Leonhard Euler · 1744 · Internet Archive
Methodus inveniendi lineas curvas
All 336 leaves · leaf 298
Transcription
ELASTICIS.
291
$l \Phi = 4,7977381525$
subtr. $= 5,3144251332$
$= 9,4833130193$
ergo $\Phi = 0,3043077545$
add. $\frac{1}{2} \pi = 1,5707963268$
$\frac{a}{c} = 1,8751040813$
quo invento, erit $\frac{A}{B} = \text{tang. } \frac{1}{2} \Phi = 0,1533390624$. Reperitur
ergo ratio constantium A & B, ex quibus & ratio reliquarum
constantium C & D ad illas cognoscetur.
75. Restat adhuc prima aequatio $b = A+B+D$, quae;
ob $D=A+B$, abit in $b=2A+2B$; ideoque $A+B
= \frac{1}{2} b$: cum ergo fit $\frac{A}{B} = \text{tang. } \frac{1}{2} \Phi$, fiet $B(1+\text{tang. } \frac{1}{2} \Phi)
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