CHAPTER XI THE LOGARITHMIC SPIRAL

equivalent to

or, eliminating the sine-function,

Obviously, in the case when a =ã₤b, this gives us the circular system which we have already considered. For other values, or ratios, of a and b, and for all values of ö¡, we can easily construct a table, of which the following is a sample:

Chords of an ellipse, whose major and minor axes (a, b) are in certain given ratios.
ö¡	aã₤ãã₤b =ã₤1ã₤ãã₤3	1ã₤ãã₤2	2ã₤ãã₤3	1ã₤ãã₤1	3ã₤ãã₤2	2ã₤ãã₤1	3ã₤ãã₤1
ã0ô¯	1ôñ0ãã	1ôñ0ãã	1ôñ0ãã	1ôñ0ãã	1ôñ0ãã	1ôñ0ãã	1ôñ0ãã
10	1ôñ01ã	1ôñ01ã	1ôñ002	ôñ985	ôñ948	ôñ902	ôñ793
20	1ôñ05ã	1ôñ03ã	1ôñ005	ôñ940	ôñ820	ôñ695	ôñ485
30	1ôñ115	1ôñ065	1ôñ005	ôñ866	ôñ666	ôñ495	ôñ289
40	1ôñ21ã	1ôñ11ã	ôñ995	ôñ766	ôñ505	ôñ342	ôñ178
50	1ôñ34ã	1ôñ145	ôñ952	ôñ643	ôñ372	ôñ232	ôñ113
60	1ôñ50ã	1ôñ142	ôñ857	ôñ500	ôñ258	ôñ152	ôñ071
70	1ôñ59ã	1ôñ015	ôñ670	ôñ342	ôñ163	ôñ092	ôñ042
80	1ôñ235	ôñ635	ôñ375	ôñ174	ôñ078	ôñ045	ôñ020
90	0ôñ0ãã	0ôñ0ãã	0ôñ0ãã	0ôñ0ãã	0ôñ0ãã	0ôñ0ãã	0ôñ0ãã

Mathematical diagram showing a series of nested ellipses originating from point O, each labeled with an angle from 0° to 90°.

The coaxial ellipses which we then draw, from the values given in the

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