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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... similar one formed from the sines , tangents , & c . in the tables . The solutions of oblique angled triangles are made by the common methods . The propositions which are used in partic- ular cases , principally by astronomers , are ...
... similar one formed from the sines , tangents , & c . in the tables . The solutions of oblique angled triangles are made by the common methods . The propositions which are used in partic- ular cases , principally by astronomers , are ...
Página 11
... similar manner . For , by art . 14 , the decimal part of the logarithm of any number is the same , as that of the number multiplied into 10 , 100 , & c . All the difference will be in the index ; and this may be supplied by the same ...
... similar manner . For , by art . 14 , the decimal part of the logarithm of any number is the same , as that of the number multiplied into 10 , 100 , & c . All the difference will be in the index ; and this may be supplied by the same ...
Página 41
... similar triangles . ( Euc . 4. 6. ) In the quadrant ACH , ( Fig . 3. ) these lines form three similar triangles , viz . ACD , BCG or LCG , and HCF . For , in each of these , there is one right angle , because the sines and tangents are ...
... similar triangles . ( Euc . 4. 6. ) In the quadrant ACH , ( Fig . 3. ) these lines form three similar triangles , viz . ACD , BCG or LCG , and HCF . For , in each of these , there is one right angle , because the sines and tangents are ...
Página 42
... similar . It should also be observed , that the line BC , between the sine and the centre of the circle , is parallel and equal to the cosine ; and that LC , between the cosine and centre , is par- allel and equal to the sine ; ( Euc ...
... similar . It should also be observed , that the line BC , between the sine and the centre of the circle , is parallel and equal to the cosine ; and that LC , between the cosine and centre , is par- allel and equal to the sine ; ( Euc ...
Página 44
... similar . ( Euc . 8. 6. ) Therefore , AH : AB : : AB : AF . That is , the diameter is to the chord , as the chord to the versed sine . * * See note E. SECTION II . THE TRIGONOMETRICAL TABLES . ART . 98. 44 TRIGONOMETRY .
... similar . ( Euc . 8. 6. ) Therefore , AH : AB : : AB : AF . That is , the diameter is to the chord , as the chord to the versed sine . * * See note E. SECTION II . THE TRIGONOMETRICAL TABLES . ART . 98. 44 TRIGONOMETRY .
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.