The Eclectic School Geometry: A Revision of Evan's School GeometryVan Antwerp, Bragg, 1884 - 155 páginas |
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Página 51
... inscribed in a circle when all its sides are chords of that circle . A circle is said to be inscribed in a polygon when all the sides of the polygon are tangents to the circle . When one figure is inscribed in another , the latter is ...
... inscribed in a circle when all its sides are chords of that circle . A circle is said to be inscribed in a polygon when all the sides of the polygon are tangents to the circle . When one figure is inscribed in another , the latter is ...
Página 55
... inscribed angle is measured by half the arc on which it stands . Let ACB be an angle inscribed in a circle . It is measured by half the arc AEB . First , suppose the center D to be within the angle . Draw the diameter CE ; also , join ...
... inscribed angle is measured by half the arc on which it stands . Let ACB be an angle inscribed in a circle . It is measured by half the arc AEB . First , suppose the center D to be within the angle . Draw the diameter CE ; also , join ...
Página 56
... inscribed in the same segment , as AEC and ADC , are equal ; for they are measured by half the same arc ABC . Cor . 2. Any angle inscribed in a semicircle is a right angle ; being measured by half a semi- circumference . B THEOREM XXXV ...
... inscribed in the same segment , as AEC and ADC , are equal ; for they are measured by half the same arc ABC . Cor . 2. Any angle inscribed in a semicircle is a right angle ; being measured by half a semi- circumference . B THEOREM XXXV ...
Página 59
... inscribed polygon be regular . Draw the radii AG , BG , CG , etc. Comparing the triangles AGB , BGC , and CGD , and ap- plying Theorems XIII and XXXII , we find AB BC = - F m E D CD , and ang . ABC BCD . Similarly , all the sides and ...
... inscribed polygon be regular . Draw the radii AG , BG , CG , etc. Comparing the triangles AGB , BGC , and CGD , and ap- plying Theorems XIII and XXXII , we find AB BC = - F m E D CD , and ang . ABC BCD . Similarly , all the sides and ...
Página 60
... inscribed or circumscribed regular polygon is the center of the circumscribed or inscribed circle . Cor . 4. The diagonals of a regular polygon drawn between vertices similarly situated with regard to each other , are equal each to each ...
... inscribed or circumscribed regular polygon is the center of the circumscribed or inscribed circle . Cor . 4. The diagonals of a regular polygon drawn between vertices similarly situated with regard to each other , are equal each to each ...
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Términos y frases comunes
allel altitude apothegm Axiom Bisect the angles Book chord circle circumference coincide cone construction convex surface diagonal diameter diedral divided draw drawn equal Theo equal to half equally distant equilateral triangle equivalent exterior angle figure frustum Geometry given angle given line given point given straight line half the product Hence hexagon homologous sides hypotenuse hypothesis inscribed inscribed angle intersection isosceles Let ABC measured by half mutually equiangular number of equal number of sides parallel parallelogram parallelopiped pendicular perimeter perpendicular plane polyedron prism Prove pyramid quadrilateral Ques radii radius ratio rectangle regular polygon respectively equal right angles right-angled triangle secant segment slant height sphere square tangent tetraedron THEOREM THEOREM XI third trapezoid trian triangles ABC triedral vertex
Pasajes populares
Página 104 - If from a point without a circle, a tangent and a secant be drawn, the tangent will be a mean proportional between the secant and its external segment.
Página 32 - If two triangles have two angles and the included side of the one, equal to two angles and the included side of the other, each to each, the two triangles will be equal.
Página 54 - The circumference of every circle is supposed to' be divided into 360 equal parts, called degrees ; each degree into 60 minutes, and each minute into 60 seconds. Degrees, minutes, and seconds are designated by the characters °, ', ". Thus 23° 14' 35" is read 23 degrees, 14 minutes, and 35 seconds.
Página 42 - The square described on the hypothenuse of a right-angled triangle is equivalent to the sum of the squares described on the other two sides.
Página 107 - The areas of two circles are to each other as the squares of their radii. For, if S and S' denote the areas, and R and R
Página 147 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles.
Página 140 - A cone is a solid figure described by the revolution of a right-angled triangle about one of the sides containing the right angle, which side remains fixed.
Página 50 - The area of a regular polygon is equal to half the product of its apothem and perimeter.
Página 141 - The altitude of a pyramid or cone is the perpendicular distance from the ve~rtex to the base.
Página 39 - The area of a rectangle is equal to the product of its base and altitude.