Lami's Theorem

Theorem

Let $B$ be a body in static equilibrium.

Let the only forces acting on $B$ be $F_a$, $F_b$ and $F_c$.

Let $F_a$, $F_b$ and $F_c$ be represented by the vectors $V_a$, $V_b$ and $V_c$ respectively, such that the magnitudes and directions of each force corresponds to the magnitudes and directions of each vectors.

Let the directions of $V_a$, $V_b$ and $V_c$ be non-parallel.

Then $V_a$, $V_b$ and $V_c$ are coplanar and concurrent, and:

$\dfrac {\size V_a} {\sin A} = \dfrac {\size V_b} {\sin B} = \dfrac {\size V_c} {\sin C}$

where:

$A$, $B$ and $C$ are the angles between the directions of $V_b$ and $V_c$, $V_a$ and $V_c$, and $V_a$ and $V_b$ respectively

$\size V_a$, $\size V_b$ and $\size V_c$ are the magnitudes of $V_a$, $V_b$ and $V_c$ respectively.

Proof

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Also known as

Lami's Theorem is also known as Lamy's Theorem.

Source of Name

This entry was named for Bernard Lamy.

Historical Note

Lami's Theorem was shown by Bernard Lamy in $1679$.

Sources

• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Lamy's theorem
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Lami's Theorem