Canon Triangulorum:

or, a Table of Artificial Sines and Tangents,
to a Radius of 10.00000000 Parts
To each Minute of the Quadrant.

By Edmund Gunter, Professor of Astronomy in Gresham-College.

London, Printed by Andrew Clark, for Francis Eglesfield, and are to be sold at the Marigold in s. Paul's Church-yard. 1672.

The Description of the Canon.

This Canon hath six Columns. The first is of Degrees and Minutes, from the beginning of the Quadrant unto 45 gr. the sixth of Degrees and Minutes from 45 gr. unto the end of the Quadrant; the other four contain the Sines and Tangents belonging to each of those Degrees and Minutes, after the manner of other Canons. The difference is in the Numbers: For these Sines are not such as half the Chords of the double Ark, nor these Tangents Perpendiculars at the end of the Diameter; but other Numbers substituted in their place, for attaining the same end by a more easie way, such as the Logarithms of the Lord of Merchiston; and thereupon I call them Artificial Sines and Tangents. SO the second and fourth Columns contain the Sines and Tangents of the Degrees and Minutes in the first Columns; the third and fifth contain the Sines and Tangents of the sixth Columns.

As if it were required to find the Artificial Sine belonging to our Latitude, which here at London is 51 gr. 32 m. you may find Sine 51 in the lower part of the Page, and M. 32 in the sixth Column, the common Angle will give 9.8937452 for the Sine required. And in the same Line you have 9.7938317 for the Sine of the Complement of this Latitude, which in one word may be called Co-sine. In the like manner, the Tangent of 51 gr. 32 m. will be found to be 10.0999134, and the Co-tangent 9.9000865.

The Secants (if there were use of them) may easily be supplied, by taking the Co-sine out of the double of the Radius.

As the double of the Radius, being 20.00000000
Take hence the Co-sine of 51 gr. 32 m. 9.7938317
The Secant of 51 gr. 32 m. will be 10.2061683

The Versed Sine may also be supplied by adding 3010300 unto the double of the Sine of half the Ark, and subtracting the Radius. As the half of 51 gr. 32 m. being 25 gr. 46 m.

Add to the Sine of 25 gr. 46 m 9.6381968
The same again, and the former Number, 9.6381968
So the Radius being subtracted, 3010300
The Versed Sine of 51 gr. 32 m. will be 9.5774236.

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