## New Plane and Solid Geometry |

### From inside the book

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Page 209

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**volume**. PRISMS AND PARALLELOPIPEDS 413. A prism is a polyedron , two of whose faces are equal polygons lying in parallel planes , having their homologous sides parallel , the other faces be- ing parallelograms ( § 107 ) . We call the ... Page 214

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**volume**of the rectangular parallelopiped . Case I. When the altitudes are commensurable . A C A P Β ' B Given P and Q rect . parallelopipeds , with equal bases , and commensurable altitudes , 44 ' and BB ' . To Prove P AA ' Q BB ' ( 1 ... Page 217

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**volumes**. 436. Def . The**volume**of a solid is its ratio to another solid , called the unit of**volume**, adopted arbitrarily as the unit of measure ( § 180 ) . The usual unit of**volume**is a cube ( § 421 ) whose edge is some linear unit ... Page 218

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**volume**, is**volume**P. ( $ 436 ) Q 438. Note . In all succeeding theorems relating to**volumes**, it is understood that the unit of**volume**is the cube whose edge is the linear unit , and the unit of surface the square whose side is the ... Page 217

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**volumes**. 436. Def . The**volume**of a solid is its ratio to another solid , called the unit of**volume**, adopted arbitrarily as the unit of measure ( § 180 ) . The usual unit of**volume**is a cube ( § 421 ) whose edge is some linear unit ...### Other editions - View all

### Common terms and phrases

adjacent angles altitude angle formed angles are equal apothem arc BC base and altitude bisector bisects centre chord circle circumference circumscribed coincide construct Converse of Prop diagonals diameter diedral angle distance Draw line equal parts occur equal respectively equally distant equilateral triangle exterior angle faces frustum Given line given point homologous sides hypotenuse intersecting isosceles trapezoid isosceles triangle lateral area lateral edges line drawn line joining lines be drawn measured by arc middle point number of sides oblique lines opposite parallel parallelogram parallelopiped perimeter perpendicular plane MN polyedron prism Proof proportional Prove pyramid quadrilateral radii radius rectangle regular polygon rhombus right angles right triangle secant segments slant height spherical polygon spherical triangle square straight line surface tangent tetraedron THEOREM trapezoid triedral vertex vertices volume

### Popular passages

Page 168 - S' denote the areas of two © whose radii are R and R', and diameters D and D', respectively. Then, | = "* § = ££ = £• <§337> That is, the areas of two circles are to each other as the squares of their radii, or as the squares of their diameters.

Page 17 - In an isosceles triangle the angles opposite the equal sides are equal.

Page 138 - ... any two parallelograms are to each other as the products of their bases by their altitudes. PROPOSITION V. THEOREM. 403. The area of a triangle is equal to half the product of its base by its altitude.

Page 168 - Similar arcs are to each other as their radii; and similar sectors are to each other as the squares of their radii.

Page 50 - If the diagonals of a quadrilateral bisect each other, the figure is a parallelogram.

Page 128 - In any triangle, the product of any two sides is equal to the product of the segments of the third side formed by the bisector of the opposite angle, plus the square of the bisector.

Page 265 - A spherical polygon is a portion of the surface of a sphere bounded by three or more arcs of great circles. The...

Page 282 - A zone is a portion of the surface of a sphere included between two parallel planes.

Page 241 - Every section of a cylinder made by a plane passing through an element is a parallelogram. Given ABCD, a section of cylinder AC, made by plane through element AB.

Page 256 - A sphere is a solid bounded by a surface all points of which are equally distant from a point within called the centre.