Elements of Geometry, and Plane and Spherical Trigonometry: With Numerous Practical ProblemsIvison, Phinney, Blakeman & Company, 1865 - 444 σελίδες |
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Σελίδα viii
... ........... 373 Spherical Trigonometry applied to Geography Table of Mean Time at Greenwich .... SECTION VI . Regular Polyedrons ...... 377 ... 379 380 GEOMETRY . DEFINITIONS . 1. Geometry is the science which viii CONTENTS .
... ........... 373 Spherical Trigonometry applied to Geography Table of Mean Time at Greenwich .... SECTION VI . Regular Polyedrons ...... 377 ... 379 380 GEOMETRY . DEFINITIONS . 1. Geometry is the science which viii CONTENTS .
Σελίδα 89
... the circle is then said to be circumscribed about the polygon . 14. A Regular Polygon is one which is both equiangu- lar and equilateral . The last three definitions are illustrated by the last figure 8 * BOOK III . 89.
... the circle is then said to be circumscribed about the polygon . 14. A Regular Polygon is one which is both equiangu- lar and equilateral . The last three definitions are illustrated by the last figure 8 * BOOK III . 89.
Σελίδα 123
... and draw BC . The triangle ABC is inscribed in the circle ; it is equi- angular to the triangle abc , and hence it is the triangle required . Proof , ( Th . 12 , B. III . R PROBLEM XXVII . To inscribe a regular pentagon in a BOOK IV . 123.
... and draw BC . The triangle ABC is inscribed in the circle ; it is equi- angular to the triangle abc , and hence it is the triangle required . Proof , ( Th . 12 , B. III . R PROBLEM XXVII . To inscribe a regular pentagon in a BOOK IV . 123.
Σελίδα 124
... regular pen- 360 ° tagon , being one fifth of the whole circumference , is equal to = 72 ° . 5 PROBLEM XXVIII . To inscribe a regular hexagon in a circle . Draw any diameter of the circle , as AB , and from one extremity , B , draw BD ...
... regular pen- 360 ° tagon , being one fifth of the whole circumference , is equal to = 72 ° . 5 PROBLEM XXVIII . To inscribe a regular hexagon in a circle . Draw any diameter of the circle , as AB , and from one extremity , B , draw BD ...
Σελίδα 125
... regular polygon of fifteen sides , which may be inscribed in any given circle . Let CB be the radius of the given circle ; divide it into extreme and mean ratio , ( Problem 24 ) , and make BD equal to CE , the greater part ; then BD ...
... regular polygon of fifteen sides , which may be inscribed in any given circle . Let CB be the radius of the given circle ; divide it into extreme and mean ratio , ( Problem 24 ) , and make BD equal to CE , the greater part ; then BD ...
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD altitude angle opposite axis bisected chord circle circumference circumscribed common cone convex surface cos.a cos.c Cosine Cotang diagonal diameter dicular difference distance divided draw equal angles equation equiangular equivalent find the angles four magnitudes frustum given line greater half Hence the theorem homologous hypotenuse included angle inscribed intersect isosceles less Let ABC logarithm measured multiplied N.sine number of sides opposite angles parallelogram parallelopipedon pendicular perpen perpendicular plane ST polyedron PROB PROBLEM produced Prop proportion PROPOSITION prove pyramid quadrantal radii radius rectangle regular polygon right angles right-angled spherical triangle right-angled triangle SCHOLIUM secant segment similar sin.a sin.b sin.c sine solid angles sphere SPHERICAL TRIGONOMETRY square straight line Tang tangent three angles three sides triangle ABC triangular prisms Trigonometry vertex vertical angle volume
Δημοφιλή αποσπάσματα
Σελίδα 322 - 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 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 123 - In a given circle to inscribe a triangle equiangular to a given triangle. Let ABC be the given circle, and DEF the given triangle ; it is required to inscribe in the circle ABC a triangle equiangular to the triangle DEF.
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 29 - If one side of a triangle is produced, the exterior angle is equal to the sum of the two interior and opposite, angles; and the three interior angles of every triangle are equal to two right angles.
Σελίδα 41 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
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 65 - In a series of equal ratios, any antecedent is to its consequent, as the sum of all the antecedents is to the sum of all the consequents. Let a: 6 = c: d = e :/. Then, by Art.
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.