The description and use of the universall quadrat.: By which is performed, with great expedition, the whole doctrine of triangles, both plain and sphericall, two severall wayes with ease and exactness. Also the resolution of such propositions as are most usefull in astronomie, navigation, and dialling. By which is also performed the proportioning of lines and superficies: the measuring of all manner of land, board, glasse; timber, stone. &c. / By Thomas Stirrup, Philomathemat.
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Title
The description and use of the universall quadrat.: By which is performed, with great expedition, the whole doctrine of triangles, both plain and sphericall, two severall wayes with ease and exactness. Also the resolution of such propositions as are most usefull in astronomie, navigation, and dialling. By which is also performed the proportioning of lines and superficies: the measuring of all manner of land, board, glasse; timber, stone. &c. / By Thomas Stirrup, Philomathemat.
Author
Stirrup, Thomas.
Publication
London :: Printed by R. & W. Leybourn, for Tho. Pierrpont, at the Sun in Pauls Church-yard,
1655.
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Subject terms
Astronomy
Dialing
Geometry
Navigation
Trigonometry
Link to this Item
http://name.umdl.umich.edu/A93912.0001.001
Cite this Item
"The description and use of the universall quadrat.: By which is performed, with great expedition, the whole doctrine of triangles, both plain and sphericall, two severall wayes with ease and exactness. Also the resolution of such propositions as are most usefull in astronomie, navigation, and dialling. By which is also performed the proportioning of lines and superficies: the measuring of all manner of land, board, glasse; timber, stone. &c. / By Thomas Stirrup, Philomathemat." In the digital collection Early English Books Online 2. https://name.umdl.umich.edu/A93912.0001.001. University of Michigan Library Digital Collections. Accessed June 9, 2024.
Pages
descriptionPage 124
CHAP. XXXII. To finde a side, by knowing the other side, and the angle next to the inquired side.
AS the Tangent of the angle given,
To the Tangent of the side given:
So is the radius,
To the sine of the side required.
Or,
As the cotangent of the side given,
To the cotangent of the angle given;
So is the radius,
To the Sine of the side required.
Thus in the rectangle ABC having the side AB 60 degrees, and the angle ACB 72 degrees 16 minutes, it is required to finde the side BC. Now here in regard the given Tangents exceed the side of the quadrat; I let passe the first proportion, and make use of the second: and opening the threed to the angle of 30 degrees, or which is all one, if I place the threed at the intersection of the contrary Sine of 90 degrees, with the right Tan∣gent of 30 degrees, (which is the complement of the side AB) it will cut the right Tangent of 17 degrees 44 mi∣nutes, (the complement of the angle ACB) at the con∣trary 〈…〉〈…〉 33 degrees 36 minutes, the side BC, or
descriptionPage 125
placing the threed at the intersection of the contrary Tan∣gent of 30 degrees, (the complement of the side AB) with the right Sine of 90 degrees, it will cut the contrary Tangent of 17 degrees 44 minutes, (the complement of the angle ACB) at the right sine of 33 degrees 36 mi∣nutes, the side BC. Or if the threed be placed at the in∣tersection of the contrary Tangent of 30 degrees, with the right Tangent of 17 degrees 44 minutes, it will cut the contrary Sine of 90 degrees, at the right Sine of 33 degrees 36 minutes, for the side BC, as before, which was required.
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