Plane and Solid GeometryGinn, 1895 - 320 sider |
Inni boken
Resultat 1-5 av 29
Side vii
... LOCI OF POINTS BOOK II . - SECTION 1 . THEOREMS 66 2 . PROBLEMS . EQUALITY OF POLYGONS . 66 3. PRACTICAL MENSURATION OF SURFACES BOOK III . CIRCLES . 08888 18 38 59 69 77 94 100 DEFINITIONS SECTION 1. - CENTRAL ANGLES 102 104 66 3 ...
... LOCI OF POINTS BOOK II . - SECTION 1 . THEOREMS 66 2 . PROBLEMS . EQUALITY OF POLYGONS . 66 3. PRACTICAL MENSURATION OF SURFACES BOOK III . CIRCLES . 08888 18 38 59 69 77 94 100 DEFINITIONS SECTION 1. - CENTRAL ANGLES 102 104 66 3 ...
Side 68
... the segment inter- cepted between two other given lines may equal a given segment . 209. Given the three mid - points of the sides of a triangle , to construct the triangle . Section 4. Loci of Points . - THE place of 68 PLANE GEOMETRY .
... the segment inter- cepted between two other given lines may equal a given segment . 209. Given the three mid - points of the sides of a triangle , to construct the triangle . Section 4. Loci of Points . - THE place of 68 PLANE GEOMETRY .
Side 69
... locus of points satisfying that condition . Indeed , the word locus ( Latin ) means simply place ( English , locality , locate , etc. ) ; the plural is loci . For example , The locus of points at a given distance r from a fixed point O ...
... locus of points satisfying that condition . Indeed , the word locus ( Latin ) means simply place ( English , locality , locate , etc. ) ; the plural is loci . For example , The locus of points at a given distance r from a fixed point O ...
Side 70
... locus of points equidistant from two given points is the perpendicular bisector of the line joining them . Given two points X and X ' , and YY ' XX ' at the mid - point O. To prove that YY ' is the locus of points equidistant from X and ...
... locus of points equidistant from two given points is the perpendicular bisector of the line joining them . Given two points X and X ' , and YY ' XX ' at the mid - point O. To prove that YY ' is the locus of points equidistant from X and ...
Side 71
... locus of points equidistant from OA and OB . Α ́ Β X- Proof . 1. Let Q be any point on neither XX ' nor YY ' ; let QB I OB , QAL OA , QA cut OX in P , PA ' OB . Draw QA ' . Since Q may be moved , P may be considered as any point on OX ...
... locus of points equidistant from OA and OB . Α ́ Β X- Proof . 1. Let Q be any point on neither XX ' nor YY ' ; let QB I OB , QAL OA , QA cut OX in P , PA ' OB . Draw QA ' . Since Q may be moved , P may be considered as any point on OX ...
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Plane and Solid Geometry David Eugene Smith,Wooster Woodruff Beman Ingen forhåndsvisning tilgjengelig - 2016 |
Vanlige uttrykk og setninger
a₁ ABCD altitude angles equal b₁ b₂ bisect bisectors C₁ called central angles chord circle circumcenter circumference circumscribed cone congruent construct convex COROLLARIES corresponding cylinder DEFINITIONS diagonals diameter dihedral angle divided draw drawn edges equal angles equidistant equilateral EXERCISES face angles figure of th frustum geometry given line given point greater Hence hypotenuse inscribed interior angles intersection isosceles triangle line-segment locus lune meet mid-points oblique opposite sides orthocenter P₁ P₂ parallel lines parallelepiped parallelogram perigon perimeter perpendicular plane plane geometry polar polyhedral angle prism Prismatoid produced Proof prove pyramid quadrilateral radii radius ratio rectangle regular polygon respectively rhombus right angle right-angled triangle segments Similarly slant height sphere spherical polygon spherical surface spherical triangle square straight angle straight line Suppose symmetric tangent tetrahedron Theorem trihedral vertex vertices
Populære avsnitt
Side 90 - The projection of a point on a line is the foot of the perpendicular from the point to the line. Thus A
Side 24 - The third side is called the base of the isosceles triangle, and the equal sides are called the sides. A triangle which has no two sides equal is called a scalene triangle. The distance from one point to another is the length of the straight line-segment joining them. The distance from a point to a line is the length of the perpendicular from that point to that line. That this perpendicular is unique will be proved later. This is the meaning of the word distance in plane geometry. In speaking of...
Side 295 - The sum of the angles of a spherical triangle is greater than two and less than six right angles ; that is, greater than 180° and less than 540°. (gr). If A'B'C' is the polar triangle of ABC...
Side 74 - Prove analytically that the perpendiculars from the vertices of a triangle to the opposite sides meet in a point.
Side 107 - XLI. 2. The perpendicular bisector of a chord passes through the center of the circle and bisects the subtended arcs.
Side 37 - If two triangles have two sides of the one respectively equal to two sides of the other, and the contained angles supplemental, the two triangles are equal.
Side 225 - Theorem. If each of two intersecting planes is perpendicular to a third plane, their line of intersection is also perpendicular to that plane. Given two planes, Q, R, intersecting in OP, and each perpendicular to plane M. To prove that OP _L M.
Side 265 - A Plane Surface, or a Plane, is a surface in which if any two points are taken, the straight line which joins these points will lie wholly in the surface.
Side 159 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Side 94 - To construct a parallelogram equal to a given triangle and having one of its angles equal to a given angle.