Elements of Geometry: Plane and SolidAmerican Book Company, 1895 - 374 σελίδες |
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Σελίδα 227
... axis , when would the revolving plane coincide with plane MN ? If the plane continued to revolve , when would it again coincide with MN ? 645. The intersection of a plane with a surface on which no straight line can be drawn , e.g. the ...
... axis , when would the revolving plane coincide with plane MN ? If the plane continued to revolve , when would it again coincide with MN ? 645. The intersection of a plane with a surface on which no straight line can be drawn , e.g. the ...
Σελίδα 240
... axis , till it reaches the position where its plane angle is bac ; which , again , may be conceived as generated by the revolution of the line ab from an initial position , ac . 463. Two dihedral angles are equal when they can be placed ...
... axis , till it reaches the position where its plane angle is bac ; which , again , may be conceived as generated by the revolution of the line ab from an initial position , ac . 463. Two dihedral angles are equal when they can be placed ...
Σελίδα 277
... axis of a regular pyramid forms equal dihedral angles with all the faces of the pyramid . 735. In order that a plane intersecting the faces of a polyhedral angle may cut off a regular pyramid , what conditions must be fulfilled in ...
... axis of a regular pyramid forms equal dihedral angles with all the faces of the pyramid . 735. In order that a plane intersecting the faces of a polyhedral angle may cut off a regular pyramid , what conditions must be fulfilled in ...
Σελίδα 280
... axis is equal to the apothem of the base , what is the inclination of each face to the base ? 738. In the same ... axis of a regular pyra- mid to the slant height is a mean proportional between the segments into which it divides it . 742 ...
... axis is equal to the apothem of the base , what is the inclination of each face to the base ? 738. In the same ... axis of a regular pyra- mid to the slant height is a mean proportional between the segments into which it divides it . 742 ...
Σελίδα 294
... axis . This side is then called the axis of the cylinder , and the radius of the base , the radius of the cylinder . B ' EXERCISE 780. Only one straight line can be drawn through a given point on a cylindrical surface . 781. A straight ...
... axis . This side is then called the axis of the cylinder , and the radius of the base , the radius of the cylinder . B ' EXERCISE 780. Only one straight line can be drawn through a given point on a cylindrical surface . 781. A straight ...
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Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
AB² ABCD AC² altitude angle formed apothem arc AC bisector bisects chord circumf circumference circumscribed coincide cone of revolution Const construct cylinder DEFINITION diagonals diagram for Prop diameter dihedral angles divided draw edges equiangular equiangular polygon equidistant equilateral triangle equivalent EXERCISE find a point frustum given circle given line given point given straight line greater homologous hypotenuse inscribed intercept interior angles intersecting isosceles triangle line drawn line joining locus meet mid point number of sides numerical measures parallel parallelogram parallelopiped pass perimeter perpendicular plane MN polyhedral angle polyhedron prism produced PROPOSITION Prove pyramid quadrilateral radii radius ratio rect rectangle regular polygon regular polyhedrons right angle right triangle SCHOLIUM secant segment similar slant height sphere spherical polygon spherical triangle square straight angle tangent THEOREM triangle ABC trihedral vertex vertical angle volume
Δημοφιλή αποσπάσματα
Σελίδα 308 - A spherical polygon is a portion of the surface of a sphere bounded by three or more arcs of great circles. The bounding arcs are the sides of the polygon ; the...
Σελίδα 298 - Sphere is a body bounded by a uniformly curved surface, all the points of which are equally distant from a point within called the center.
Σελίδα 283 - 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 113 - To express that the ratio of A to B is equal to the ratio of C to D, we write the quantities thus : A : B : : C : D; and read, A is to B as C to D.
Σελίδα 373 - The object of these primers is to convey information in such a manner as to make it both intelligible and interesting to very young pupils, and so to discipline their minds as to incline them to more systematic after-studies. They are not only an aid to the pupil, but to the teacher, lightening the task of each by an agreeable, easy, and natural method of instruction.
Σελίδα 178 - ... the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the perpendicular let fall on it from the opposite angle, and the acute angle.
Σελίδα 123 - In a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent.
Σελίδα 118 - If the product of two numbers is equal to the product of two others, either two may be made the extremes of a proportion and the other two the means.
Σελίδα 179 - In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square of the side subtending the obtuse angle, is greater than the squares of the sides containing the obtuse angle, by twice the rectangle contained by the side upon which, when produced, the perpendicular falls, and the straight line intercepted without the triangle, between the perpendicular and the obtuse angle.
Σελίδα 272 - Two prisms are to each other as the products of their bases by their altitudes ; prisms having equivalent bases are to each other as their altitudes; prisms having equal altitudes are to each other as their bases ; prisms having equivalent bases and equal altitudes are equivalent.