## 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 |

### From inside the book

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**SO IS THE AREA OF THE CIRCLE , TO THE AREA OF THE SECTOR**. It is evident , that the area of the sector has the same ratio to the area of the circle , which the length of the arc has to the length of the whole circumference ; or which ...### Other editions - View all

### 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.