The Essentials of GeometryD.C. Heath & Company, 1899 - 395 σελίδες |
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Σελίδα
... proof is left to the pupil . Another important improvement consists in giving figures and suggestions for the exercises . In Book I. , the pupil has a figure for every non - numerical exercise ; after that , they are only given with the ...
... proof is left to the pupil . Another important improvement consists in giving figures and suggestions for the exercises . In Book I. , the pupil has a figure for every non - numerical exercise ; after that , they are only given with the ...
Σελίδα
... proof , of turning the page for reference to the figure . The Appendix to the Plane Geometry contains proposi tions ... proofs of the limit statements made in §§ 639 , 650 , 667 , and 674 . The author wishes to acknowledge , with thanks ...
... proof , of turning the page for reference to the figure . The Appendix to the Plane Geometry contains proposi tions ... proofs of the limit statements made in §§ 639 , 650 , 667 , and 674 . The author wishes to acknowledge , with thanks ...
Σελίδα 14
... Proof . Let AF intersect CD at E , and draw line BE . Now BE + EF > BF . [ A str . line is the shortest line between two points . ] But , BE = AE . ( Ax . 4 ) [ If a be erected at the middle point of a str . line , any point in the is ...
... Proof . Let AF intersect CD at E , and draw line BE . Now BE + EF > BF . [ A str . line is the shortest line between two points . ] But , BE = AE . ( Ax . 4 ) [ If a be erected at the middle point of a str . line , any point in the is ...
Σελίδα 15
... Proof . Let line HK be to line FG at H. [ At a given point in a str . line , a to the line can be drawn . ] ( § 25 ) Apply line FG to line AB , and move it along until HK passes through C ; let point H fall at D , and draw line CD ...
... Proof . Let line HK be to line FG at H. [ At a given point in a str . line , a to the line can be drawn . ] ( § 25 ) Apply line FG to line AB , and move it along until HK passes through C ; let point H fall at D , and draw line CD ...
Σελίδα 18
... is the greater . A E D F B I. Given CD the L from point C to line AB ; and CE and CF oblique lines from C to AB , cutting off equal distances from the foot of CD . To Prove CE = CF Proof . By hyp . 18 PLANE GEOMETRY . - BOOK I.
... is the greater . A E D F B I. Given CD the L from point C to line AB ; and CE and CF oblique lines from C to AB , cutting off equal distances from the foot of CD . To Prove CE = CF Proof . By hyp . 18 PLANE GEOMETRY . - BOOK I.
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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.