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.

This arises from the different form of the name of Bernard Lamy, that is: Bernard Lami.

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 (B. Lamy, 1679)
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Lami's Theorem