Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry and Mensuration. Accompanied with All the Necessary Logarithmic and Trigonometric TablesD. Appleton & Company, 1856 - 235 σελίδες |
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Σελίδα v
... circumscribed polygons . Of secant and tangent circles . PROBLEMS . Of perpendiculars , angles , and parallels . Construction of polygons .. Of contact Of common measure 42 47 51 • 57 61 • 66 69 70 Definitions . Proportional lines ...
... circumscribed polygons . Of secant and tangent circles . PROBLEMS . Of perpendiculars , angles , and parallels . Construction of polygons .. Of contact Of common measure 42 47 51 • 57 61 • 66 69 70 Definitions . Proportional lines ...
Σελίδα 41
... circumscribe the polygon . A circle is inscribed in a polygon when its circumference touches each side , and the polygon is said to be circumscribed about the circle . By an angle in a segment of a circle , is to be understood an angle ...
... circumscribe the polygon . A circle is inscribed in a polygon when its circumference touches each side , and the polygon is said to be circumscribed about the circle . By an angle in a segment of a circle , is to be understood an angle ...
Σελίδα 51
... to either side of the triangle , it will be inscribed in the triangle , and consequently the triangle will circumscribe the circle . Scholium I. Since , in the first case , the SECOND BOOK . 51 Of inscribed and circumscribed polygons.
... to either side of the triangle , it will be inscribed in the triangle , and consequently the triangle will circumscribe the circle . Scholium I. Since , in the first case , the SECOND BOOK . 51 Of inscribed and circumscribed polygons.
Σελίδα 52
... equal sides . If the triangle is equilateral , the centres of the two circles will coincide , and the circumscribed and inscribed circles will then be concentric . THEOREM XIII . In any inscribed quadrilateral , the sum 52 GEOMETRY .
... equal sides . If the triangle is equilateral , the centres of the two circles will coincide , and the circumscribed and inscribed circles will then be concentric . THEOREM XIII . In any inscribed quadrilateral , the sum 52 GEOMETRY .
Σελίδα 55
... circumscribe the circle . Scholium . The point F , the common centre of the inscribed and circumscribed circles , is called the centre of the regular polygon . The radius of the circumscribing circle is called the radius of the polygon ...
... circumscribe the circle . Scholium . The point F , the common centre of the inscribed and circumscribed circles , is called the centre of the regular polygon . The radius of the circumscribing circle is called the radius of the polygon ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
a+b+c altitude apothem bisect centre chord circumference circumscribed cone consequently corresponding cosec Cosine Cotang cube cubic cylinder decimal denote diameter dicular divided draw drawn equation equivalent exterior angles feet figure frustum Geom give greater half hence hypotenuse inches intersection logarithm measure multiplied number of sides opposite parallel parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedral angle polyedron prism PROBLEM proportion pyramid quadrant radii radius ratio rectangle regular inscribed regular polygon respectively equal right angles right-angled triangle Scholium secant sector similar similar triangles Sine slant height solid solve the triangle sphere spherical triangle square straight line subtract suppose surface Tang tangent THEOREM three sides triangle ABC triangular prism volume ΙΟ
Δημοφιλή αποσπάσματα
Σελίδα 35 - 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.
Σελίδα 80 - 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. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw the altitudes BD and B'D'.
Σελίδα 139 - If a straight line is perpendicular to each of two straight lines at their point of intersection, it is perpendicular to the plane of those lines.
Σελίδα 17 - The sum of all the angles of a polygon is equal to twice as many right angles as the polygon has sides, less two.
Σελίδα 176 - The radius of a sphere is a straight line, drawn from the centre to any point of the...
Σελίδα 182 - Every section of a sphere, made by a plane, is a circle.
Σελίδα 28 - If two triangles have two sides of the one equal respectively to two sides of the other, but the included angle of the first greater than the included angle of the second, then the third side of the first is greater than the third side of the second. Given A ABC and A'B'C ' with Proof STATEMENTS Apply A A'B'C ' to A ABC so that A'B
Σελίδα 165 - ... bases simply : hence two prisms of the same altitude are to each other as their bases. For a like reason, two prisms of the same base are to each other as their altitudes.
Σελίδα 29 - ... to two sides of the other, but the third side of the first greater than the third side of the second, the angle opposite the third side of the first is.
Σελίδα 13 - If equals be added to unequals, the wholes are unequal. V. If equals be taken from unequals, the remainders are unequal. VI. Things which are double of the same, are equal to one another.