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 6-10 of 21
Page 93
... Proportional required . For , as Db is to Dc , fo is D d to De . e These two Problems do the Work of the Rule of Three , without the Ufe of Arithmetic . 94 Problem 22 . To find a Mean Proportional between Pro- PRACTICAL GEOMETRY . 93.
... Proportional required . For , as Db is to Dc , fo is D d to De . e These two Problems do the Work of the Rule of Three , without the Ufe of Arithmetic . 94 Problem 22 . To find a Mean Proportional between Pro- PRACTICAL GEOMETRY . 93.
Page 94
... Mean Proportional between two Right Lines given . Let A and B be the two given Lines , and let it be re- quired to find a Mean Proportional between them . A D F D B E Conftruction . Firft , draw the Line D E at Pleasure , upon which fet ...
... Mean Proportional between two Right Lines given . Let A and B be the two given Lines , and let it be re- quired to find a Mean Proportional between them . A D F D B E Conftruction . Firft , draw the Line D E at Pleasure , upon which fet ...
Page 95
... mean Proportion ; that is , to cut a Line fo 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 fo divided . F D d B A. E C Conftruction . First ...
... mean Proportion ; that is , to cut a Line fo 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 fo divided . F D d B A. E C Conftruction . First ...
Page 127
... mean Proportion be- tween the two Parts of the Diameter ; it will therefore ever hold , —as the versed Sine is to half the Chord :: fo is half the Chord to the remaining Part of the Diameter . Problem 16 . To find the Area of a Circular ...
... mean Proportion be- tween the two Parts of the Diameter ; it will therefore ever hold , —as the versed Sine is to half the Chord :: fo is half the Chord to the remaining Part of the Diameter . Problem 16 . To find the Area of a Circular ...
Page 151
... mean Circumference ; then of which Circumference they make the mean Side of a Square , and measure it as fquare Timber , by multiplying that Side by itself , and that Product by the Length , and di- viding by 1728 , if the Length was ...
... mean Circumference ; then of which Circumference they make the mean Side of a Square , and measure it as fquare Timber , by multiplying that Side by itself , and that Product by the Length , and di- viding by 1728 , if the Length was ...
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...