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 16, 2024.

Pages

CASE I. In a Right-Angled Plain Triangle, The Base and the Angle at the Base being given, To find the Perpendicular.

SUppose that the Line CA (in the following Figure) in the Right-Angled Trian∣gle, were a Tree, Tower, or Steeple, and that you would know the Height thereof; you must observe with your Instrument the Angle CBA, and measure the Distance BA.

So have you in the Right-Angled Triangle ABC, the Base 405 Foot (Miles or Leagues the denomination might have been as well) and the Angle at the Base 32 deg. and it is required to find the Perpendicular AC.

Now because the Angle CBA is given, the Angle BCA is also given, it being the Complement of the other to 90 deg. and therefore the Angle BCA is 58 Degrees: Then to find the Perpendicular CA, the Proportion is,

As the Sine of the Angle BCA 58 deg. (which is)	9928420
Is to the Logarithm of the Side BA 405 Foot	2607455
So is the Sine of the Angle CBA 32 deg. (which is)	9724210
The Sum of the Second and Third added	12331665
The first Number substracted from the Sum	9928420
To the Logarithm of the Side CA	2403245

The nearest Absolute Number answering to this Logarithm 2403245, is 253 fere; and that is the Length of the Side CA in Miles or Leagues, or the Height of the Tree, Tower, or Steeple, which was required.