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altitude arithmetical complement axis base calculation cask circle circular segment circumference column cone cosecant cosine cotangent course cylinder decimal 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 inscribed JEREMIAH DAY length less line of chords logarithm measured Mercator's Merid meridional difference middle latitude miles minutes multiplied negative number of degrees number of sides object oblique opposite parallel of latitude parallelogram parallelopiped perimeter perpendicular plane sailing prism PROBLEM proportion pyramid quadrant quantity quotient radius ratio regular polygon right angled triangle right cylinder rods root scale secant segment sine sines and cosines slant-height sphere spherical spirit level square subtract tables tangent term theorem trapezium triangle ABC Trig trigonometry whole wine gallons
Page 47 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds.
Page 50 - The surface of a sphere is equal to the product of its diameter by the circumference of a great circle.
Page 53 - ... 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 21 - RULE. Find the area of the sector which has the same arc, and also the area of the triangle formed by the chord of the segment and the radii of the sector. Then...
Page 119 - 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. By Theorem II. we have a : b : : sin. A : sin. B.
Page 29 - CUBIC MEASURE 1728 cubic inches = 1 cubic foot 27 cubic feet = 1 cubic yard...
Page 67 - GF : hence also, the sum of the eastings is equal to the sum of the westings. We therefore conclude, that when any survey is correctly made, the sum of the northings will be equal to the sum of the southings, and the sum of the eastings to the sum of the westings.
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.