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 39
... drawn , within and about the circle , a number of straight lines , called Sines , Tangents , Secants , & c . With these the learner should make himself perfectly familiar . 32. The SINE of an arc is a straight line drawn from one end of ...
... drawn , within and about the circle , a number of straight lines , called Sines , Tangents , Secants , & c . With these the learner should make himself perfectly familiar . 32. The SINE of an arc is a straight line drawn from one end of ...
Página 40
... drawn per- pendicular from the extremity of the diameter which passes through one end of the arc , and extended till it meets a line drawn from the centre through the other end . Thus AD ( Fig . 3. ) is the tangent of the arc AG . 85 ...
... drawn per- pendicular from the extremity of the diameter which passes through one end of the arc , and extended till it meets a line drawn from the centre through the other end . Thus AD ( Fig . 3. ) is the tangent of the arc AG . 85 ...
Página 52
... drawn , with sides parallel to these , will all have the same angles . So that one of the parts given must always be ... drawing a perpendicular from one of the angles to the opposite side . 116. One of the six parts in a right angled ...
... drawn , with sides parallel to these , will all have the same angles . So that one of the parts given must always be ... drawing a perpendicular from one of the angles to the opposite side . 116. One of the six parts in a right angled ...
Página 67
... drawn perpendicular to the opposite side . This will fall either within or without the tri- angle . 1. Let it fall within as in Fig . 23. Then , in the right an- gled triangles ACD and BCD , according to art . 126 . R : 6 :: Sin A : p R ...
... drawn perpendicular to the opposite side . This will fall either within or without the tri- angle . 1. Let it fall within as in Fig . 23. Then , in the right an- gled triangles ACD and BCD , according to art . 126 . R : 6 :: Sin A : p R ...
Página 69
... drawn from C upon AB ; AB : CB + CA :: CB - CA : BP - PA * Demonstration . Describe a circle , on the centre C , and with the radius BC . Through A and C , draw the diameter LD , and extend BA to H. Then by Euc . 35 , 3 , ABXAH AL × AD ...
... drawn from C upon AB ; AB : CB + CA :: CB - CA : BP - PA * Demonstration . Describe a circle , on the centre C , and with the radius BC . Through A and C , draw the diameter LD , and extend BA to H. Then by Euc . 35 , 3 , ABXAH AL × AD ...
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 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
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 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.
Página 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.
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 12 - 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 20 - THEN, IF THE SEGMENT BE LESS THAN A SEMI-CIRCLE, SUBTRACT THE AREA OF THE TRIANGLE FROM THE AREA OF THE SECTOR.
Página 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.