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ARISTO - HYPERBOLOG   ( 25 cm Scales )



ARISTO-Werke Dennert & Pape, Hamburg / Germany               (1958)
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S C A L E S   of  the    ARISTO   » HYPERBOLOG «         Model 0971
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Front Side               [ inverse / RED ]                Back Side
===================================================================

[LL01]   [exp(-0.01X)]
[LL02]   [exp(-0.1X)]      Th  <0.1 .. 3>     TanH(0.1X)
[LL03]   [exp(-X)]         K                  X3
DF       πX                A                  X2
-------------------------------------------------------------------
CF       πX                B                  X2
[CIF]    [1/πX]            T                  tan(0.1X);[cot(0.1X)]
L        lgX               ST                 arc(0.01X)
[CI]     [1/X]             S                  sin(0.1X);[cos(0.1X)]
C        X                 C                  X
-------------------------------------------------------------------
D        X                 D                  X
LL3      exp(X)            [DI]               [1/X]
LL2      exp(0.1X)         Sh2 <0.85 .. 3>    SinH(X)
LL1      exp(0.01X)        Sh1 <0.1 .. 0.9>   SinH(0.1X)

R E M A R K S :
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Production Code = 58_2 = Hamburg, 1958, Lot 2

The DEFINITIVE FORMS for the HYPERBOLIC FUNCTIONS are:

CosH(X) = ( exp(+X) + exp(-X) ) / 2   <==  this is the "Chain Line"
SinH(X) = ( exp(+X) - exp(-X) ) / 2       ( eg. suspension bridge )
TanH(X) =  SinH(X)  / CosH(X)
 exp(X) =  SinH(X)  + CosH(X)
      1 =  CosH2(X) - SinH2(X)

CosH(X) =  SinH(X) / TanH(X)  =  sqrt( 1 + SinH2(X) )  =  H(X)

Using the Hyperbolic Functions:
Start with value on the Sh scales ==>> reading SinH on D scale,
  start with value on the D scale ==>> reading ArcSinH on Sh.
Start with value on the Th scale  ==>> reading TanH on D scale,
  start with value on the D scale ==>> reading ArcTanH on Th.

The SR came in a leather case together with the  »1367« RULER  with
"Norm Zahlen" = NZ = "Standard Number Sequences"   and  »Tabelle-A«
with CONVERSION-TABLES.
                            Historical Remarks ...
impressum:
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© C.HAMANN    http://public.beuth-hochschule.de/~hamann    08/30/14