An Elementary Geometry: Plane, Solid and Spherical1880 - 240 σελίδες |
Αναζήτηση στο βιβλίο
Αποτελέσματα 1 - 5 από τα 38.
Σελίδα
... propositions usually proved by the indirect ( see 85 , last part of 87 , and 102 , in Book I. ) . In the preparation of this work the author has obtained valu- able suggestions from many European works on Elementary Geometry , and ...
... propositions usually proved by the indirect ( see 85 , last part of 87 , and 102 , in Book I. ) . In the preparation of this work the author has obtained valu- able suggestions from many European works on Elementary Geometry , and ...
Σελίδα
... Propositions XVIII . ( including its Corollaries ) and XX . of Book I .; the definition and consequent discussion of Similar Polygons ( II . 52-58 , 76-78 ) ; the use made of Proposition X. , of Book III . , in subsequent demonstra ...
... Propositions XVIII . ( including its Corollaries ) and XX . of Book I .; the definition and consequent discussion of Similar Polygons ( II . 52-58 , 76-78 ) ; the use made of Proposition X. , of Book III . , in subsequent demonstra ...
Σελίδα 2
... Proposition is either a theorem or a problem . 17. A Corollary is an inference from a proposition or state- ment . 18. A Scholium is a remark appended to a proposition . 19. An Hypothesis is a supposition in the statement of a proposition ...
... Proposition is either a theorem or a problem . 17. A Corollary is an inference from a proposition or state- ment . 18. A Scholium is a remark appended to a proposition . 19. An Hypothesis is a supposition in the statement of a proposition ...
Σελίδα 8
... proposition ; therefore angle B = angle E. PARALLEL LINES . 50. Definition . Parallel Lines are such as A- have the same direction ; as A B and CD . C- -B -D 51. Corollary . Parallel lines can never meet . For , since parallel lines ...
... proposition ; therefore angle B = angle E. PARALLEL LINES . 50. Definition . Parallel Lines are such as A- have the same direction ; as A B and CD . C- -B -D 51. Corollary . Parallel lines can never meet . For , since parallel lines ...
Σελίδα 22
... proposition EB EC ; hence , FE + EB FC . But ( 29 ) FE + EB > FB , and ( 90 ) FB > FG ; hence , F C F G. If BAC is an obtuse angle , the point F may be so situated that the perpendicular from F to A C may fall at A , in which case ( 90 ) ...
... proposition EB EC ; hence , FE + EB FC . But ( 29 ) FE + EB > FB , and ( 90 ) FB > FG ; hence , F C F G. If BAC is an obtuse angle , the point F may be so situated that the perpendicular from F to A C may fall at A , in which case ( 90 ) ...
Άλλες εκδόσεις - Προβολή όλων
An Elementary Geometry: Plane, Solid and Spherical William Frothingham Bradbury Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
Συχνά εμφανιζόμενοι όροι και φράσεις
A B D altitude angles are equal apothem arcs A B centre chord circle circumference circumscribed cone construct the triangle convex surface Corollary diagonals diameter diedral angles distance divided draw equally distant equivalent bases face angles feet frustum given angle given line given point hence homologous homologous lines hypothenuse inscribed intersection isosceles triangle lines bisecting locus medial line middle points mutually equiangular number of sides opposite sides parallelogram parallelopiped perimeter perpendicular plane M N polar triangle polyedral angle polyedrons produced proposition quadrilateral radius ratio rectangle rectangular parallelopiped regular polygon respectively equal right prism right triangle Scholium similar slant height sphere spherical angle spherical polygon spherical triangle square straight line tangent tetraedrons THEOREM triangle A B C triangle is equal triangular prism triedral vertex vertices
Δημοφιλή αποσπάσματα
Σελίδα 166 - Any two rectangles are to each other as the products of their bases by their altitudes.
Σελίδα 13 - If two triangles have two sides and the inchtded angle of the one respectively equal to two sides and the included angle of the other, the two triangles are equal in all respects.
Σελίδα 41 - If any number of quantities are proportional, any antecedent is to its consequent as the sum of all the antecedents is to the sum of all the consequents. Let a : b = c : d...
Σελίδα 198 - Each side of a spherical triangle is less than the sum of the other two sides.
Σελίδα 75 - A Circle is a plane figure bounded by a curved line every point of which is equally distant from a point within called the center.
Σελίδα 203 - In an isosceles spherical triangle, the angles opposite the equal sides are equal. In the spherical triangle ABC, let AB equal AC.
Σελίδα 220 - If one angle of a triangle is equal to the sum of the other two, the triangle can be divided into two isosceles triangles.
Σελίδα 136 - A STRAIGHT line is perpendicular to a plane, when it is perpendicular to every straight line which it meets in that plane.
Σελίδα 199 - THEOREM. The sum of the sides of a spherical polygon is less than the circumference of a great circle.
Σελίδα 162 - An oblique prism is equivalent to a right prism whose base is a right section of the oblique prism, and whose altitude is equal to a lateral edge of the oblique prism. Hyp. GM is a right section of oblique prism AD', and GM.' a right prism whose altitude is equal to a lateral edge of AD'. To prove AD' =0= GM'. Proof. The lateral edges of GM