Elements of Geometry, and Plane and Spherical Trigonometry: With Numerous Practical Problems |
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Page vi
... ... 248 Equations for the Sines of the Angles .... 260 Natural Sines , Cosines , etc ..... 265 Trigonometrical Lines for Arcs exceeding 90 ° ...... 270 SECTION II . Plane Trigonometry , Practically Applied ..... 272 vi CONTENTS .
... ... 248 Equations for the Sines of the Angles .... 260 Natural Sines , Cosines , etc ..... 265 Trigonometrical Lines for Arcs exceeding 90 ° ...... 270 SECTION II . Plane Trigonometry , Practically Applied ..... 272 vi CONTENTS .
Page vii
With Numerous Practical Problems Horatio Nelson Robinson. SECTION II . Plane Trigonometry , Practically Applied ..... 272 Logarithms .... 278 GENERAL APPLICATIONS WITH THE USE OF LOGARITHMS . I. Right - Angled Trigonometry .... II ...
With Numerous Practical Problems Horatio Nelson Robinson. SECTION II . Plane Trigonometry , Practically Applied ..... 272 Logarithms .... 278 GENERAL APPLICATIONS WITH THE USE OF LOGARITHMS . I. Right - Angled Trigonometry .... II ...
Page viii
... applied to Astronomy .... 370 Application of Oblique - Angled Spherical Triangles ............. 373 Spherical Trigonometry applied to Geography Table of Mean Time at Greenwich .... SECTION VI . Regular Polyedrons ...... 377 ... 379 380 ...
... applied to Astronomy .... 370 Application of Oblique - Angled Spherical Triangles ............. 373 Spherical Trigonometry applied to Geography Table of Mean Time at Greenwich .... SECTION VI . Regular Polyedrons ...... 377 ... 379 380 ...
Page 14
... applied the one to the other , will coincide throughout their whole extent . 46. Equivalent Magnitudes are those which , though they do not admit of coincidence when applied the one to the other , still have common measures , and are ...
... applied the one to the other , will coincide throughout their whole extent . 46. Equivalent Magnitudes are those which , though they do not admit of coincidence when applied the one to the other , still have common measures , and are ...
Page 138
... applying the formulæ of Prob . 5 to them and to the successive results ob- tained , we may construct the following table : 3 INSCRIBED POLYGONS . 28 = 2.59807621 33.0000000 CIRCUMSCRIBED POLYGONS . 23-3.46410161 1 12 = 3.2153904 2 + √3 ...
... applying the formulæ of Prob . 5 to them and to the successive results ob- tained , we may construct the following table : 3 INSCRIBED POLYGONS . 28 = 2.59807621 33.0000000 CIRCUMSCRIBED POLYGONS . 23-3.46410161 1 12 = 3.2153904 2 + √3 ...
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Common terms and phrases
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
Popular passages
Page 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.
Page 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.
Page 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.
Page 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.
Page 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.
Page 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.
Page 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.
Page 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.
Page 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.
Page 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.