Thesaurarium mathematicae, or, The treasury of mathematicks containing variety of usefull practices in arithmetick, geometry, trigonometry, astronomy, geography, navigation and surveying ... to which is annexed a table of 10000 logarithms, log-sines, and log-tangents / by John Taylor.

PROP. III. In a Rectangled Triangle, the Base, and Cathetus given to find the other parts thereof.

In the Triangle ABC, the Base AB is 736 parts, and the Cathetus BC is 467 4/10 parts, and the Angle B, between them is a right angle o•• 90°: And here you may make either side of the Triangle, Radius, but I shall make BC the Cathetus Radius, and then to find the Angle at the Cathetus C, this is the Analogy or ••••••∣portion.

As Log. Cathet, BC 467 4/10 parts,* 1.1

To Radius or S 90°.

So Log. Base AB 736 parts,

To T. V. Cathe C 57° 35', as required.

Secondly, I find the other Angle, at A to be* 1.2 32° 25', it being the Complement, to C 57 35', unto 90°.

Thirdly, To find out the Hypothenuse AC this is the analogy or proportion.

As S. V. Cathe C. 57° 35',

To Log. Base AB 736 parts,

So Radius or S. 90°,

To Log. Hypothenuse AC 871 8/10 parts, 〈…〉〈…〉∣quired. But making the Base AB Radius, yo•• may find the Hypothenuse AC, by this anal〈…〉〈…〉 or proportion.

[illustration]

Plate 1 Page 65

As Radius or S. 90°,

To Log. Base AB 736 parts.

So Sc. V. Base A 32° 25',

To Log. Hypothenuse AE 871 8/10 parts required,* 1.3 and thus you have all the parts of the Trian∣gle propounded.

Notes

• * 1.1

  Fig. 35.
• * 1.2

  〈…〉〈…〉
• * 1.3

  Fig. 35.