Elements of Geometry, and Plane and Spherical Trigonometry: With Numerous Practical Problems |
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Page vi
... Measurement of Polygons and Circles . 130 Practical Problems .... 142 BOOK VI . On the Intersections of Planes , the Relative Positions of Planes , and of Planes and Lines ... BOOK VII . Solid Geometry . Practical Problems ... BOOK VIII ...
... Measurement of Polygons and Circles . 130 Practical Problems .... 142 BOOK VI . On the Intersections of Planes , the Relative Positions of Planes , and of Planes and Lines ... BOOK VII . Solid Geometry . Practical Problems ... BOOK VIII ...
Page vii
... Measuring Heights and Distances . 298 Practical Problems .. 305 PART II . SPHERICAL GEOMETRY AND TRIGONOMETRY . SECTION I. Spherical Geometry ... 310 SECTION II . Right - Angled Spherical Trigonometry .... 330 Napier's Circular Parts ...
... Measuring Heights and Distances . 298 Practical Problems .. 305 PART II . SPHERICAL GEOMETRY AND TRIGONOMETRY . SECTION I. Spherical Geometry ... 310 SECTION II . Right - Angled Spherical Trigonometry .... 330 Napier's Circular Parts ...
Page 9
... measurements , mutual relations , and pro- perties of limited portions of space . SPACE extends without limit in all directions , and contains all bodies . 2. A Point is mere position , and has no magnitude . 3. Extension is a term ...
... measurements , mutual relations , and pro- perties of limited portions of space . SPACE extends without limit in all directions , and contains all bodies . 2. A Point is mere position , and has no magnitude . 3. Extension is a term ...
Page 10
... measured by degrees . B 14. A Degree is one of the three hundred and sixty equal parts of the space about a point in a plane . If , in the above figure , we suppose AC to coincide with AB , there will be but one line , and no angle ...
... measured by degrees . B 14. A Degree is one of the three hundred and sixty equal parts of the space about a point in a plane . If , in the above figure , we suppose AC to coincide with AB , there will be but one line , and no angle ...
Page 15
... measured by the arc intercepted by its sides . Thus , the arc AB measures the angle AOB ; and in gen- eral , to ... measuring unit is any straight line of fixed value , as an inch , a foot , a rod , etc .; and for surfaces , the ...
... measured by the arc intercepted by its sides . Thus , the arc AB measures the angle AOB ; and in gen- eral , to ... measuring unit is any straight line of fixed value , as an inch , a foot , a rod , etc .; and for surfaces , the ...
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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.