The Essentials of GeometryD.C. Heath & Company, 1899 - 395 σελίδες |
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Σελίδα 72
... radius is a straight line drawn from the centre to the circumference ; as OA . B D C A diameter is a straight line drawn through the centre , having its extremities in the circumference ; as AC . 143. It follows from the definition of ...
... radius is a straight line drawn from the centre to the circumference ; as OA . B D C A diameter is a straight line drawn through the centre , having its extremities in the circumference ; as AC . 143. It follows from the definition of ...
Σελίδα 83
... radius of a circle at its extremity is tangent to the circle . E A D B Given line ABL to radius OC of O EC at C. To Prove AB tangent to the O. Proof . Let D be any point of AB except C , and draw line OD . .. OD > OC . Therefore , point ...
... radius of a circle at its extremity is tangent to the circle . E A D B Given line ABL to radius OC of O EC at C. To Prove AB tangent to the O. Proof . Let D be any point of AB except C , and draw line OD . .. OD > OC . Therefore , point ...
Σελίδα 86
... radius will pass through A , B , and C. Again , the centre of any circumference drawn through A , B , and C must be in each of the Is DF and EG . ( § 42 ) Then as DF and EG intersect in but one point , only one circumference can be ...
... radius will pass through A , B , and C. Again , the centre of any circumference drawn through A , B , and C must be in each of the Is DF and EG . ( § 42 ) Then as DF and EG intersect in but one point , only one circumference can be ...
Σελίδα 92
... radius OC ' . Then , since by const . , arcs AB and BC " are commensurable , ZAOB ZBOC arc AB arc BC ( § 189 , Case I. ) Now let the number of subdivisions of arc AB be indefi- nitely increased . Then the unit of measure will be ...
... radius OC ' . Then , since by const . , arcs AB and BC " are commensurable , ZAOB ZBOC arc AB arc BC ( § 189 , Case I. ) Now let the number of subdivisions of arc AB be indefi- nitely increased . Then the unit of measure will be ...
Σελίδα 94
... radius OB ; then , OA = OB . Then A OAB is isosceles , and △ B = ZA . But since BOC is an ext . Z of △ OAB , ZBOCZA + ZB . : . / BOC = 2 Z≤ A , or ZA = } ≤ BOC . But , BOC is measured by arc BC . Whence , is measured by arc BC ...
... radius OB ; then , OA = OB . Then A OAB is isosceles , and △ B = ZA . But since BOC is an ext . Z of △ OAB , ZBOCZA + ZB . : . / BOC = 2 Z≤ A , or ZA = } ≤ BOC . But , BOC is measured by arc BC . Whence , is measured by arc BC ...
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
AB² ABCD AC² adjacent angles altitude apothem approach the limit axis base and altitude BC² bisector bisects centre chord circle circumference circumscribed coincide cone of revolution Converse of Prop diagonals diameter diedral angle distance Draw line equal respectively equally distant equilateral equivalent exterior angle faces Find the area frustum Given line given point Hence homologous homologous sides hypotenuse intersecting isosceles triangle lateral area lateral edges line drawn line joining middle point number of sides parallel parallelogram parallelopiped perimeter perpendicular plane MN polyedral polyedron prism Prove pyramid quadrilateral radii radius rectangle regular inscribed regular polygon rhombus right angles right triangle segment side BC similar slant height spherical polygon spherical triangle square tangent tetraedron THEOREM trapezoid triangle ABC triangular prism triedral vertex vertices volume Whence
Δημοφιλή αποσπάσματα
Σελίδα 58 - The straight line joining the middle points of two sides of a triangle is parallel to the third side, and equal to half of it.
Σελίδα 322 - A right circular cylinder may be generated by the revolution of a rectangle about one of its sides as an axis.
Σελίδα 371 - A zone is a portion of the surface of a sphere included between two parallel planes.
Σελίδα 49 - ... the three sides of one are equal, respectively, to the three sides of the other. 2. Two right triangles are congruent if...
Σελίδα 336 - A spherical polygon is a portion of the surface of a sphere bounded by three or more arcs of great circles. The...
Σελίδα 151 - If one leg of a right triangle is double the other, the perpendicular from the vertex of the right angle to the hypotenuse divides it into segments which are to each other as 1 to 4.
Σελίδα 328 - A sphere is a solid bounded by a surface all points of which are equally distant from a point within called the centre.
Σελίδα 205 - 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.
Σελίδα 73 - A chord is a straight line joining the extremities of an arc ; as AB.
Σελίδα 202 - The circumferences of two circles are to each other as their radii. Given C and C" the circumferences of two © whose radii are R and R', respectively.