Essentials of Solid Geometry |
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Σελίδα
56 PREFACE Demonstrative geometry is taught for the purpose of giving the
student an insight into deductive reasoning , of allowing him to know what it
means to prove a statement , of giving him the privilege of " standing upon the
vantage ...
56 PREFACE Demonstrative geometry is taught for the purpose of giving the
student an insight into deductive reasoning , of allowing him to know what it
means to prove a statement , of giving him the privilege of " standing upon the
vantage ...
Σελίδα 13
To prove that a line or group of lines is a locus we must show that ( a ) every point
on the line or lines satisfies the given condition , and ( 6 ) every point which
satisfies the given condition lies on the line or lines . 2. The locus of points at a
given ...
To prove that a line or group of lines is a locus we must show that ( a ) every point
on the line or lines satisfies the given condition , and ( 6 ) every point which
satisfies the given condition lies on the line or lines . 2. The locus of points at a
given ...
Σελίδα 22
Proposition 1. Intersection of Planes 32. Theorem . If two planes meet , they
intersect in a straight line . a A р $$ 32-36 PERPENDICULAR , OBLIQUE ,
PARALLEL 23 a m. B В Given two planes p and a which meet . Prove that p and
q intersect ...
Proposition 1. Intersection of Planes 32. Theorem . If two planes meet , they
intersect in a straight line . a A р $$ 32-36 PERPENDICULAR , OBLIQUE ,
PARALLEL 23 a m. B В Given two planes p and a which meet . Prove that p and
q intersect ...
Σελίδα 24
Prove that AO is I to m . Proof . Through o draw any other line ox in the plane m ,
and draw PR , cutting OP , Ox , OR in P , Q , and R respectively . On AO produced
take OA ' = 0A . Join A and A ' to P , Q , and R respectively . Then AP = A'P and ...
Prove that AO is I to m . Proof . Through o draw any other line ox in the plane m ,
and draw PR , cutting OP , Ox , OR in P , Q , and R respectively . On AO produced
take OA ' = 0A . Join A and A ' to P , Q , and R respectively . Then AP = A'P and ...
Σελίδα 25
Prove that 0A , OB , OC , ... lie in m . Proof . Suppose that the plane p , determined
by OA and OY , does not intersect m in OA , but intersects it in OA ' . Then OA ' is I
to OY . $ 33 But OA is I to OY . Given Hence the supposition is false . Post .
Prove that 0A , OB , OC , ... lie in m . Proof . Suppose that the plane p , determined
by OA and OY , does not intersect m in OA , but intersects it in OA ' . Then OA ' is I
to OY . $ 33 But OA is I to OY . Given Hence the supposition is false . Post .
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Συχνά εμφανιζόμενοι όροι και φράσεις
altitude base called chord circle circumscribed common compute cone congruent Consider construct Corollary corresponding cube cubic cylinder determine diagonal diameter dihedral angles dimensions distance divided Draw drawn edges equal equilateral equivalent Exercises faces figure Find the area Find the volume follows formed formula four frustum geometry given given line greater Hence inches included inscribed intersection lateral area lateral edges lateral faces length locus lune measured meet oblique opposite parallel parallel planes pass perpendicular plane polar pole polyhedral angles polyhedron prism projection Proof proportional Proposition Prove pyramid radii radius regular pyramid respectively segment shown shows sides similar Similarly slant height solid sphere spherical spherical triangle square straight line student surface symmetric tangent tetrahedron Theorem third total surface triangle triangular trihedral unit vertex vertices volume zone
Δημοφιλή αποσπάσματα
Σελίδα 7 - The line joining the midpoints of two sides of a triangle is parallel to the third side and equal to one-half of it.
Σελίδα 40 - A line which joins the midpoints of two sides of a triangle is parallel to the third side and equal to half of it.
Σελίδα 176 - 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 10 - If two triangles have two sides of the one equal respectively to two sides of the other, but the included angle of the first greater than the included angle of the second, then the third side of the first is greater than the third side of the second. Given A ABC and A'B'C...
Σελίδα 15 - In any triangle, the square of the side opposite an acute angle is equal to the sum of the squares of the other two sides diminished by twice the product of one of those sides and the projection of the other upon that side.
Σελίδα 77 - The height of a cone is the perpendicular distance from the vertex to the plane of the base.
Σελίδα 3 - If the first of three quantities is greater than the second, and the second is greater than the third, then the first is greater than the third.
Σελίδα 24 - If a straight line is perpendicular to each of two other straight lines at their point of intersection, it is perpendicular to the plane of the two lines.
Σελίδα 16 - If two chords intersect in a circle, the product of the segments of one is equal to the product of the segments of the other.
Σελίδα 15 - The sum of the squares of two sides of a triangle is equal to twice the square of half the third side increased by twice the square of the median upon that side.
Πληροφορίες βιβλιογραφίας
| Τίτλος | Essentials of Solid Geometry Wentworth-Smith mathematical series |
| Συγγραφέας | David Eugene Smith |
| Εκδότης | Ginn & Company, 1924 |
| Πρωτότυπο από | το Πανεπιστήμιο της Καλιφόρνια |
| Ψηφιοποιήθηκε στις | 30 Νοεμ. 2007 |
| Μέγεθος | 238 σελίδες |
| Εξαγωγή αναφοράς | BiBTeX EndNote RefMan |