Plane and Solid GeometryLongmans, Green and Company, 1898 - 210 σελίδες |
Αναζήτηση στο βιβλίο
Αποτελέσματα 1 - 5 από τα 11.
Σελίδα x
... 100 118 124 139 145 155 159 164 • 164 178 BOOK VIII . THE SPHERE . Definitions . 192 Spherical Angles and Polygons 194 The Sphere • 204 Formulæ 209 GEOMETRY . PRELIMINARY DEFINITIONS . 1. Space has extension in X CONTENTS .
... 100 118 124 139 145 155 159 164 • 164 178 BOOK VIII . THE SPHERE . Definitions . 192 Spherical Angles and Polygons 194 The Sphere • 204 Formulæ 209 GEOMETRY . PRELIMINARY DEFINITIONS . 1. Space has extension in X CONTENTS .
Σελίδα 194
... Spherical Geometry usually signifies a quadrant of a great circle . SPHERICAL ANGLES AND POLYGONS . DEFINITIONS . 490. The Angle between two intersecting arcs of circles on the surface of a sphere is the diedral angle between the planes ...
... Spherical Geometry usually signifies a quadrant of a great circle . SPHERICAL ANGLES AND POLYGONS . DEFINITIONS . 490. The Angle between two intersecting arcs of circles on the surface of a sphere is the diedral angle between the planes ...
Σελίδα 195
James Howard Gore. 492. A Spherical Triangle is a spherical polygon of three sides . A spherical triangle is Right or Oblique , Scalene , Isosceles , or Equilateral , in the same cases as a plane triangle . 493. A Spherical Pyramid is a ...
James Howard Gore. 492. A Spherical Triangle is a spherical polygon of three sides . A spherical triangle is Right or Oblique , Scalene , Isosceles , or Equilateral , in the same cases as a plane triangle . 493. A Spherical Pyramid is a ...
Σελίδα 196
... spherical angle BAB ' is measured by the arc BB ' . Since ( by 359 ) BOB ' is a plane angle , it is ( by 368 ) the measure of the diedral angle BACB ' . But ( by 174 ) the arc BB ' is the measure of BOB ' . Therefore the spherical angle ...
... spherical angle BAB ' is measured by the arc BB ' . Since ( by 359 ) BOB ' is a plane angle , it is ( by 368 ) the measure of the diedral angle BACB ' . But ( by 174 ) the arc BB ' is the measure of BOB ' . Therefore the spherical angle ...
Σελίδα 197
... spherical polygon ABC , etc. ( by 451 ) . We may therefore speak of all the parts of a spherical polygon as Angles , meaning AND thereby the face - angles , and the diedral angles between the faces , of the polyedral angle whose vertex ...
... spherical polygon ABC , etc. ( by 451 ) . We may therefore speak of all the parts of a spherical polygon as Angles , meaning AND thereby the face - angles , and the diedral angles between the faces , of the polyedral angle whose vertex ...
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD AC² acute angle AD² adjacent adjacent angles altitude angle formed angles are equal apothem arc BC base and altitude bisect bisector called centre chord circumference circumscribed cone cylinder diagonals diameter diedral angles distance divided draw drawn ECDH equally distant equilateral equivalent EXERCISES faces four right angles frustum given point given straight line hence homologous homologous sides hypotenuse inscribed polygon interior angles intersection isosceles triangle join lateral area lateral edges Let ABC lune mean proportional measured by one-half middle point number of sides parallelogram parallelopiped perimeter perpendicular polyedral angle polyedron PROPOSITION XI prove pyramid Q.E.D. PROPOSITION quadrilateral radii radius ratio rectangle rectangular parallelopiped regular polygon right triangle SCHOLIUM segments semiperimeter sphere spherical angle spherical polygon spherical triangle surface tangent THEOREM triangle ABC triangles are equal triangular triangular prism V-ABC vertex vertical angle
Δημοφιλή αποσπάσματα
Σελίδα 46 - PERIPHERY of a circle is its entire bounding line ; or it is a curved line, all points of which are equally distant from a point within called the centre.
Σελίδα 105 - ... any two parallelograms are to each other as the products of their bases by their altitudes. PROPOSITION V. THEOREM. 403. The area of a triangle is equal to half the product of its base by its altitude.
Σελίδα 82 - 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 = e :f Now ab = ab (1) and by Theorem I.
Σελίδα 192 - A sphere is a solid bounded by a surface all points of which are equally distant from a point within called the centre.
Σελίδα 108 - Two triangles having 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 146 - A STRAIGHT line is perpendicular to a plane, when it is perpendicular to every straight line which it meets in that plane.
Σελίδα 30 - In an isosceles triangle, the angles opposite the equal sides are equal.
Σελίδα 80 - In any proportion the terms are in proportion by Composition ; that is, the sum of the first two terms is to the first term as the sum of the last two terms is to the third term.
Σελίδα 79 - If the product of two quantities is equal to the product of two others, one pair may be made the extremes, and the other pair the means, of a proportion. Let ad = ос.
Σελίδα 148 - Equal oblique lines from a point to a plane meet the plane at equal distances from the foot of the perpendicular ; and of two unequal oblique lines the greater meets the plane at the greater distance from the foot of the perpendicular.