## New Plane and Solid Geometry |

### From inside the book

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**equally distant**from a point within A called the centre . An arc is any portion of the circum- ference ; as AB . B B Q A Q A radius is a straight line drawn from the centre to the circumference ; as OA . CONSTRUCTIONS 24. At a given ... Page 19

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**equally distant**from the extremities of the line . II . Any point without the perpendicular is unequally distant from the extremities of the line . C E a B D At the middle point D of any line AB erect a 1 DC . From E , any point in DC ... Page 20

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**equally distant**from the extremities of the line . ] 4. Substituting for BE its equal AE , AE + EF > BF , or AF > BF . ( $ 54 , I ) 55. It follows from Prop . VI that every point which is**equally distant**from the extremities of a ... Page 21

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**equally distant**from the extremities of a straight line , determine a perpendicular to that line at its middle point ...**equally distant**from points D and E ; and CF is perpendicular to AB by § 56 . In § 25 , points C and Fare each ... Page 26

... equal distances from the foot of CD . To Prove a = b . Proof . Since CD is 1 EF at its middle point D , a = b . [ If a be erected at the middle point of a str . line , any point in the is

... equal distances from the foot of CD . To Prove a = b . Proof . Since CD is 1 EF at its middle point D , a = b . [ If a be erected at the middle point of a str . line , any point in the is

**equally distant**from the extremities of the line ...### 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.