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 164
... segment EebB is equal to half the sum of the two arcs EB , eb , multiplied by Ee , the distance between the two arcs . Scholium . 1. The space enclosed between two concentrie circles is called a circular ring , or an annular space ...
... segment EebB is equal to half the sum of the two arcs EB , eb , multiplied by Ee , the distance between the two arcs . Scholium . 1. The space enclosed between two concentrie circles is called a circular ring , or an annular space ...
Page 224
... segment . Ex . 1 What is the area of the segment ABC , the arc of the segment being 60 ° and radius 12 ? By Prop . V. B. V. , the chord of the segment equals the radius ... CIRCULAR SEGMENTS . 이 1.01 224 MENSURATION OF SUPERFICIES .
... segment . Ex . 1 What is the area of the segment ABC , the arc of the segment being 60 ° and radius 12 ? By Prop . V. B. V. , the chord of the segment equals the radius ... CIRCULAR SEGMENTS . 이 1.01 224 MENSURATION OF SUPERFICIES .
Page 225
Nathan Scholfield. TABLE OF THE AREAS OF CIRCULAR SEGMENTS . 이 1.01 00133.11.04701.21.11990.31.20738.41.30319 ... segment ABO , its chord AB being 12 , and the radius CB or CO 10 ? Here ( BC - BP2 ) = √ ( 100-36 ) = √64 = S = OP ...
Nathan Scholfield. TABLE OF THE AREAS OF CIRCULAR SEGMENTS . 이 1.01 00133.11.04701.21.11990.31.20738.41.30319 ... segment ABO , its chord AB being 12 , and the radius CB or CO 10 ? Here ( BC - BP2 ) = √ ( 100-36 ) = √64 = S = OP ...
Page 226
... segments GAH and EBL to the trapezoid ABDH . M R H D F Ex . What is the area of the zone ABDH , if AB is 7.75 , DH 6.93 , and the diameter of the circle S ? The area of the whole circle is - - - - 50.26 of the segment ABC - of the segment ...
... segments GAH and EBL to the trapezoid ABDH . M R H D F Ex . What is the area of the zone ABDH , if AB is 7.75 , DH 6.93 , and the diameter of the circle S ? The area of the whole circle is - - - - 50.26 of the segment ABC - of the segment ...
Page 75
... circular sector , as DCF or FCH , E describes a solid , which is named a spherical sector . 16. The radius of a ... segment is that portion of the solid sphere , included between two parallel planes which form its bases . One of ...
... circular sector , as DCF or FCH , E describes a solid , which is named a spherical sector . 16. The radius of a ... segment is that portion of the solid sphere , included between two parallel planes which form its bases . One of ...
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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 arithmetical progression 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 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.