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 38
... pyramid is regular , if its base is a regular poly- gon , and if a line from the centre of the base to the vertex of the pyramid is perpendicular to the base . This line is called the axis of the pyramid . IX . The height of a pyramid ...
... pyramid is regular , if its base is a regular poly- gon , and if a line from the centre of the base to the vertex of the pyramid is perpendicular to the base . This line is called the axis of the pyramid . IX . The height of a pyramid ...
Page 39
... pyramid , in having its ends dissimilar . It is a rectangular prismoid , when its ends are right parallelograms . XIV . A linear side or edge of a solid is the line of intersec- tion of two of the planes which form the surface . 42. The ...
... pyramid , in having its ends dissimilar . It is a rectangular prismoid , when its ends are right parallelograms . XIV . A linear side or edge of a solid is the line of intersec- tion of two of the planes which form the surface . 42. The ...
Page 42
... whose perimeter is 6 feet , and if the height be 17 feet , what is the surface ? The area of the triangle is 1.732 . ( Art . 11. ) And the whole surface is 105.464 . PROBLEM III . To find the SOLIDITY of a PYRAMID 42 MENSURATION OF SOLIDS .
... whose perimeter is 6 feet , and if the height be 17 feet , what is the surface ? The area of the triangle is 1.732 . ( Art . 11. ) And the whole surface is 105.464 . PROBLEM III . To find the SOLIDITY of a PYRAMID 42 MENSURATION OF SOLIDS .
Page 43
... pyramid is of a prism of the same base and altitude . ( Sup . Euc . 15 , 3. Cor . 1 . ) * Therefore the solidity of a pyramid whether right or oblique , is equal to the product of the base into of the perpendicular height . Ex . 1. What ...
... pyramid is of a prism of the same base and altitude . ( Sup . Euc . 15 , 3. Cor . 1 . ) * Therefore the solidity of a pyramid whether right or oblique , is equal to the product of the base into of the perpendicular height . Ex . 1. What ...
Page 44
... PYRAMID . 49. MULTIPLY HALF THE SLANT - HEIGHT INTO THE PERIM◅ ETER OF THE BASE . A C P B Let the triangle ABC be one of the sides of a regular pyramid . As the sides AC and BC are equal , the angles A and B are equal . Therefore a ...
... PYRAMID . 49. MULTIPLY HALF THE SLANT - HEIGHT INTO THE PERIM◅ ETER OF THE BASE . A C P B Let the triangle ABC be one of the sides of a regular pyramid . As the sides AC and BC are equal , the angles A and B are equal . Therefore a ...
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.