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 CollegesOliver Steele, printer, 1815 - 96 páginas |
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Página 83
... , the bung diameter 24 inches , and the distance from the bung to the surface of the liquor , 6 inches ; what is the ullage ? Ans . 74 ale gallons , or 9 wine gallons . NOTES . NOTE A. Page 9 . WHEN a trapezium GAUGING . 83.
... , the bung diameter 24 inches , and the distance from the bung to the surface of the liquor , 6 inches ; what is the ullage ? Ans . 74 ale gallons , or 9 wine gallons . NOTES . NOTE A. Page 9 . WHEN a trapezium GAUGING . 83.
Página 84
... trapezium can be inscribed in a circle , the area may be found by either of the following rules . I. Multiply together any two adjacent sides , and also the two other sides ; then multiply half the s sum of these products by the sine of ...
... trapezium can be inscribed in a circle , the area may be found by either of the following rules . I. Multiply together any two adjacent sides , and also the two other sides ; then multiply half the s sum of these products by the sine of ...
Página 85
... trapezium equal to √ ( 2ad + 2bc ) 2 - b2 + c2 - a - d2 ) 2 The expression under the radical sign is the difference of two squares , and may be resolved , as in Trig . 221 , into the factors 2 ( b + c2 - a - d2 ) x ( a + d2 - b - c2 ) ...
... trapezium equal to √ ( 2ad + 2bc ) 2 - b2 + c2 - a - d2 ) 2 The expression under the radical sign is the difference of two squares , and may be resolved , as in Trig . 221 , into the factors 2 ( b + c2 - a - d2 ) x ( a + d2 - b - c2 ) ...
Página 77
... trapezium AEFΙΑ , ( Fig . 40. ) and then add the spaces between the offsets , if they fall with- in the boundary line ; or subtract them , if they fall without , as AIK . When any part of a side of a field is inaccessible , equal off ...
... trapezium AEFΙΑ , ( Fig . 40. ) and then add the spaces between the offsets , if they fall with- in the boundary line ; or subtract them , if they fall without , as AIK . When any part of a side of a field is inaccessible , equal off ...
Página 85
... trapezium consists of two parts , the triangle ABC , and the trapezoid ACED . As the angles and one side of the former are given , its area may be found . Sub- tracting this from the given area , we have the area of the trapezoid , from ...
... trapezium consists of two parts , the triangle ABC , and the trapezoid ACED . As the angles and one side of the former are given , its area may be found . Sub- tracting this from the given area , we have the area of the trapezoid , from ...
Otras ediciones - Ver todas
A Practical Application of the Principles of Geometry to the Mensuration of ... Jeremiah Day Sin vista previa disponible - 2023 |
A Practical Application of the Principles of Geometry to the Mensuration of ... Jeremiah Day Sin vista previa disponible - 2015 |
Términos y frases comunes
ABCD arithmetical complement 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 logarithm measured Mercator's Merid meridian meridional difference middle latitude miles minutes multiplied negative number of degrees number of sides object oblique opposite parallelogram parallelopiped perimeter perpendicular plane sailing polygon prism PROBLEM proportion pyramid quadrant quantity quotient radius regular polygon right angled triangle right ascension right cylinder rods root secant segment sine sines and cosines slant-height sphere square subtract surface tables tangent term theorem tion trapezium triangle ABC Trig trigonometry whole
Pasajes populares
Página 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.
Página 37 - 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.
Página 67 - 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.
Página 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.
Página 8 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Página 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.
Página 16 - THEN, IF THE SEGMENT BE LESS THAN A SEMI-CIRCLE, SUBTRACT THE AREA OF THE TRIANGLE FROM THE AREA OF THE SECTOR.
Página 42 - 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.