Elements of Geometry: With Practical Applications ...H.H. Howley and Company, 1847 - 308 sider |
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Side 71
... chord . The chord is said to subtend the arc . 3. The portion of the circle in- cluded by an arc and its chord , is called a segment . H Thus the space FGDF , included by the arc FGD and the chord FD , is a segment ; so also is the ...
... chord . The chord is said to subtend the arc . 3. The portion of the circle in- cluded by an arc and its chord , is called a segment . H Thus the space FGDF , included by the arc FGD and the chord FD , is a segment ; so also is the ...
Side 72
... chord of said arc ; and by an angle at the centre , is meant one whose vertex is at the centre . In both cases , the angles are said to be subtended by the chords or arcs which their sides include . 12. The circumference of a circle may ...
... chord of said arc ; and by an angle at the centre , is meant one whose vertex is at the centre . In both cases , the angles are said to be subtended by the chords or arcs which their sides include . 12. The circumference of a circle may ...
Side 73
... chord , it will be perpendicular to the chord ; or , if the line be perpendicular to the chord , it will bisect both the chord and the arc of the chord . Let AB be any chord in a circle , and CD a line drawn from the centre C to the ...
... chord , it will be perpendicular to the chord ; or , if the line be perpendicular to the chord , it will bisect both the chord and the arc of the chord . Let AB be any chord in a circle , and CD a line drawn from the centre C to the ...
Side 74
... chord at right angles , passes through the centre of the circle . ( 60. ) By means of this proposition , we may find ... chords AB , BC ; bisect them with the perpendiculars DF and GH ; then will the point K , in which they in- tersect ...
... chord at right angles , passes through the centre of the circle . ( 60. ) By means of this proposition , we may find ... chords AB , BC ; bisect them with the perpendiculars DF and GH ; then will the point K , in which they in- tersect ...
Side 76
... the sum of GB , HD is greater than GH , which is absurd . Consequently , as in the last proposition , the centre H cannot be out of the line FC . PROPOSITION IV . THEOREM . Chords in a circle , 76 ELEMENTS OF GEOMETRY . 76.
... the sum of GB , HD is greater than GH , which is absurd . Consequently , as in the last proposition , the centre H cannot be out of the line FC . PROPOSITION IV . THEOREM . Chords in a circle , 76 ELEMENTS OF GEOMETRY . 76.
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Vanlige uttrykk og setninger
a+b+c AC² altitude angle ACD angle BAC bisect centre chord circ circular sector circumference cone consequently convex surface cylinder diagonal diameter distance draw equal and parallel equiangular equilateral triangle equivalent exterior angle figure formed four right angles given line greater half the arc hypothenuse inscribed circle intersection isosceles join less Let ABC lines drawn magnitude measured by half meet multiplied number of sides opposite angles parallel planes parallelogram parallelopipedon pendicular perimeter perpendicular plane MN point G prism PROBLEM produced Prop PROPOSITION pyramid radii radius rectangle regular polygon respectively equal right angles right-angled triangle Sabc Schol Scholium semicircle semicircumference side AC similar similar triangles solid angle solid described sphere spherical triangle square straight line suppose tangent THEOREM three sides triangle ABC triangular prism vertex VIII
Populære avsnitt
Side 37 - The sum of all the angles of a polygon is equal to twice as many right angles as the polygon has sides, less two.
Side 180 - THEOREM. If one of two parallel lines is perpendicular to a plane, the other will also be perpendicular to this plane. Let AP & ED be parallel lines, of which AP is perpendicular to the plane MN ; then will ED be also perpendicular to this plane.
Side 139 - 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.
Side 224 - The radius of a sphere is a straight line, drawn from the centre to any point of the...
Side 43 - In a right-angled triangle, the side opposite the right angle is" called the Hypothenuse ; and the other two sides are cal4ed the Legs, and sometimes the Base and Perpendicular.
Side 184 - THEOREM. If two angles, not situated in the same plane, have their sides parallel and lying in the same direction, they will be equal, and the planes in which they are situated will be parallel.
Side 10 - 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.
Side 226 - We conclude then, that the solidity of a cylinder is equal to the product of its base by its altitude.
Side 22 - If two sides and the included angle of the one are respectively equal to two sides and the included angle of the other...
Side 12 - 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.