Plane GeometryAmerican Book Company, 1899 - 242 σελίδες |
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Σελίδα 213
William James Milne. BOOK VI REGULAR POLYGONS AND MEASUREMENT OF THE CIRCLE 374. A polygon which is equilateral and equiangular is called a Regular Polygon . An equilateral triangle and a square are regular polygons . Proposition I 375 ...
William James Milne. BOOK VI REGULAR POLYGONS AND MEASUREMENT OF THE CIRCLE 374. A polygon which is equilateral and equiangular is called a Regular Polygon . An equilateral triangle and a square are regular polygons . Proposition I 375 ...
Σελίδα 214
... polygon has been formed ? Theorem . If the circumference of a circle is divided into any number of equal arcs , 1. The chords joining the extremities of the arcs in suc- cession form a regular inscribed polygon . 2. The tangents drawn ...
... polygon has been formed ? Theorem . If the circumference of a circle is divided into any number of equal arcs , 1. The chords joining the extremities of the arcs in suc- cession form a regular inscribed polygon . 2. The tangents drawn ...
Σελίδα 215
... regular polygon is called the center of the polygon . 380. The angle between the radii drawn to the extremities of any side of a regular polygon is called the angle at the center of the polygon . Proposition III 381. 1. Draw any regular ...
... regular polygon is called the center of the polygon . 380. The angle between the radii drawn to the extremities of any side of a regular polygon is called the angle at the center of the polygon . Proposition III 381. 1. Draw any regular ...
Σελίδα 216
... regular polygon is equal to four right angles divided by the number of sides of the polygon . Proposition IV 384. Draw a circle and a regular inscribed polygon ; at the middle points of the arcs subtended by its sides draw tangents and ...
... regular polygon is equal to four right angles divided by the number of sides of the polygon . Proposition IV 384. Draw a circle and a regular inscribed polygon ; at the middle points of the arcs subtended by its sides draw tangents and ...
Σελίδα 217
... regular circumscribed polygon . Therefore , etc. Q.E.D. 385. Cor . Regular inscribed and circumscribed polygons of the same number of sides may be so placed that their sides are parallei and their vertices will then lie upon the radii ...
... regular circumscribed polygon . Therefore , etc. Q.E.D. 385. Cor . Regular inscribed and circumscribed polygons of the same number of sides may be so placed that their sides are parallei and their vertices will then lie upon the radii ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
AABC AB² ABCD AC² adjacent angles angle formed angles are equal apothem arc intercepted base and altitude BC² bisector bisects CD² central angle chord circle whose center circumference circumscribing circle compare in length Construct a square Construct a triangle Data diagonals diameter divided equal circles equidistant equilateral triangle exterior extremities FGHJK given line given parallelogram given point given triangle Hence homologous sides hypotenuse inscribed angle interior angles intersecting isosceles trapezoid isosceles triangle line drawn measured by arc meet middle point MILNE'S number of sides opposite sides parallel lines perimeter perpendicular produced proportion prove Q.E.D. Proposition quadrilateral radii radius ratio rect rectangle formed regular inscribed regular polygon rhombus right angle right triangle secant similar polygons similar triangles square equivalent subtended tangent Theorem third side transversal trapezoid triangle ABC triangle equivalent triangle is equal vertex vertical angle
Δημοφιλή αποσπάσματα
Σελίδα 67 - The line joining the middle points of two sides of a triangle is parallel to the third side and equal to half of the third side.
Σελίδα 105 - 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 46 - Any exterior angle of a triangle is equal to the sum of the two opposite interior angles.
Σελίδα 74 - If two parallel lines are cut by a third straight line, the sum of the two interior angles on the same side of the transversal is equal to two right angles, (p.
Σελίδα 64 - From 56 and 57 the pupils should learn that two triangles are equal in every respect (a) when two sides and the included angle of one are equal to two sides and the included angle of the other...
Σελίδα 53 - If two angles of a triangle are unequal, the sides opposite are unequal, and the greater side is opposite the greater angle.
Σελίδα 61 - If the opposite sides of a quadrilateral are equal, the figure is a parallelogram.
Σελίδα 126 - DE and on the same side of it ; but equal triangles on the same base, and on the same side of it, are between the same parallels ; [I.
Σελίδα 90 - Theorem. In the same circle, or in equal circles, equal chords are equally distant from the center; conversely, chords equally distant from the center are equal.
Σελίδα 149 - Sines that the bisector of an angle of a triangle divides the opposite side into parts proportional to the adjacent sides.