Page:The Construction of the Wonderful Canon of Logarithms.djvu/103

NOTES ON TRIGONOMETRICAL PROPOSITIONS. 79

Let there be given

the base 69°,
the angles at the base	$\scriptstyle {\left\{{\begin{matrix}\ \\\ \end{matrix}}\right.}$	42°	29′	59″
		31°	6′	5″
‍		73°	36′	4″	sum.
		36°	48′	2″	half sum.
		73°	36′	4″	complement of ½ sum.
		11°	23′	54″	difference.
		5°	41′	57″	half difference.
		84°	18′	3″	complement of ½ diff.

						Logarithms.
Propor- tion 1.	$\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \ \end{matrix}}\right.}$	Sine half difference	5°	41′	57″	23095560
		Sine half sum	36°	48′	2″	5124410
		Sine difference	11°	23′	54″	16213641
		Sum of sines				−1757509
Propor- tion 2.	$\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \ \end{matrix}}\right.}$	Sine of sum	73°	36′	4″	415312
		Sum of sines				−1757509
		Tangent half base	34°	30′	0″	3750122
		Tangent ½ sum of sides	40°	30′	0″	1577301
Propor- tion 3.	$\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \ \end{matrix}}\right.}$	Sine ½ sum of angles	36°	48′	2″	5124410
		Sine ½ diff. of angles	5°	41′	57″	23095560
		Tangent ½ base	34°	30′	0″	3750122
		Tangent ½ diff. of sides	6°	30′	0″	21721272

40°	30′
6°	30′	‍
47°	0′	$\scriptstyle {\left.{\begin{matrix}\ \\\ \end{matrix}}\right\}\,}$	sides
34°	0′

These are the operations described by the Author. But
I replace the first two by another, retaining
the third.

Proportion.