## 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 |

### From inside the book

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**polyedroids**, it is presumed will be found both novel and interesting , by means of which the de- monstrations in relation to the surface and solidity of the sphere are rendered more rigorous than by the methods usu- ally pursued . Book ... Page 5

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**POLYEDROID**, AND SPHERE— THEIR SURFACES AND SOLIDITIES . BOOK FOURTH . ISOPERIMETRY OF SOLIDS . NOTES . DISCUSSIONS RESPECTING ELEMENTARY PRISMS , PYRAMIDS , & C. - ON SOME NEW GEOMETRICAL FIGURES INTRODUCED INTO THE ELEMENTS OF GEOME ... Page 74

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**polyedroid**is a solid formed by the revolution of a semipolygon about its axis . 12. A regular**polyedroid**is one formed by the revolution of a regular semipolygon about its axis . 13.**Polyedroids**receive particular names according to ... Page 94

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**polye- droid**( Def.11 . ) and the semicircle will describe a sphere ( Def . 14 ) . The**polyedroid**may be divided into the sections described by AHB which will be a cone , HLDB which will be a conic frustum , LNED which will be a cylin ... Page 95

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**polyedroid**is equal to the product of its altitude into the cir- cumference of its inscribed sphere . PROPOSITION XIX . THEOREM . The surface of a regular**polyedroid**, whose axis terminates in two equal plane bases , is equal to the ...### Other editions - View all

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.