Spherical Law of Sines/Historical Note/Mistake

Source Work

 * Chapter $5$: Eternal Triangles
 * Early trigonometry
 * Early trigonometry

Mistake

 *  calculated sines for a circle of radius $10^{15}$ -- effectively, tables accurate to $15$ decimal places, but multiplying all numbers by $10^{15}$ to get integers -- for all multiples of one second of arc. He stated the law of sines for spherical triangles
 * $\dfrac {\sin a} {\sin A} = \dfrac {\sin b} {\sin B} = \dfrac {\sin c} {\sin C}$
 * and the law of cosines
 * $\cos a = \cos b \cos c + \sin b \sin c \cos A$
 * in his De Triangulis, written in $1462$-$3$ but not published until $1533$.

Correction
The tables published by appeared in fact in his.

This was published in $1596$, some $20$ years after the death of its author.

The tables contained in it were computed in intervals of $10$ seconds of arc, not $1$ seconds of arc, and calculated to $10$ decimal places, not $15$.

The Spherical Law of Sines and Spherical Law of Cosines actually appeared in by, not , who was not born until $1514$.

As for the suggestion that was not published until $1533$, this is suspect, as no corroboration for this can be found online.

It is accepted that there exists a $1533$ edition of this work, as this can be found everwhere you look. But while evidence of an actual $1464$ edition may be elusive, the fact that no online biographies mention the fact that its publication was delayed until $1533$, the suggestion is that this is false.

It is possible that has conflated the two works in question:  by, and  by.