Elementary GeometryJ.B. Lippincott Company, 1893 |
From inside the book
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Page 55
... diameter . By the definition of a circle , all its radii are equal ; also all its diameters are equal , each being double the radius . If one extremity , O , of a line OA is fixed , while the line revolves in a plane , the other ...
... diameter . By the definition of a circle , all its radii are equal ; also all its diameters are equal , each being double the radius . If one extremity , O , of a line OA is fixed , while the line revolves in a plane , the other ...
Page 57
... diameter bisects the circle and its circumference . Let AMBN be a circle whose centre is O ; then any diameter AOB bisects the circle and its circumference . M N B For , if the figure ANB be turned about AB as an axis and superposed ...
... diameter bisects the circle and its circumference . Let AMBN be a circle whose centre is O ; then any diameter AOB bisects the circle and its circumference . M N B For , if the figure ANB be turned about AB as an axis and superposed ...
Page 58
... diameters , AOC , BCD , divide the circumference into four quadrants , AB , BC , CD , DA . 0 PROPOSITION IV . - THEOREM . 11. In equal circles , or in the same circle , equal arcs are sub- tended by equal chords . Let O , O ' , be the ...
... diameters , AOC , BCD , divide the circumference into four quadrants , AB , BC , CD , DA . 0 PROPOSITION IV . - THEOREM . 11. In equal circles , or in the same circle , equal arcs are sub- tended by equal chords . Let O , O ' , be the ...
Page 59
... diameter is greater than any other chord . B B 2. Theorem . - The shortest line that can be drawn from a point within a circle to the cir- cumference is a portion of the diameter drawn through the point . PROPOSITION V. - THEOREM . 13 ...
... diameter is greater than any other chord . B B 2. Theorem . - The shortest line that can be drawn from a point within a circle to the cir- cumference is a portion of the diameter drawn through the point . PROPOSITION V. - THEOREM . 13 ...
Page 60
... diameter perpendicular to a chord bisects the chord and the arcs subtended by it . The triangles ACO , BCO , are equal , by Proposition X. , Book I. Therefore AC = CB . = The triangles AOD , BOD , are equal , by Proposition VI . , Book ...
... diameter perpendicular to a chord bisects the chord and the arcs subtended by it . The triangles ACO , BCO , are equal , by Proposition X. , Book I. Therefore AC = CB . = The triangles AOD , BOD , are equal , by Proposition VI . , Book ...
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Common terms and phrases
ABCD adjacent angles altitude angle BAC angles are equal apothem bisects centre chord coincide common cone construct convex Corollary cylinder Definition diagonal diameter dicular diedral angle distance divided draw equal circles equally distant equilateral equivalent Exercise find the locus frustum given circle given line given point given straight line greater Hence hypotenuse included angle inscribed angle intercepted arcs isosceles triangle lateral area lateral edges mean proportional middle point number of sides parallel lines parallelogram parallelopiped pass a plane pendicular perimeter perpen perpendicular plane MN plane passed polyedral angle Proposition VI Proposition VII quadrilateral radii radius ratio rectangle regular inscribed regular polygon respectively equal right angles right triangle Scholium secant secant line segment similar slant height sphere spherical polygon spherical triangle square surface tangent tetraedron Theorem triangle ABC triangles are equal triangular prism triedral upper base vertex volume
Popular passages
Page 127 - The area of a rectangle is equal to the product of its base and altitude.
Page 196 - If a straight line is perpendicular to each of two straight lines at their point of intersection, it is perpendicular to the plane of those lines.
Page 131 - Two triangles having an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles.
Page 245 - A truncated triangular prism is equivalent to the sum of three pyramids whose common base is the base of the prism, and whose vertices are the three vertices of the inclined section.
Page 278 - A lune is to the, surface of the sphere as the angle of the lune is to four right angles. Let...
Page 111 - The square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other two sides.
Page 48 - The three perpendiculars from the vertices of a triangle to the opposite sides meet in the same point.
Page 57 - A tangent to a circle is perpendicular to the radius drawn to the point of contact.
Page 34 - The sum of the three angles of any triangle is equal to two right angles.