The Essentials of GeometryD.C. Heath & Company, 1899 - 395 σελίδες |
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Σελίδα 12
... Prop . is the converse of Prop . II . PROP . IV . THEOREM . 40. If two straight lines intersect , the vertical angles equal . A B Given str . lines AB and CD intersecting at 0 . To Prove LAOC BOD . = Proof . Since AOC and AOD have their ...
... Prop . is the converse of Prop . II . PROP . IV . THEOREM . 40. If two straight lines intersect , the vertical angles equal . A B Given str . lines AB and CD intersecting at 0 . To Prove LAOC BOD . = Proof . Since AOC and AOD have their ...
Σελίδα 13
... PROP . V. THEOREM . 41. If a perpendicular be erected at the middle point of a straight line , I. Any point in the perpendicular is equally distant from the extremities of the line . II . Any point without the perpendicular is unequally ...
... PROP . V. THEOREM . 41. If a perpendicular be erected at the middle point of a straight line , I. Any point in the perpendicular is equally distant from the extremities of the line . II . Any point without the perpendicular is unequally ...
Σελίδα 15
Webster Wells. PROP . VI . THEOREM . 45. From a given point without a straight line , a perpen- dicular can be drawn to the line , and but one . K A -B F- G Ε D H ... PROP . VII . THEOREM . 46. The perpendicular is RECTILINEAR FIGURES . 15.
Webster Wells. PROP . VI . THEOREM . 45. From a given point without a straight line , a perpen- dicular can be drawn to the line , and but one . K A -B F- G Ε D H ... PROP . VII . THEOREM . 46. The perpendicular is RECTILINEAR FIGURES . 15.
Σελίδα 19
... equals CF and CE , respectively , we have 2 CF 2 CE . .. CFCE . Note . The theorem holds equally if oblique line CE is on the opposite side of perpendicular CD from CF. PROP . X. THEOREM . 50. ( Converse of Prop RECTILINEAR FIGURES . 19.
... equals CF and CE , respectively , we have 2 CF 2 CE . .. CFCE . Note . The theorem holds equally if oblique line CE is on the opposite side of perpendicular CD from CF. PROP . X. THEOREM . 50. ( Converse of Prop RECTILINEAR FIGURES . 19.
Σελίδα 20
Webster Wells. PROP . X. THEOREM . 50. ( Converse of Prop . IX . , I. ) If oblique lines be drawn from a point to a straight line , two equal oblique lines cut off equal distances from the foot of the perpendicular from the point to the ...
Webster Wells. PROP . X. THEOREM . 50. ( Converse of Prop . IX . , I. ) If oblique lines be drawn from a point to a straight line , two equal oblique lines cut off equal distances from the foot of the perpendicular from the point to the ...
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
AB² ABCD AC² adjacent angles altitude apothem approach the limit area ABC 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 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 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 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 261 - The projection of a point on a plane is the foot of the perpendicular drawn from the point to the plane.
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 73 - A chord is a straight line joining the extremities of an arc ; as AB.
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 170 - The areas of two triangles which have 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.
Σελίδα 224 - The perpendiculars from the vertices of a triangle to the opposite sides are the bisectors of the angles of the triangle formed by joining the feet of the perpendiculars.
Σελίδα 325 - A right circular cone may be generated by the revolution of a right triangle about one of its legs as an axis.