersu
=a (dxiX. Et dl rdx = a :X. Ergo debet
es
AY = a = AH: Ex 1) agatur parallela ipsi
C AB occurrens Logarithmicae intas et compleatur
rectangulum A1IFC erit . A numerus prima
pius que voletur A hujus logunthinus a erit unitas seu AH
Et quia ipsis AI pstentibus propessionis AH seu lexistem
tons progressionis authmeficae ipse Tk seu X sunt
glometricae eut X = B uni se l20 erit X= I.
et si l= l erit X = h. Ex his patet descripta Loganithmica
jas
utcunque per puncta, quod fit continua interpositione
s
medimum proportionalium, ope esse ejus langente ut
st
periatur Hy
eut I
perbola cujus est quadratuix. Nam seperta
ordinatim applicata ad tioqe te inter loga–
micam et Asquemplotoq erit AH et Ae AHeunt
ae t completoque rectangulo AHV
cic Acentrum Hyperbolae V, verlex AH
potenta
AT Asymptoti. unde Hyperbota facile descubi poterit
o inventa A5) habetur numerus primarius AF, ipsu
tanquam logarithm respondens
milturct
ex
e
 edianus a pometricas desii-
sa
ilram minitina
plo K, (1)) asumatur in
se
i Reguiantiam recta
A 
s
a
27
 S+
a
I
s
5
a
F
a
e
a
s
len
 asquplote