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 38
... gles 360 ° ; and in any other angle , as many degrees , as in the arc by which it is subtended . 76. The sum of the three angles of any triangle being equal to two right angles , ( Euc . 32. 1. ) is equal to 180 ° . Hence , there can ...
... gles 360 ° ; and in any other angle , as many degrees , as in the arc by which it is subtended . 76. The sum of the three angles of any triangle being equal to two right angles , ( Euc . 32. 1. ) is equal to 180 ° . Hence , there can ...
Página 40
... gle is spoken of ; we are to suppose a circle to be drawn whose centre is the angular point ; and that the lines men- tioned belong to that arc of the periphery which subtends the angle . 88. The sine , and tangent of an acute angle ...
... gle is spoken of ; we are to suppose a circle to be drawn whose centre is the angular point ; and that the lines men- tioned belong to that arc of the periphery which subtends the angle . 88. The sine , and tangent of an acute angle ...
Página 41
... gles is the complement of the other ; ( Art . 77. ) the sine , tan- gent , and secant of one of these angles , are the cosine , co- tangent , and cosecant of the other . 90. The sine , tangent , and secant of the supplement of an angle ...
... gles is the complement of the other ; ( Art . 77. ) the sine , tan- gent , and secant of one of these angles , are the cosine , co- tangent , and cosecant of the other . 90. The sine , tangent , and secant of the supplement of an angle ...
Página 47
... gles less than 45 ° , and v . v . Now , to bring the trigonometrical tables within a small compass , the same column is made to answer for the sines of a number of angles above 45 ° , and for the cosines of an equal number below 45 ...
... gles less than 45 ° , and v . v . Now , to bring the trigonometrical tables within a small compass , the same column is made to answer for the sines of a number of angles above 45 ° , and for the cosines of an equal number below 45 ...
Página 54
... gle ; the angle at C is common to them all ; and the other acute angle in each is the complement of that at C. ( Art . 77. ) We have , then , the following proportions . ( Euc . 4. 6. ) 1. CG : Cg :: BG : bg . That is , one radius is to ...
... gle ; the angle at C is common to them all ; and the other acute angle in each is the complement of that at C. ( Art . 77. ) We have , then , the following proportions . ( Euc . 4. 6. ) 1. CG : Cg :: BG : bg . That is , one radius is to ...
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.