Elements of Geometry, and Plane and Spherical Trigonometry: With Numerous Practical Problems |
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Page 12
... sides of the polygon . The least number of sides that can bound a polygon is three , and by the figure thus bounded all other polygons are analyzed . FIGURES OF THREE SIDES . 24. A Triangle is a polygon having three sides and three ...
... sides of the polygon . The least number of sides that can bound a polygon is three , and by the figure thus bounded all other polygons are analyzed . FIGURES OF THREE SIDES . 24. A Triangle is a polygon having three sides and three ...
Page 13
... SIDES . 32. A Quadrilateral is a polygon having four sides and four angles . 33. A Parallelogram is a quadrilateral which has its opposite sides parallel . Parallelograms are denominated from the rela- tions both of their sides and ...
... SIDES . 32. A Quadrilateral is a polygon having four sides and four angles . 33. A Parallelogram is a quadrilateral which has its opposite sides parallel . Parallelograms are denominated from the rela- tions both of their sides and ...
Page 14
... sides . Polygons may be similar without being equal ; that is , the angles and the number of sides may be equal , and the length of the sides and the size of the figures unequal . THE CIRCLE . 48. A Circle is a plane figure bound- ed by ...
... sides . Polygons may be similar without being equal ; that is , the angles and the number of sides may be equal , and the length of the sides and the size of the figures unequal . THE CIRCLE . 48. A Circle is a plane figure bound- ed by ...
Page 15
... sides , of the equal circles having their centers at the vertices of the angles . UNITS OF MEASURE . 54. The ... side may be any linear unit , as an inch , a foot , a mile , etc. The linear unit being arbitrary , the surface unit is ...
... sides , of the equal circles having their centers at the vertices of the angles . UNITS OF MEASURE . 54. The ... side may be any linear unit , as an inch , a foot , a mile , etc. The linear unit being arbitrary , the surface unit is ...
Page 30
... sides . Let ABCDE be any polygon ; we are to prove that the sum of all its interior angles , A + B + C + D + E , is equal to twice as many right angles , less four , as the figure has sides . A E D B From any point , p , within the ...
... sides . Let ABCDE be any polygon ; we are to prove that the sum of all its interior angles , A + B + C + D + E , is equal to twice as many right angles , less four , as the figure has sides . A E D B From any point , p , within the ...
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Common terms and phrases
ABē ABCD altitude angle opposite axis bisected chord circle circumference circumscribed common cone convex surface cos.a cos.b cos.c Cosine Cotang diagonal diameter dicular difference distance divided draw equal angles equation equiangular equivalent find the angle 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 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 straight line subtracting Tang tangent three angles three sides triangle ABC triangular prisms triedral angles TRIGONOMETRY vertex vertical angle volume
Popular passages
Page 320 - 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 65 - If four magnitudes are in proportion, the sum of the first and second is to their difference as the sum of the third and fourth is to their difference.
Page 121 - 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 56 - 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 34 - Conversely: if two angles of a triangle are equal, the sides opposite to them are equal, and the triangle it itosceles.
Page 126 - 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.
Page 22 - If two parallel lines are cut by a third straight line, the sum of the two interior angles on the same side of the secant line is equal to two right angles.
Page 277 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 94 - 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 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.