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
Results 1-5 of 11
Page 39
... whose Height is about 4 Miles ? B The Circumference of the Earth has been found by Ad- measurement to be about 25.020 Miles : Its Diameter therefore must be about 7964 ; and its Semi - diameter 3982 Miles . Then in the Triangle AB C ...
... whose Height is about 4 Miles ? B The Circumference of the Earth has been found by Ad- measurement to be about 25.020 Miles : Its Diameter therefore must be about 7964 ; and its Semi - diameter 3982 Miles . Then in the Triangle AB C ...
Page 53
... whose Cube Root is required . First , reduce it to a Decimal thus . 9 As 9 : 4 :: 100000000 4 . 9 ) 4000000000 ( 4 over . .444444444 the Decimal Fraction . Then extract the Cube Root of .444444444 ( .763 Root . Cube of 7 = 343 Square of ...
... whose Cube Root is required . First , reduce it to a Decimal thus . 9 As 9 : 4 :: 100000000 4 . 9 ) 4000000000 ( 4 over . .444444444 the Decimal Fraction . Then extract the Cube Root of .444444444 ( .763 Root . Cube of 7 = 343 Square of ...
Page 119
... whose Area is bounded by one continued Line , called the Circumference , or Peri- phery ; and it is every where equally diftant from a Point within , called its Center . Note . The Line going through the Center of the Circle , dividing ...
... whose Area is bounded by one continued Line , called the Circumference , or Peri- phery ; and it is every where equally diftant from a Point within , called its Center . Note . The Line going through the Center of the Circle , dividing ...
Page 132
... whose Di- menfions are expreffed in it ; what is its Area ? B 34 D 30 A 12 E Having divided the Figure as above into one Trapezium , and one Triangle , or rather into three Triangles , the Areas will be as under . Area of the Triangle B ...
... whose Di- menfions are expreffed in it ; what is its Area ? B 34 D 30 A 12 E Having divided the Figure as above into one Trapezium , and one Triangle , or rather into three Triangles , the Areas will be as under . Area of the Triangle B ...
Page 141
... whose Sides is the Circumference of the Cylinder , and the other the Length thereof . - * All Cylinders are compofed of a Number of Circular Surfaces of the fame Size laid upon each other . Problem 6 . To measure a Cone . Def . Pra ...
... whose Sides is the Circumference of the Cylinder , and the other the Length thereof . - * All Cylinders are compofed of a Number of Circular Surfaces of the fame Size laid upon each other . Problem 6 . To measure a Cone . Def . Pra ...
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...