Elements of Geometry: With, Practical ApplicationsD. Appleton and Company, 1850 - 320 páginas |
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Página 15
... opposite the right - angle is called the hypothenuse . Thus BAC is a right - angled triangle , right - angled at A ; the side BC is the hypothenuse . XVII . When the opposite sides of a quadrilateral are parallel , the figure is called ...
... opposite the right - angle is called the hypothenuse . Thus BAC is a right - angled triangle , right - angled at A ; the side BC is the hypothenuse . XVII . When the opposite sides of a quadrilateral are parallel , the figure is called ...
Página 23
... opposite angle AGC , ( Prop . 11 :) hence the angle BGD is equal to AGC . Which is necessary , that the angle of incidence and the angle of reflection of the light may be equal . ( 30. ) Suppose AC and BD to represent two trees standing ...
... opposite angle AGC , ( Prop . 11 :) hence the angle BGD is equal to AGC . Which is necessary , that the angle of incidence and the angle of reflection of the light may be equal . ( 30. ) Suppose AC and BD to represent two trees standing ...
Página 26
... opposite those sides will be equal . If the triangle ABC have the side AC equal to the side BC , then will the angle B be equal to the angle A. C A D B For , conceive the angle C to be bisected , or divided into two equal parts , by the ...
... opposite those sides will be equal . If the triangle ABC have the side AC equal to the side BC , then will the angle B be equal to the angle A. C A D B For , conceive the angle C to be bisected , or divided into two equal parts , by the ...
Página 27
... opposite angles . Let ABC be a triangle , having the side AB produced to D ; then will the exterior angle CBD be greater than either of the interior and opposite angles BAC or BCA . A B H For , conceive the side BC to be bisected in the ...
... opposite angles . Let ABC be a triangle , having the side AB produced to D ; then will the exterior angle CBD be greater than either of the interior and opposite angles BAC or BCA . A B H For , conceive the side BC to be bisected in the ...
Página 28
... opposite to them are also equal , and the tri- angle will be isosceles . In the triangle ABC , let the angle CAB be equal to the angle CBA ; then will the side CB be equal to CA. D A B For , if these sides are not equal , one must be ...
... opposite to them are also equal , and the tri- angle will be isosceles . In the triangle ABC , let the angle CAB be equal to the angle CBA ; then will the side CB be equal to CA. D A B For , if these sides are not equal , one must be ...
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Términos y frases comunes
a+b+c altitude angle ABC angle BAC angle BCD bisect centre chord circ circular sector circumference circumscribed polygon coincide cone consequently convex surface cylinder denote diagonal diameter dicular distance draw equal and parallel equiangular equilateral triangle equivalent exterior angle figure formed given line greater half the arc hypothenuse inscribed circle intersection isosceles join less Let ABC line AC line CD lines drawn measured by half meet multiplied number of sides parallel planes parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN point G prism PROBLEM produced Prop PROPOSITION pyramid radii radius rectangle regular polygon respectively equal right-angled triangle Sabc Schol Scholium scribed semicircle semicircumference side AC similar similar triangles solid angle sphere spherical triangle square straight line suppose tangent THEOREM three sides triangle ABC triangular prism vertex VIII
Pasajes populares
Página 231 - THE sphere is a solid terminated by a curve surface, all the points of which are equally distant from a point within, called the centre.
Página 147 - PROBLEM. To inscribe a circle in a given triangle. Let ABC be the given triangle : it is required to inscribe a circle in the triangle ABC.
Página 17 - A circle is a plane figure contained by one line, which is called the circumference, and is such, that all straight lines drawn from a certain point within the figure to the circumference are equal to one another.
Página 28 - If two sides and the included angle of the one are respectively equal to two sides and the included angle of the other...
Página 233 - The volume of a cylinder is equal to the product of its base by its altitude. Let the volume of the cylinder be denoted by V, its base by B, and its altitude by H.
Página 276 - THEOREM. Two triangles on the same sphere, or on equal spheres, are equal in all their parts, when they have each an equal angle included between equal sides. Suppose the side...
Página 120 - 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. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C' Proof. Draw the altitudes BD and B'D'.
Página 18 - 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.
Página 232 - A spherical triangle is a portion of the surface of a sphere, bounded by three arcs of great circles.
Página 96 - Similar figures, are those that have all the angles of the one equal to all the angles of the other, each to each, and the sides about the equal angles proportional.