The Young Geometrician's Companion: Being A New and Comprehensive Course of Practical Geometry ... Containing. An easy introduction to decimal arithmetic .... Such definitions, axioms, problems, theorems, and characters, as necessarily lead to the knowledge of this science. Planometry, or the mensuration of superficies. Stereometry, ot he mensuration of solids. The sections of a cone .... The Platonic bodies ... To which is added a collection of problems shewing that lines and angles may be divided in infinitum; that superficies and solids may be so cut as to appear considerably augmented; and, that the famous problem of Archimedes, of moving the earth, is capable of an easy and accurate demonstration, Volume 6 |
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Page vii
... shall be equal to three given Right Lines To make a Square whofe Sides shall be equal to a given Right Line To make a Parallelogram whofe Length and Breadth fhall be equal to two Right Lines given " To make a Rhombus , each of whofe ...
... shall be equal to three given Right Lines To make a Square whofe Sides shall be equal to a given Right Line To make a Parallelogram whofe Length and Breadth fhall be equal to two Right Lines given " To make a Rhombus , each of whofe ...
Page 30
... shall have one De- cimal Place in the Root ; as in this Example . What's the Square Root of 2268741 ? 1 2268741 ( 1506.23 I 25 ) 126 125 3006 ) 18741 18036 30122 ) 70500 60244 301243 ) 1025600 903729 ( 121871 ) Note . In this Example ...
... shall have one De- cimal Place in the Root ; as in this Example . What's the Square Root of 2268741 ? 1 2268741 ( 1506.23 I 25 ) 126 125 3006 ) 18741 18036 30122 ) 70500 60244 301243 ) 1025600 903729 ( 121871 ) Note . In this Example ...
Page 55
... shall be equal in Solidity thereto . Rule . Extract the Cube Root of the Solid Content of the given Body , and that Root will be the Side of the Cube required . Example 1 . Suppose the Solid Content of a Globe , or Cylinder , Py- ramid ...
... shall be equal in Solidity thereto . Rule . Extract the Cube Root of the Solid Content of the given Body , and that Root will be the Side of the Cube required . Example 1 . Suppose the Solid Content of a Globe , or Cylinder , Py- ramid ...
Page 89
... shall pass through a given Point . Let BDE be the given Circle , C its Center , and A the Point from whence the Tangent is to be drawn . A a E Conftruction . First , from the Center of the Circle C , draw the Line CA , and divide it ...
... shall pass through a given Point . Let BDE be the given Circle , C its Center , and A the Point from whence the Tangent is to be drawn . A a E Conftruction . First , from the Center of the Circle C , draw the Line CA , and divide it ...
Page 95
... shall be equal to the Square of the other Part . Let A B be the Right Line given to be fo divided . F D d B A. E C Conftruction . First , on the Point A , erect the Perpen- dicular AD ; and produce it downwards alfo toward C. Next ...
... shall be equal to the Square of the other Part . Let A B be the Right Line given to be fo divided . F D d B A. E C Conftruction . First , on the Point A , erect the Perpen- dicular AD ; and produce it downwards alfo toward C. Next ...
Common terms and phrases
12 Inches alfo Anſwer Archimedes Axis Bafe Baſe becauſe Breadth called Center Chord Circle Circum Circumference Compaffes Cone confequently confifts Conftruction Conic Sections Conoid Crample Cube Root Cyphers defcribe the Arch Diameter A B Dimenfions Diſtance divide Dividend Divifor draw the Line Ellipfis Example faid fame Feet fet one Foot Figure find the Area find the Length find the Solidity Firft firſt fome fought Fruftum fubtract fuch Geometrical give the Solidity given Line given Number half Hexaëdron Hyperbola Icofaëdron Inches interfecting itſelf laft Product Laftly laſt Latus Rectum lefs Let ABCD Line A B Line given Magic Squares Mean Proportional meaſure multiplied muſt Operation Parabola Parallelogram Platonic Solids Point Problem Pyramid Quotient Refolvend Rhombus Right Angle Rule Segment Solid Content Solidity required Sphere Spheroid Square Root Stereometry Superficial Content Suppofe Theorem theſe thofe thoſe Tranfverfe Diameter Trapezium Triangle uſeful Vertex Vulgar Fraction whole Number whoſe
Popular passages
Page 95 - To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part. Let AB be the given straight line; it is required to divide it into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal to thcsquare of the other part.
Page 181 - Rule: To twice the square of the middle diameter, add the square of the diameter of...
Page 33 - Multiply the two given numbers together, and extract the square root of the product, which root will be the mean proportional sought. EXAMPLES. (1) What is the mean proportional between 4 and 9 ? (2) What is the mean proportional between 16 and 36?
Page 149 - For the surface of a segment or frustum, multiply the whole circumference of the sphere by the height of the part required.
Page 120 - As 7 is to 22, so is the diameter to the circumference. Or as 113 is to 355, so is the diameter to the circumference. • Or as 1 is to 3.1416, so is the diameter to the circumferenc".
Page 138 - This error, though it. is b«! small, when the depth and breadth are pretty near equal, yet if the difference...
Page 175 - To find the solidity of a spheroid. — Multiply the square of the revolving axe by the fixed axe, and this product again by -5236, and it will give the solidity required.
Page 213 - DF'E. Hence the entire area of the (!i GP cycloid is equal to three times the area of the generating circle.
Page 133 - To find the side of a square equal in area to any given superfices.
Page 28 - Divifion, write the anfwer in the Quotient, and alfo on the right hand of the Divifor...