The mariners magazine, or, Sturmy's mathematical and practical arts containing the description and use of the scale of scales, it being a mathematical ruler, that resolves most mathematical conclusions, and likewise the making and use of the crostaff, quadrant, and the quadrat, nocturnals, and other most useful instruments for all artists and navigators : the art of navigation, resolved geometrically, instrumentally, and by calculation, and by that late excellent invention of logarithms, in the three principal kinds of sailing : with new tables of the longitude and latitude of the most eminent places ... : together with a discourse of the practick part of navigation ..., a new way of surveying land ..., the art of gauging all sorts of vessels ..., the art of dialling by a gnomical scale ... : whereunto is annexed, an abridgment of the penalties and forfeitures, by acts of parliaments appointed, relating to the customs and navigation : also a compendium of fortification, both geometrically and instrumentally / by Capt. Samuel Sturmy.

About this Item

Title

Author

Sturmy, Samuel, 1633-1669.

Publication

London :: Printed by E. Cotes for G. Hurlock, W. Fisher, E. Thomas, and D. Page ...,

1669.

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Link to this Item

http://name.umdl.umich.edu/A61915.0001.001

Cite this Item

"The mariners magazine, or, Sturmy's mathematical and practical arts containing the description and use of the scale of scales, it being a mathematical ruler, that resolves most mathematical conclusions, and likewise the making and use of the crostaff, quadrant, and the quadrat, nocturnals, and other most useful instruments for all artists and navigators : the art of navigation, resolved geometrically, instrumentally, and by calculation, and by that late excellent invention of logarithms, in the three principal kinds of sailing : with new tables of the longitude and latitude of the most eminent places ... : together with a discourse of the practick part of navigation ..., a new way of surveying land ..., the art of gauging all sorts of vessels ..., the art of dialling by a gnomical scale ... : whereunto is annexed, an abridgment of the penalties and forfeitures, by acts of parliaments appointed, relating to the customs and navigation : also a compendium of fortification, both geometrically and instrumentally / by Capt. Samuel Sturmy." In the digital collection Early English Books Online 2. https://name.umdl.umich.edu/A61915.0001.001. University of Michigan Library Digital Collections. Accessed June 8, 2024.

Pages

CASE III. The Hypothenusal and Angle at the Base being given, To find the Perpendicular.

IN the same Triangle let there be given the Hypothenusal BC 478 Feet, Poles, Miles, Leagues, and the Angle at the Base CBA 32 deg. To find the Perpen∣dicular CA.

The Angle CAB is a Right Angle, or 90 Degrees; Therefore the Proportion is,

As the Sine of the Angle CAB 90 deg	10, 000000
Is to the Logarithm of the Side BC 478	2, 679428
So is the Sine of the Angle CBA 32 deg.	9, 724210
To the Logarithm of the Side AC 253	12, 403638

The Number answering to this Logarithm is 253 fere; and that is the Length of the Side CA in Feet, Poles, Miles, or Leagues.

Here the Work is something abbreviated; for the Angle CAB being a Right Angle, and being the first Term, when the second and third Terms are added together, the first is easily substracted from it, by cancelling the Figure next your left hand, as you see in the Example; and so the rest of that Number is the Logarithm of the Num∣ber sought.

By the Line of Sines and Numbers.

EXtend the Compasses from the Sine of 90 Degrees, to 478; the same Extent will reach from the Sine of 32 Degrees, to 253.

Or, Extend the Compasses from the Sine of 90 Degrees, to the Sine of 32 Degrees; the same Extent will reach from 478, to 253; and that is the S••le CA.