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 |
From inside the book
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Page xi
... Base and Height given To find the Length of the Transverse and Conjugate Axis of an Hyperbola To delineate an Hyperbola , the Tranfverfe and Con- jugate Diameters being given To find the Solidity of a Circular , Elliptical , Parabo ...
... Base and Height given To find the Length of the Transverse and Conjugate Axis of an Hyperbola To delineate an Hyperbola , the Tranfverfe and Con- jugate Diameters being given To find the Solidity of a Circular , Elliptical , Parabo ...
Page 36
... Base . Operation . C Perpendicular . A Perpendicular fquar'd . 40 40 1600 Sum 2500 ( 50 Yards the Length of the Hypo- 25 thenufe A C , required . 100 ) 0000 Problem 4 . The Hypothenuse and one Side being given Pro- 36 The EXTRACTION of ...
... Base . Operation . C Perpendicular . A Perpendicular fquar'd . 40 40 1600 Sum 2500 ( 50 Yards the Length of the Hypo- 25 thenufe A C , required . 100 ) 0000 Problem 4 . The Hypothenuse and one Side being given Pro- 36 The EXTRACTION of ...
Page 37
... the Square of the Distance 900 • Remains Square of the Height of 1600 ( 40 Yards , the the Tower 16 Height from the Base . 80 ) 000 Example 2 . A Tree or a Fort ftanding on Exam : The EXTRACTION of the SQUARE ROOT . 37 .
... the Square of the Distance 900 • Remains Square of the Height of 1600 ( 40 Yards , the the Tower 16 Height from the Base . 80 ) 000 Example 2 . A Tree or a Fort ftanding on Exam : The EXTRACTION of the SQUARE ROOT . 37 .
Page 103
... Base , and ftanding between the fame parallel Lines , are equal to one another . A D E F B C That is , the ... Bases . Theorem 9 . An Angle at the Center of a F 4 The PRACTICAL GEOMETRY . 103.
... Base , and ftanding between the fame parallel Lines , are equal to one another . A D E F B C That is , the ... Bases . Theorem 9 . An Angle at the Center of a F 4 The PRACTICAL GEOMETRY . 103.
Page 113
... Base by the Perpendicular Height , and the Product is the Area . Example . Let ABCD be a Quarry of Glafs , or Marble ; and fup- pofe the Bafe DC be 12.5 Inches ; and the Perpendicular AE 9.25 Inches ; what is the Area ? A D E B ...
... Base by the Perpendicular Height , and the Product is the Area . Example . Let ABCD be a Quarry of Glafs , or Marble ; and fup- pofe the Bafe DC be 12.5 Inches ; and the Perpendicular AE 9.25 Inches ; what is the Area ? A D E B ...
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...