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 3
... IV . The Cylinder , Cone , and Sphere , Promiscuous examples of Solids , V. Isoperimetry , Gauging of Casks , Notes , APPENDIX . • Page 5 19 34 37 56 76 78 . 92 99 SECTION I. AREAS OF FIGURES BOUNDED BY RIGHT LINES .
... IV . The Cylinder , Cone , and Sphere , Promiscuous examples of Solids , V. Isoperimetry , Gauging of Casks , Notes , APPENDIX . • Page 5 19 34 37 56 76 78 . 92 99 SECTION I. AREAS OF FIGURES BOUNDED BY RIGHT LINES .
Page 56
... CONE , AND SPHERE . ART . 61. DEFINITION I. A right cylinder is a solid de- scribed by the revolution of a rectangle about one of its sides . The ends or bases are evidently equal and parallel circles . And the axis , which is a line ...
... CONE , AND SPHERE . ART . 61. DEFINITION I. A right cylinder is a solid de- scribed by the revolution of a rectangle about one of its sides . The ends or bases are evidently equal and parallel circles . And the axis , which is a line ...
Page 57
... cone is also a circle , but is not per- pendicular to the axis . The height of a cone is the perpen- dicular distance from the vertex to the plane of the base . In a right cone , it is the length of the axis . The slant - height of a ...
... cone is also a circle , but is not per- pendicular to the axis . The height of a cone is the perpen- dicular distance from the vertex to the plane of the base . In a right cone , it is the length of the axis . The slant - height of a ...
Page 59
... cone in which it is inscribed . A cylinder is there- fore considered , by many writers , as a prism of an infinite number of sides ; and a cone , as a pyramid of an infinite number of sides . ( For the meaning of the term " infinite ...
... cone in which it is inscribed . A cylinder is there- fore considered , by many writers , as a prism of an infinite number of sides ; and a cone , as a pyramid of an infinite number of sides . ( For the meaning of the term " infinite ...
Page 60
... CONE . 65. MULTIPLY HALF THE SLANT - HEIGHT INTO THE CIR- CUMFERENCE OF THE BASE . If the convex surface of a right cone be spread out into a plane , it will evidently form a sector of a circle whose radius . is equal to the slant ...
... CONE . 65. MULTIPLY HALF THE SLANT - HEIGHT INTO THE CIR- CUMFERENCE OF THE BASE . If the convex surface of a right cone be spread out into a plane , it will evidently form a sector of a circle whose radius . is equal to the slant ...
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.