## 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

Page 95

... Line given into extreme and mean Proportion ; that is , to cut a Line so that the Product of the whole Line and one of the Parts shall

... Line given into extreme and mean Proportion ; that is , to cut a Line so that the Product of the whole Line and one of the Parts shall

**be equal to the Square of the other Part . Let A B be the**Right Line given to be so divided .### What people are saying - Write a review

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### Common terms and phrases

ABCD added alſo Anſwer Arch Axis Baſe becauſe Body Breadth called Center Chord Circle Circumference Compaſſes Cone Conjugate Conſtruction contained continued Crample Cube Cube Root Cyphers Decimal deſcribe the Arch Diameter Difference Diſtance divide Dividend Dperation draw the Line drawn Ellipfis equal exactly Example extract fame Feet Figure find the Area find the Solidity Firſt Focus Form Fraction Fruftum Geometrical given gives greater half Hand Height Hyperbola Inches laſt Laſtly Length leſs Line given mean meaſure Middle multiplied muſt Note Number Operation Parabola parallel Parallelogram Period Perpendicular Places Point Power Problem Product Proportion Pyramid Quotient reduce Remainder Right Angle Right Line Rule ſame Segment ſetting one Foot ſhall Side Solid Content Sphere Square Root Subtract Superficial Content Suppoſe taken third thoſe Tranſverſe Triangle Uſe whole whole Number whoſe Yards

### 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...