Elements of Geometry: With Practical Applications ...H.H. Howley and Company, 1847 - 308 páginas |
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Página 71
... inscribed in a circle , when its extremities are in the circumference . 8. An angle is inscribed in a circle , when BOOK III . 71 BOOK THIRD. ...
... inscribed in a circle , when its extremities are in the circumference . 8. An angle is inscribed in a circle , when BOOK III . 71 BOOK THIRD. ...
Página 72
... inscribed . 9. A polygon is inscribed in a circle when its sides are inscribed ; and under the same circumstances , the circle is said to circumscribe the polygon . Thus AB is an inscribed line , ABC an inscribed angle , and the figure ...
... inscribed . 9. A polygon is inscribed in a circle when its sides are inscribed ; and under the same circumstances , the circle is said to circumscribe the polygon . Thus AB is an inscribed line , ABC an inscribed angle , and the figure ...
Página 82
... inscribed in a circle , is equal to two right angles ; for , as each inscribed angle is measured by half the arc on which it stands , it follows that the two opposite angles of an inscribed quadrilateral , together , must be measured ...
... inscribed in a circle , is equal to two right angles ; for , as each inscribed angle is measured by half the arc on which it stands , it follows that the two opposite angles of an inscribed quadrilateral , together , must be measured ...
Página 83
... inscribed in a circle , be produced to F , the out- ward angle DAF will be equal to the inward and opposite angle C. F For , the sum of the two adja- cent angles DAF and DAB is equal to two right angles ( B. I , Prop . 1 ) , and the sum ...
... inscribed in a circle , be produced to F , the out- ward angle DAF will be equal to the inward and opposite angle C. F For , the sum of the two adja- cent angles DAF and DAB is equal to two right angles ( B. I , Prop . 1 ) , and the sum ...
Página 88
... inscribed in the segment AHB , is equal to the angle BGC , the half of BGA ; but the angle BGC is equal to the alternate angle FBG ( B. I , Prop . XVII ) , which was made equal to the given angle K ; there- fore the angle AHB , in the ...
... inscribed in the segment AHB , is equal to the angle BGC , the half of BGA ; but the angle BGC is equal to the alternate angle FBG ( B. I , Prop . XVII ) , which was made equal to the given angle K ; there- fore the angle AHB , in the ...
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Términos y frases comunes
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
Pasajes populares
Página 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.
Página 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.
Página 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.
Página 224 - The radius of a sphere is a straight line, drawn from the centre to any point of the...
Página 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.
Página 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.
Página 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.
Página 226 - We conclude then, that the solidity of a cylinder is equal to the product of its base by its altitude.
Página 22 - If two sides and the included angle of the one are respectively equal to two sides and the included angle of the other...
Página 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.