Law of Species

Theorem

Let $T$ be a right spherical triangle whose angles are $A$, $B$ and $C$ and whose respective sides opposite those angles are $a$, $b$ and $c$.

Let $C$ be the right angle of $T$.

Then:

$(1): \quad$ $A$ and $a$ are of the same species, and $B$ and $B$ are of the same species

$(2): \quad$ if $c < 90 \degrees$, then $a$ and $b$ are of the same species, as are $A$ and $B$

$(3): \quad$ if $c > 90 \degrees$, then $a$ and $b$ are of the opposite species, as are $A$ and $B$.

Proof

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