Elements of plane (solid) geometry (Higher geometry) and trigonometry (and mensuration), being the first (-fourth) part of a series on elementary and higher geometry, trigonometry, and mensuration |
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Page 7
... REGULAR POLYGONS AND THE MEASUREMENT OF THE CIRCLE - DEFINITIONS— GENERAL PROPOSITIONS - PROBLEMS . BOOK SIXTH . ISOPERIMETRY - DEFINITIONS - GENERAL PROPOSITIONS . NOTES . ON SOME DEFINITIONS - SPECULATIONS ON SOME OF THE SUBJECTS ...
... REGULAR POLYGONS AND THE MEASUREMENT OF THE CIRCLE - DEFINITIONS— GENERAL PROPOSITIONS - PROBLEMS . BOOK SIXTH . ISOPERIMETRY - DEFINITIONS - GENERAL PROPOSITIONS . NOTES . ON SOME DEFINITIONS - SPECULATIONS ON SOME OF THE SUBJECTS ...
Page 10
... regular se- ries of inductions . A Demonstration is indirect , when the conclusion shows that the introduction of any supposition , contrary to the truth advanced , necessarily leads to an absurdity . A Problem proposes an operation to ...
... regular se- ries of inductions . A Demonstration is indirect , when the conclusion shows that the introduction of any supposition , contrary to the truth advanced , necessarily leads to an absurdity . A Problem proposes an operation to ...
Page 145
... two , D and E , are also right ( Prop . XXVII . Cor . 1. B. II . ) Hence ( Prop . IX . B. III . ) , the line DE is tangent to the two circles . 19 BOOK V. REGULAR POLYGONS AND THE MEASUREMENT OF THE CIRCLE BOOK IV . 145.
... two , D and E , are also right ( Prop . XXVII . Cor . 1. B. II . ) Hence ( Prop . IX . B. III . ) , the line DE is tangent to the two circles . 19 BOOK V. REGULAR POLYGONS AND THE MEASUREMENT OF THE CIRCLE BOOK IV . 145.
Page 146
... regular polygon . Regular polygons may have any number of sides : the equilateral triangle is one of three sides ; the square is one of four . PROPOSITION I. THEOREM . Two regular polygons of the same number of sides are simi- lar ...
... regular polygon . Regular polygons may have any number of sides : the equilateral triangle is one of three sides ; the square is one of four . PROPOSITION I. THEOREM . Two regular polygons of the same number of sides are simi- lar ...
Page 147
... regular polygon may be inscribed in a circle and cir- cumscribed about one . Let ABCDE , & c . , be a regular poly- gon ; describe a circle through the three points A , B , C , the centre being 0 , and OP the perpendicular let fall from ...
... regular polygon may be inscribed in a circle and cir- cumscribed about one . Let ABCDE , & c . , be a regular poly- gon ; describe a circle through the three points A , B , C , the centre being 0 , and OP the perpendicular let fall from ...
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Elements of Plane (Solid) Geometry (Higher Geometry) and Trigonometry (and ... Nathan Scholfield No preview available - 2015 |
Common terms and phrases
ABCD abscissa altitude axis bisect chord circle circular segment circum circumference circumscribing cone conjugate construction convex surface cosec cosine cube curve cylinder described diameter distance divided draw ellipse equal to half equation equivalent feet figure formed frustum Geom geometry given hence hyperbola hypothenuse inches inscribed inscribed sphere latus rectum length logarithm magnitude measured multiplied by one-third number of sides opposite ordinates parabola parallel parallelogram perimeter perpendicular plane polyedroid polyedron polygon portion prism PROBLEM Prop proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon revoloid rhomboid right angled triangle right line root Scholium sector segment similar similar triangles sine slant height solid angle sphere spherical square straight line tangent THEOREM triangle ABC triangular triangular prism ungula vertex vertical virtual centre
Popular passages
Page 36 - Prove that parallelograms on the same base and between the same parallels are equal in area.
Page 35 - The sum of any two sides of a triangle, is greater than the third side.
Page 60 - A tangent to a circle is perpendicular to the radius drawn to the point of contact.
Page 56 - In the same circle, or in equal circles, equal arcs are subtended by equal chords ; and, conversely, equal chords subtend equal arcs.
Page 38 - The volumes of similar solids are to each other as the cubes of their like dimensions.
Page 75 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 86 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line. Let...
Page 211 - To find the solidity of a hyperbolic conoid, or otherwise called a hyperboloid. RULE. To the square of the radius of the base, add the square of the diameter...
Page 48 - Hence, the interior angles plus four right angles, is equal to twice as many right angles as the polygon has sides, and consequently, equal to the sum of the interior angles plus the exterior angles.