A Treatise of Plane Trigonometry, and the Mensuration of Heights and Distances: To which is Prefixed a Summary View of the Nature and Use of Logarithms. Adapted to the Method of Instruction in Schools and Academies |
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Page 11
... quantity , +.90309 from each . The remainders will be equal , and therefore the quantities from which the subtraction is made must be equal . With this alteration , 1.90309 The logarithm 2.90309becomes 3.90309 9.90309 NATURE OF ...
... quantity , +.90309 from each . The remainders will be equal , and therefore the quantities from which the subtraction is made must be equal . With this alteration , 1.90309 The logarithm 2.90309becomes 3.90309 9.90309 NATURE OF ...
Page 13
... quantities increase by a common multiplier ; ( Alg . 359. ) That is , each succeeding term is the product of the preceding term into the ratio . But the logarithm of this product is the sum of the logarithms of the preceding term and ...
... quantities increase by a common multiplier ; ( Alg . 359. ) That is , each succeeding term is the product of the preceding term into the ratio . But the logarithm of this product is the sum of the logarithms of the preceding term and ...
Page 23
... quantities in algebra . But it must be kept in mind , that the decimal part of the loga- rithm is positive . ( Art . 10. ) Therefore , that which is car- ried from the decimal part to the index , must be considered positive also . Mult ...
... quantities in algebra . But it must be kept in mind , that the decimal part of the loga- rithm is positive . ( Art . 10. ) Therefore , that which is car- ried from the decimal part to the index , must be considered positive also . Mult ...
Page 24
... quantities are multiplied , by means of loga- rithms , in the same manner as those which are positive . ( Art . 16. ) But , after the operation is ended , the proper sign must be applied to the natural number expressing the product ...
... quantities are multiplied , by means of loga- rithms , in the same manner as those which are positive . ( Art . 16. ) But , after the operation is ended , the proper sign must be applied to the natural number expressing the product ...
Page 26
... by 3.68 , is 0.01687 43. To divide negative quantities , proceed in the same manner as if they were positive , ( Art . 40. ) and prefix to the INVOLUTION BY LOGARITHMS . 27 quotient , the sign which 26 DIVISION BY LOGARITHMS .
... by 3.68 , is 0.01687 43. To divide negative quantities , proceed in the same manner as if they were positive , ( Art . 40. ) and prefix to the INVOLUTION BY LOGARITHMS . 27 quotient , the sign which 26 DIVISION BY LOGARITHMS .
Other editions - View all
A Treatise of Plane Trigonometry, and the Mensuration of Heights and ... Jeremiah Day No preview available - 2016 |
A Treatise Of Plane Trigonometry, And The Mensuration Of Heights And ... Jeremiah Day No preview available - 2008 |
Common terms and phrases
ac AC arithmetical complement base bung diameter calculation cask centre circle circular segment circumference cosecant Cosine Sine Cotang cube cubic decimal dicular difference distance divided equal to half equal to radius extend feet figure find the angles frustum given angle given side gles greater hypothenuse inches inscribed lateral surface length less line of chords line of numbers loga logarithm measure miles multiplied natural number negative number of degrees number of sides oblique parallelogram parallelopiped perimeter perpen perpendicular perpendicular height plane prism PROBLEM proportion pyramid quadrant quantity quotient radius regular polygon right angled triangle right cylinder rithm rods root scale secant sector segment slant-height sphere square subtended subtracting tables Tang tangent term Theorem Thomson's Legendre trapezium triangle ABC Trig trigonometry vulgar fraction whole wine gallons zone
Popular passages
Page 19 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Page 19 - To find then the logarithm of a vulgar fraction, subtract the logarithm of the denominator from that of the numerator. The difference will be the logarithm of the fraction. Or the logarithm may be found, by first reducing the vulgar fraction to a decimal. If the numerator is less than the denominator, the index of the logarithm must be negative, because the value of the fraction is less than a unit. ( Art* 9.) Required the logarithm of f 4.
Page 129 - From half the sum of the sides, subtract each side severally; multiply together the half sum and the three remainders; and extract the square root of the product.
Page 56 - A cylinder is a solid described by the revolution of a rectangle about one of its sides, which remains fixed.
Page 92 - One of the required angles is found, by beginning with a side, and, according to Theorem I, stating the proportion, As the side opposite the given angle, To the sine of that angle ; So is the side opposite the required angle, To the sine of that angle. The third angle is found, by subtracting the sum of the other two from 180° ; and the remaining side is found, by the proportion in the preceding article.
Page 39 - CUBIC MEASURE 1728 cubic inches = 1 cubic foot 27 cubic feet = 1 cubic yard...
Page 34 - But the difference of two squares is equal to the product of the sum and difference of their roots.
Page 27 - ... base. For the area of a circle is equal to the product of half the diameter into half the circumference ; (Art.
Page 18 - The sum of the logarithms of two numbers, is the logarithm of the product of those numbers ; and the difference of the logarithms of two numbers, is the logarithm of the quotient of one of the numbers divided by the other. (Art. 2.) In Briggs' system, the logarithm of 10 is 1.
Page 38 - Find the amount of 1 dollar for 1 year ; multiply its logarithm by the number of years ; and to the product, add the logarithm of the principal. The 'sum will be the logarithm of the amount for the given time. From the amount subtract the principal, and the remainder will be the interest.