Elements of Geometry and Conic SectionsHarper, 1849 - 226 páginas |
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Página 44
... radii of a circle are equal ; all the diameters are equal also , and each double of the radius . 3. An arc of a circle is any part of the circumference . The chord of an arc is the straight line which joins its two extremities . 4. A ...
... radii of a circle are equal ; all the diameters are equal also , and each double of the radius . 3. An arc of a circle is any part of the circumference . The chord of an arc is the straight line which joins its two extremities . 4. A ...
Página 46
... radii CD , GH are drawn , the two triangles ACD , EGH will have their three sides equal , each to each , viz .: AC to EG , CD to GH , and AD equal to EH ; the tri- angles are consequently equal ( Prop . XV . , B. I. ) , and the an- gle ...
... radii CD , GH are drawn , the two triangles ACD , EGH will have their three sides equal , each to each , viz .: AC to EG , CD to GH , and AD equal to EH ; the tri- angles are consequently equal ( Prop . XV . , B. I. ) , and the an- gle ...
Página 47
... radii CA , CD , CE . Now , if the arc AE were equal to the arc AD , the angle ACE would be equal to the an- gle ACD ( Prop . IV . ) ; hence it is clear that if the arc AE be greater than the arc AD , the angle ACE must be greater than ...
... radii CA , CD , CE . Now , if the arc AE were equal to the arc AD , the angle ACE would be equal to the an- gle ACD ( Prop . IV . ) ; hence it is clear that if the arc AE be greater than the arc AD , the angle ACE must be greater than ...
Página 48
... radii CA , CB . The two right- angled triangles CDA , CDB have the side AC equal to CB , and CD common ; there- A fore the triangles are equal , and the base AD is equal to the base DB ( Prop . XIX . , B. I. ) . E B D Secondly , since ...
... radii CA , CB . The two right- angled triangles CDA , CDB have the side AC equal to CB , and CD common ; there- A fore the triangles are equal , and the base AD is equal to the base DB ( Prop . XIX . , B. I. ) . E B D Secondly , since ...
Página 52
... radii . It is plain that the centers of the circles and the point of F B A -D G E -D F G B contact are in the same straight line ; for , if possible , let the point of contact , A , be without the straight line CD . From A let fall upon ...
... radii . It is plain that the centers of the circles and the point of F B A -D G E -D F G B contact are in the same straight line ; for , if possible , let the point of contact , A , be without the straight line CD . From A let fall upon ...
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ELEMENTS OF GEOMETRY & CONIC S Elias 1811-1889 Loomis,Making of America Project Sin vista previa disponible - 2016 |
Términos y frases comunes
75 cents ABCD AC is equal allel altitude angle ABC angle ACB angle BAC Anthon's base BCDEF bisected chord circle circumference cone contained convex surface curve described diameter dicular draw drawn ellipse equal angles equal to AC equally distant equiangular equivalent exterior angle foci four right angles frustum greater Hence Prop hyperbola inscribed intersection join latus rectum Let ABC lines AC major axis mean proportional measured by half meet Muslin number of sides ordinate parabola parallelogram parallelopiped pendicular perimeter perpen perpendicular plane MN principal vertex prism PROPOSITION pyramid radii radius ratio rectangle regular polygon right angles Prop Scholium segment Sheep extra side AC similar slant height solid angle sphere spherical triangle square subtangent tangent THEOREM triangle ABC vertex vertices
Pasajes populares
Página 60 - Any two rectangles are to each other as the products of their bases by their altitudes.
Página 27 - VIf two triangles have two angles and the included side of the one, equal to two angles and the included side of the other, each to each, the...
Página 11 - A rhombus, is that which has all its sides equal, but its angles are not right angles.
Página 63 - IF a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the' rectangle contained by the parts.
Página 18 - BC common to the two triangles, which is adjacent to their equal angles ; therefore their other sides shall be equal, each to each, and the third angle of the one to the third angle of the other, (26.
Página 10 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.
Página 15 - If, at a point in a straight line, two other straight lines, upon the opposite sides of it, make the adjacent angles together equal to two right angles, these two straight lines shall be in one and the same straight line.
Página 17 - 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.
Página 148 - I.), that every section of a sphere made by a plane is a circle.