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 1-3Durrie and Peck, 1838 - Geometry |
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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 angle of elevation axis base calculation cask chord circle circular segment circumference column cosecant cosine cotangent cube cubic decimal departure and difference Diff difference of latitude difference of longitude divided earth equator feet field figure find the area find the SOLIDITY frustum given sides greater hypothenuse inches inscribed lateral surface length logarithm measured Mercator's Merid meridian distances meridional difference middle diameter middle latitude miles minutes number of degrees number of sides object oblique parallel of latitude parallel sailing parallelogram parallelopiped perimeter perpendicular perpendicular height plane sailing prism PROBLEM proportion pyramid quadrant quotient radius regular polygon right angled triangle right cylinder rods secant sector segment ship sails sine slant-height sphere spherical square subtract tables tangent theorem trapezium triangle ABC Trig trigonometry wine gallons zone
Popular passages
Page 120 - 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 83 - 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 45 - A cone is a solid figure described by the revolution of a right angled triangle about one of the sides containing the right angle, which side remains fixed.
Page 57 - ... the square of the hypothenuse is equal to the sum of the squares of the other two sides.
Page 73 - 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 63 - When a quantity is greater than any other of the same class, it is called a maximum. A multitude of straight lines, of different lengths, may be drawn within a circle. But among them all, the diameter is a maximum. Of all sines of angles, which can be drawn in a circle, the sine of 90° is a maximum. When a quantity is less than any other of the same class, it is called a minimum. Thus, of all straight lines drawn from a given point to a given straight line, that which is perpendicular to the given...
Page 16 - 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 124 - From half the sum of the three sides subtract each side separately ; multiply together the half sum and the three remainders, and extract the square root of the product.
Page 100 - 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 58 - 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.