A Course of Mathematics: Containing the Principles of Plane Trigonometry, Mensuration, Navigation, and Surveying : Adapted to the Method of Instruction in the American Colleges, Volumes 1-3 |
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Page 3
... ship's mast which is known to be 99 feet high , finds the angle of elevation 3 degrees . What is the distance of the ship from the observer ? Ans . 98 rods . 8. If the observer be stationed at the top of the perpen- dicular BC , ( Fig ...
... ship's mast which is known to be 99 feet high , finds the angle of elevation 3 degrees . What is the distance of the ship from the observer ? Ans . 98 rods . 8. If the observer be stationed at the top of the perpen- dicular BC , ( Fig ...
Page 7
... ships in a harbor , wishing to ascertain how far they are from a fort on shore , find that their mutual distance is 90 rods , and that the angles formed between a line from one to the other , and lines drawn from each to the fort are 45 ...
... ships in a harbor , wishing to ascertain how far they are from a fort on shore , find that their mutual distance is 90 rods , and that the angles formed between a line from one to the other , and lines drawn from each to the fort are 45 ...
Page 11
... ship's mast 132 feet high is just visible in the horizon , to an observer whose eye is 33 feet above the surface of the water . What is the distance of the ship ? Ans . 21 miles . 25. The distance to which a person can see the smooth ...
... ship's mast 132 feet high is just visible in the horizon , to an observer whose eye is 33 feet above the surface of the water . What is the distance of the ship ? Ans . 21 miles . 25. The distance to which a person can see the smooth ...
Page 15
... ship on the ocean . The most accurate method of ascertaining the situation of a vessel at sea is to find , by astronomical obser- vations , her latitude and longitude . But this requires a view of the heavenly bodies ; and these are ...
... ship on the ocean . The most accurate method of ascertaining the situation of a vessel at sea is to find , by astronomical obser- vations , her latitude and longitude . But this requires a view of the heavenly bodies ; and these are ...
Page 16
... ship is uniform , she sails as many miles in an hour , as she does knots in half a minute . The time is measured by a half minute - glass , constructed like an hour glass . This is turned when the log is thrown upon the water ; and the ...
... ship is uniform , she sails as many miles in an hour , as she does knots in half a minute . The time is measured by a half minute - glass , constructed like an hour glass . This is turned when the log is thrown upon the water ; and the ...
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Common terms and phrases
ABCD altitude arithmetical complement axis base calculation circle circular segment circumference column cone cosecant cosine cotangent course cylinder decimal diameter Diff difference of latitude difference of longitude divided earth equator feet figure find the area find the SOLIDITY frustum given side greater horizon hypothenuse inches JEREMIAH DAY length less line of chords logarithm measured Mercator's Merid meridional difference miles minutes multiplied negative number of degrees number of sides object oblique parallel of latitude parallelogram parallelopiped perimeter perpendicular plane sailing prism PROBLEM proportion pyramid quadrant quantity quotient radius ratio regular polygon right angled triangle right ascension right cylinder rods root scale secant segment sine sines and cosines slant-height sphere spherical square subtract tables tangent term theorem trapezium triangle ABC Trig trigonometry whole
Popular passages
Page 81 - C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference.
Page 55 - ... the square of the hypothenuse is equal to the sum of the squares of the other two sides.
Page 71 - It will be sufficient to lay the edge of a rule on C, so as to be parallel to a line supposed to pass through B and D, and to mark the point of intersection G. 126. If after a field has been surveyed, and the area computed, the chain is found to be too long or too short ; the true contents may be found, upon the principle that similar figures are to each other as the squares of their homologous sides.
Page 118 - The sum of any two sides of a triangle is to their difference, as the tangent of half the sum of the angles opposite to those sides, to the tangent of half their difference.
Page 21 - AND ALSO THE AREA OF THE TRIANGLE FORMED BY THE CHORD OF THE SEGMENT AND THE RADII OF THE SECTOR. THEN...
Page 29 - CUBIC MEASURE 1728 cubic inches = 1 cubic foot 27 cubic feet = 1 cubic yard...
Page 14 - A circle is a plane figure contained by one line, which is called the circumference, and is such, that all straight lines drawn from a certain point within the figure to the circumference are equal to one another : 16. And this point is called the centre of the circle.
Page 98 - For, by art. 14, the decimal part of the logarithm of any number is the same, as that of the number multiplied into 10, 100, &c.
Page 79 - T8T of the axis, and the product by .7854. Ex. If the axis of a parabolic spindle be 30, and the middle diameter 17, what is the solidity ? Ans.
Page 56 - CoR. 9. From the same demonstration it likewise follows that the arc which a body, uniformly revolving in a circle by means of a given centripetal force, describes in any time is a mean proportional between the diameter of the circle and the space which the same body falling by the same given force would descend through in the same given time.