A Practical Application of the Principles of Geometry to the Mensuration of Superficies and Solids: Being the Third Part of a Course of Mathematics, Adapted to the Method of Instruction in the American Colleges |
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Page 38
... quadrant , and con- tains 90 degrees . 74. To measure an angle , a circle is so described that its centre shall be the angular point , and its periphery shall cut the two lines which include the angle . The arc between the two lines is ...
... quadrant , and con- tains 90 degrees . 74. To measure an angle , a circle is so described that its centre shall be the angular point , and its periphery shall cut the two lines which include the angle . The arc between the two lines is ...
Page 41
... quadrant ACH , ( Fig . 3. ) these lines form three similar triangles , viz . ACD , BCG or LCG , and HCF . For , in each of these , there is one right angle , because the sines and tangents are , by definition , perpendicular to AC ; as ...
... quadrant ACH , ( Fig . 3. ) these lines form three similar triangles , viz . ACD , BCG or LCG , and HCF . For , in each of these , there is one right angle , because the sines and tangents are , by definition , perpendicular to AC ; as ...
Page 43
... quadrant ACH , ( Fig . 5. ) the arc AH is 90 ° . The sine of this , according to the definition , ( Art . 82. ) is CH , the radius of the circle . 2. Let AS be an arc of 60 ° . Then the angle ACS , be- ing measured by this arc , will ...
... quadrant ACH , ( Fig . 5. ) the arc AH is 90 ° . The sine of this , according to the definition , ( Art . 82. ) is CH , the radius of the circle . 2. Let AS be an arc of 60 ° . Then the angle ACS , be- ing measured by this arc , will ...
Page 45
... quadrant , and arranged in tables . These constitute what is called the Trigonometrical Canon . * It is not ... quadrants of a circle , as in the others . Thus the sine of 30 is equal to that of 150 ° . ( Art . 90. ) 99. And in any ...
... quadrant , and arranged in tables . These constitute what is called the Trigonometrical Canon . * It is not ... quadrants of a circle , as in the others . Thus the sine of 30 is equal to that of 150 ° . ( Art . 90. ) 99. And in any ...
Page 46
... any given angle within the quadrant is greater than 45 ° , its * Or the tables may be supposed to be calculated to the radius 10000000000 , whose logarithm is 10 . complement is less ; and , on the other hand 46 THE TRIGONOMETRICAL.
... any given angle within the quadrant is greater than 45 ° , its * Or the tables may be supposed to be calculated to the radius 10000000000 , whose logarithm is 10 . complement is less ; and , on the other hand 46 THE TRIGONOMETRICAL.
Other editions - View all
A Practical Application of the Principles of Geometry to the Mensuration of ... Jeremiah Day No preview available - 2023 |
A Practical Application of the Principles of Geometry to the Mensuration of ... Jeremiah Day No preview available - 2015 |
Common terms and phrases
ABCD axis base calculation centre circle circular segment circumference column cone cosecant cosine cotangent course cylinder decimal departure diameter Diff difference of latitude difference of longitude distance divided earth equal equator errour feet figure find the area find the SOLIDITY frustum given side gles greater half horizon hypothenuse inches JEREMIAH DAY length less line of chords logarithm measured Mercator's Merid meridian meridional difference middle latitude miles minutes multiplied negative number of degrees number of sides object oblique opposite parallel sailing parallelogram parallelopiped perimeter perpendicular plane sailing polygon prism PROBLEM proportion pyramid quadrant quantity quotient radius regular polygon right angled triangle right cylinder rithms rods root scale secant segment sine sines and cosines slant-height sphere spherical square subtract surface tables tangent term theorem tion trapezium triangle ABC Trig trigonometry whole
Popular passages
Page 68 - 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 41 - A right cone is a solid described by the revolution of a right angled triangle about one of the sides which contain the right angle.
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 105 - 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 12 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Page 49 - ... at the head of the column, take the degrees at the top of the table, and the minutes on the left; but if the title be at the foot of the column, take the degrees at the bottom, and the minutes on the right.
Page 20 - THEN, IF THE SEGMENT BE LESS THAN A SEMI-CIRCLE, SUBTRACT THE AREA OF THE TRIANGLE FROM THE AREA OF THE SECTOR.
Page 46 - Jidd together the areas of the two ends, and the square root of the product of these areas ; and multiply the sum by \ of the perpendicular height.