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 53
... base of the triangle be equal to the tabular radius . Then , if a circle be described , with this radius , about the angle C as a centre , DA will be the tangent , and DC the secant of that angle . ( Art . 84 , 85. ) So that the radius ...
... base of the triangle be equal to the tabular radius . Then , if a circle be described , with this radius , about the angle C as a centre , DA will be the tangent , and DC the secant of that angle . ( Art . 84 , 85. ) So that the radius ...
Página 55
... base AB is the sine of the angle C , and the cosine of the angle A. If the base is made radius , as in Fig . 15 , the perpendicular BC is the tangent of the angle A , and the cotangent of the angle C ; while the hypothenuse is the ...
... base AB is the sine of the angle C , and the cosine of the angle A. If the base is made radius , as in Fig . 15 , the perpendicular BC is the tangent of the angle A , and the cotangent of the angle C ; while the hypothenuse is the ...
Página 56
... base in one be a cosine , the base in the other will be a cosine , & c . If the hypothenuse in each triangle be made radius , as in Fig . 14 , the perpendicular be will be the tabular sine of the angle at a ; and the perpendicular BC ...
... base in one be a cosine , the base in the other will be a cosine , & c . If the hypothenuse in each triangle be made radius , as in Fig . 14 , the perpendicular be will be the tabular sine of the angle at a ; and the perpendicular BC ...
Página 60
... base AB ; ac : AC :: ab : AB Or R : AC :: Sin C : AB By natural Sines . 1:45 :: 0.84495 : 38.023 = AB Computation by Logarithms . As Radius 10.00000 To the hypothenuse So is the Sine of C 45 1.65321 57 ° 40 ′ 9.92683 To the base 38.023 ...
... base AB ; ac : AC :: ab : AB Or R : AC :: Sin C : AB By natural Sines . 1:45 :: 0.84495 : 38.023 = AB Computation by Logarithms . As Radius 10.00000 To the hypothenuse So is the Sine of C 45 1.65321 57 ° 40 ′ 9.92683 To the base 38.023 ...
Página 61
... base 26 ; what is the length of the perpendicular , and the quantity of each of the acute angles ? To find the angles it is necessary that one of the given sides be made radius . ( Art . 130. ) If the hypothenuse be radius , the base ...
... base 26 ; what is the length of the perpendicular , and the quantity of each of the acute angles ? To find the angles it is necessary that one of the given sides be made radius . ( Art . 130. ) If the hypothenuse be radius , the base ...
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.