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 iv
... because he has not by him a full Ex- plication of the Caufe of Mufcular Motion , and the Nature of Maftication and Digeftion of his Food . Befides , many of the Rules arife only from Algebraical and Fluxionary Proceffes , which are ...
... because he has not by him a full Ex- plication of the Caufe of Mufcular Motion , and the Nature of Maftication and Digeftion of his Food . Befides , many of the Rules arife only from Algebraical and Fluxionary Proceffes , which are ...
Page 1
... because it always fuppofes the Unit or Integer , let it be what it will , whether Pound , 1 Mile , 1 Gallon , to be divided into ten equal Parts , and each of those into 10 more , and fo on , as far as we please . Definitions . A ...
... because it always fuppofes the Unit or Integer , let it be what it will , whether Pound , 1 Mile , 1 Gallon , to be divided into ten equal Parts , and each of those into 10 more , and fo on , as far as we please . Definitions . A ...
Page 4
... because there are three Cyphers in the Denominator , and but two Fi- gures in the Numerator , we must therefore prefix a Cypher before the 16 , and fet it down thus , .016 . A mixt Number is compofed of a whole Number and a Fraction ...
... because there are three Cyphers in the Denominator , and but two Fi- gures in the Numerator , we must therefore prefix a Cypher before the 16 , and fet it down thus , .016 . A mixt Number is compofed of a whole Number and a Fraction ...
Page 5
... because there are 4 Decimals in the third Line , four Figures are feparated or cut off towards the Right Hand in the total Sum . Subtraction of Decimals . IN this Rule , we muft B 3 Sub- [ 5 ] N Addition of Decimals TOTATION of Decimals.
... because there are 4 Decimals in the third Line , four Figures are feparated or cut off towards the Right Hand in the total Sum . Subtraction of Decimals . IN this Rule , we muft B 3 Sub- [ 5 ] N Addition of Decimals TOTATION of Decimals.
Page 11
... Because here are not fo many Places of Decimals in the Dividend as they are in the Divifor ; we annex Cyphers to the Dividend to make them equal , and the Quotient is in this Cafe a whole Number . Example 5 . Divide 500l . among 26 Men ...
... Because here are not fo many Places of Decimals in the Dividend as they are in the Divifor ; we annex Cyphers to the Dividend to make them equal , and the Quotient is in this Cafe a whole Number . Example 5 . Divide 500l . among 26 Men ...
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...