Elements of Geometry, Plane and Spherical: With Numerous Practical ProblemsIvison, Phinney, Blakeman & Company, 1868 - 262 σελίδες |
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Σελίδα 244
... Pole of a circle of a sphere is a point on the sur- face of the sphere equally distant from every point in the ... poles of the sides of the other . PROPOSITION I. Any two sides of a spherical triangle are together greater than the third ...
... Pole of a circle of a sphere is a point on the sur- face of the sphere equally distant from every point in the ... poles of the sides of the other . PROPOSITION I. Any two sides of a spherical triangle are together greater than the third ...
Σελίδα 245
... poles of the great circle , and these points are also the poles of all small circles parallel to the great circle . Let O be the center of the sphere , and BD the axis of the great circle , Cm Am " ; then will B and D , the extremities ...
... poles of the great circle , and these points are also the poles of all small circles parallel to the great circle . Let O be the center of the sphere , and BD the axis of the great circle , Cm Am " ; then will B and D , the extremities ...
Σελίδα 246
... pole of the circle , FnE . In like manner we prove the arcs , DF , Dn , DE , etc. , equal , and therefore D is the other pole of the same circle . ' Hence the proposition , etc. Cor . 1. A point on the surface of a sphere at the ...
... pole of the circle , FnE . In like manner we prove the arcs , DF , Dn , DE , etc. , equal , and therefore D is the other pole of the same circle . ' Hence the proposition , etc. Cor . 1. A point on the surface of a sphere at the ...
Σελίδα 248
... poles to the great circle , POP ' ; and P and P ' are the poles to the great circle , ABA ' . Now , CPD is a spherical triangle , right - angled at D , and its sides CP and CD are complemental respectively to the sides BC and AC of the ...
... poles to the great circle , POP ' ; and P and P ' are the poles to the great circle , ABA ' . Now , CPD is a spherical triangle , right - angled at D , and its sides CP and CD are complemental respectively to the sides BC and AC of the ...
Σελίδα 249
... poles are respectively A , B , and C. Produce the three arcs until they meet in D , E , and F. We are now to prove that E is the pole of the arc AC ; D the pole of the arc BC ; F the pole to the arc AB . Also , that the side EF , is ...
... poles are respectively A , B , and C. Produce the three arcs until they meet in D , E , and F. We are now to prove that E is the pole of the arc AC ; D the pole of the arc BC ; F the pole to the arc AB . Also , that the side EF , is ...
Άλλες εκδόσεις - Προβολή όλων
Elements of Geometry, Plane and Spherical: With Numerous Practical Problems Horatio Nelson Robinson Προβολή αποσπασμάτων - 1868 |
Συχνά εμφανιζόμενοι όροι και φράσεις
AB² ABCD AC² altitude angle ABC axis base and altitude bisected chord circ circumference circumscribed polygon common cone convex surface cylinder diagonal diameter dicular distance divided draw equal altitudes equal and parallel equal angles equal bases equal sides equation equiangular equivalent four magnitudes frustum given line greater half Hence the theorem homologous edges hypotenuse interior angles isosceles Let ABC line drawn lune measured middle point multiplied number of sides opposite angles parallel lines parallelogram parallelopipe parallelopipedon pendicular perimeter perpen perpendicular plane ST polyedron PROB PROBLEM produced proportion PROPOSITION prove radii radius regular polygon right angles right-angled triangle SCHOLIUM secant segment semi-polygon slant height solid angles sphere spherical polygon spherical triangle square described straight line tangent three angles triangle ABC triangular prisms triedral angles vertex vertical angle volume
Δημοφιλή αποσπάσματα
Σελίδα 30 - Therefore all the interior angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Σελίδα 96 - The angle in a semicircle is a right angle ; the angle in a segment greater than a semicircle is less than a right angle ; and the angle in a segment less than a semicircle is greater than a right angle.
Σελίδα 128 - To inscribe a regular polygon of a certain number of sides in a given circle, we have only to divide the circumference into as many equal parts as the polygon has sides : for the arcs being equal, the chords AB, BC, CD, &c.
Σελίδα 174 - A cylinder is conceived to be generated by the revolution of a rectangle about one of its sides as an axis.
Σελίδα 254 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Σελίδα 77 - FGL ; (vi. 6.) and therefore similar to it ; (vi. 4.) wherefore the angle ABE is equal to the angle FGL: and, because the polygons are similar, the whole angle ABC is equal to the whole angle FGH ; (vi.
Σελίδα 113 - From a given point, to draw a line parallel to a given line. Let A be the given point, and BC the given line.
Σελίδα 160 - THEOREM. If two planes are perpendicular to the same straight line, they are parallel to each other. Let the planes MN...
Σελίδα 58 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.
Σελίδα 61 - A fourth proportional to three quantities is the fourth term of a proportion, whose first three terms are the three quantities taken in their order. Thus, in the proportion a : b = c : d, d is a fourth proportional to a, b, and c.