A Treatise on Special Or Elementary GeometrySheldon, 1872 - 239 sivua |
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ABCD acute angle adjacent adjacent angles angle or arc base and altitude bisect centre chord circumference coincide conceive construct corresponding cosine DEM.-In DEM.-Let diagonals diameter diedral distance dividers draw drawn equal angles equally distant equiangular equilateral equivalent exterior angles facial angles figure frustum Geometry given line given point greater Hence homologous sides hypotenuse inches included angle inscribed inscribed angle intersect less LOGARITHMIC FUNCTIONS measured number of sides oblique lines parallel parallelogram parallelopiped passing pendicular perpendicular plane triangle prism Prob Prob.-To produced project the triangle PROP pyramid quadrant quadrilateral radii rectangle regular polygon revolve right angled triangle secant secant line sine solution sphere spherical angle spherical triangle square straight line student surface take the direction tang tangent Theorem.-The triangle ABC triedral trigonometrical trigonometrical functions vertex whence
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Sivu 60 - The homologous sides of similar triangles are to each other as the square roots of their areas. This theorem is involved in the theorem that the areas of similar triangles are to each other as the squares of their homologous sides.
Sivu 137 - If two triangles have two sides and the included angle of the one, equal to two sides and the included angle of the other, each to each, the two triangles will be equal in all their parts." Axiom 1. "Things which are equal to the same thing, are equal to each other.
Sivu 216 - A sphere is a solid, bounded by one continued convex surface, every point of which is equally distant from a point within, called the centre.
Sivu 145 - Theorem — Two triangles are equal when the three sides of the one are respectively equal to the three sides of the other.
Sivu 113 - The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles.
Sivu 116 - If the opposite sides of a quadrilateral are equal, the figure is a parallelogram.
Sivu 9 - LEMMA 4. — A common divisor of two numbers is a divisor of their sum and also of their difference.
Sivu 165 - The perimeters of two regular polygons of the same number of sides, are to each other as their homologous sides, and their areas are to each other as the squares of those sides (Prop.
Sivu 14 - The logarithm of a quotient equals the logarithm of the dividend minus the logarithm of the divisor.
Sivu 156 - 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.