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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Resultados 1-5 de 58
Página 40
... . The sine complement or COSINE of an angle , is the sine of the COMPLEMENT of that angle . Thus , if the diameter HO ( Fig . 3. ) be perpendicular to MA , the angle HCG is the 1 complement of ACG ; ( Art . 77. ) 40 TRIGONOMETRY .
... . The sine complement or COSINE of an angle , is the sine of the COMPLEMENT of that angle . Thus , if the diameter HO ( Fig . 3. ) be perpendicular to MA , the angle HCG is the 1 complement of ACG ; ( Art . 77. ) 40 TRIGONOMETRY .
Página 41
... cosine of GCA . On the other hand GB is the sine of GCA , and the * cosine of GCH . 4 So also the cotangent of an angle is the tangent of the complement of the angle . Thus HI is the cotangent of GCA . And the cosecant of an angle is ...
... cosine of GCA . On the other hand GB is the sine of GCA , and the * cosine of GCH . 4 So also the cotangent of an angle is the tangent of the complement of the angle . Thus HI is the cotangent of GCA . And the cosecant of an angle is ...
Página 42
... cosine ; and that LC , between the cosine and centre , is par- allel and equal to the sine ; ( Euc . 34. 1. ) so that one may be taken for the other , in any calculation . 93. From these similar triangles , are derived the following ...
... cosine ; and that LC , between the cosine and centre , is par- allel and equal to the sine ; ( Euc . 34. 1. ) so that one may be taken for the other , in any calculation . 93. From these similar triangles , are derived the following ...
Página 43
... sine of 30 ° is equal to half the chord of 60 ° . ( Art . 82. cor . ) * Sine is here put for the square of the sine , cos for the square of the cosine , & c . But , by the preceding article , the chord of SINES , TANGENTS , & c . 43.
... sine of 30 ° is equal to half the chord of 60 ° . ( Art . 82. cor . ) * Sine is here put for the square of the sine , cos for the square of the cosine , & c . But , by the preceding article , the chord of SINES , TANGENTS , & c . 43.
Página 44
... cosine of 60o is equal to half radius . For the cosine of 60 ° is the sine of 30 ° . ( Art . 89. ) 97. The chord of any arc is a mean proportional , between the diameter of the circle , and the versed sine of the arc . Let ADB ( Fig . 6 ...
... cosine of 60o is equal to half radius . For the cosine of 60 ° is the sine of 30 ° . ( Art . 89. ) 97. The chord of any arc is a mean proportional , between the diameter of the circle , and the versed sine of the arc . Let ADB ( Fig . 6 ...
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.