The semicircle on a sector in two books. Containing the description of a general and portable instrument; whereby most problems (reducible to instrumental practice) in astronomy, trigonometry, arithmetick, geometry, geography, topography, navigation, dyalling, &c. are speedily and exactly resolved. By J. T.
About this Item
Title
The semicircle on a sector in two books. Containing the description of a general and portable instrument; whereby most problems (reducible to instrumental practice) in astronomy, trigonometry, arithmetick, geometry, geography, topography, navigation, dyalling, &c. are speedily and exactly resolved. By J. T.
Author
Taylor, John, 1666 or 7-1687.
Publication
London :: printed for William Tompson, bookseller at Harborough in Leicestershire,
1667.
Rights/Permissions
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Subject terms
Mathematics -- Early works to 1800.
Navigation -- Early works to 1800.
Dialing -- Early works to 1800.
Link to this Item
http://name.umdl.umich.edu/A64223.0001.001
Cite this Item
"The semicircle on a sector in two books. Containing the description of a general and portable instrument; whereby most problems (reducible to instrumental practice) in astronomy, trigonometry, arithmetick, geometry, geography, topography, navigation, dyalling, &c. are speedily and exactly resolved. By J. T." In the digital collection Early English Books Online. https://name.umdl.umich.edu/A64223.0001.001. University of Michigan Library Digital Collections. Accessed May 30, 2025.
Pages
PROBL. 7.
Sailing by the Ark of a great Circle.
For this purpose the tangent lines on the
index will be a ready help, using the lesser
for small, and the greater tangent line, for
great latitudes. The way is thus,
Account the pont 60/0, on the outward
limb of the moveable piece to be the point,
or port of your departure; thereto lay the
fiducial edge of the index, and reckoning
the latitude of the Port you departed from
upon the index, strike a pin directly touch∣ing
descriptionPage 87
it, into the table your instrument lies
upon. This pin shall represent the Port of
your departure. Therefore hanging a thread,
or hair, on the center, whereon the index
moves; and winding it about this pin. Count
the difference of longitude 'twixt the port of
your departure, and the Port you sail to∣ward,
from 60/0 on the moveable piece to∣ward
0/60, on the loose piece; and thereto
laying the same fiducial edge of the index,
reckon the latitude of this last Port upon the
index, directly touching of it, strike down
another pin upon the table, and draw the
thread strait about this pin fastening it there∣to.
This done, the thread betwixt the two
pins represents the ark of your great Circle;
and laying the fiducial edge of the index to
any degree of difference of longitude ac∣counted
from 60/0 on the moveable piece,
the thread shows upon the index what lati∣tude
you are in, and how much you have
raised, or depressed the pole since your de∣parture.
On the contrary, laying the lati∣tude
you are in (numbred upon the index)
to the thread, the index shows the difference
of longitude upon the limb; counting from
60/0 on the moveable piece. So, that were
it possible to sail exactly by the ark of a great
Circle, it would be no difficulty to deter∣mine
descriptionPage 88
the longitude in any latitude you
make.
But I intend not a treatise of Navigation;
wherefore let it suffice, that I have already
shown how the most material Problems
therein, may easily, speedily, and (if the in∣strument
be large) exactly, be performed by
the instrument without the trouble of Cal∣culation,
or Projection.
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