Elements of Geometry, and Plane and Spherical Trigonometry: With Numerous Practical Problems |
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Page iii
... surface of the sphere ; and that , by having the propositions of Spherical Geometry fresh in his mind when he begins the study of Spherical Trigonometry , he will be as little embarrassed with it as with Plane Trigonometry . ( iii ) ...
... surface of the sphere ; and that , by having the propositions of Spherical Geometry fresh in his mind when he begins the study of Spherical Trigonometry , he will be as little embarrassed with it as with Plane Trigonometry . ( iii ) ...
Page 9
... Surface or Superficies is that which has extension in length and breadth only . 9. A Plane Surface , or a Plane , is a surface such that ( 9 ) 15109 if any two of its points be joined by a PLANE GEOMETRY DEFINITIONS Geometrical ...
... Surface or Superficies is that which has extension in length and breadth only . 9. A Plane Surface , or a Plane , is a surface such that ( 9 ) 15109 if any two of its points be joined by a PLANE GEOMETRY DEFINITIONS Geometrical ...
Page 10
... surface . 10. A Curved Surface is one which is neither a plane , nor composed of plane surfaces . 11. A Plane Angle , or simply an Angle , is the difference in the direction of two lines proceeding from the same point . The other angles ...
... surface . 10. A Curved Surface is one which is neither a plane , nor composed of plane surfaces . 11. A Plane Angle , or simply an Angle , is the difference in the direction of two lines proceeding from the same point . The other angles ...
Page 15
... surfaces , the measuring unit is a square whose side may be any linear unit , as an inch , a foot , a mile , etc. The linear unit being arbitrary , the surface unit is equally so ; and its selection is determined by considerations of ...
... surfaces , the measuring unit is a square whose side may be any linear unit , as an inch , a foot , a mile , etc. The linear unit being arbitrary , the surface unit is equally so ; and its selection is determined by considerations of ...
Page 42
... surface . C E F B From B draw the line BD , par- allel to AF ; and from A draw the line AC , parallel to BE ; and produce EF , if necessary , to C and D ; now the parallelogram ABDF = the parallelogram ABEC , ( Th . 27 ) . But the ...
... surface . C E F B From B draw the line BD , par- allel to AF ; and from A draw the line AC , parallel to BE ; and produce EF , if necessary , to C and D ; now the parallelogram ABDF = the parallelogram ABEC , ( Th . 27 ) . But 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.