Elements of Geometry and Conic SectionsHarper & Brothers, 1857 - 226 páginas |
Dentro del libro
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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 ACD ...
... 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 ACD ...
Página 47
... radii CA , CD , CE . Now , if the arc AE were equal to the arc AD , A 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 D E B AD , the angle ACE must be ...
... radii CA , CD , CE . Now , if the arc AE were equal to the arc AD , A 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 D E B AD , the angle ACE must be ...
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. ) . G ID B E Secondly ...
... 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. ) . G ID B E Secondly ...
Página 53
... radii CA , DA ; and when they touch internally , the dis- tance CD is equal to the difference of the radii CA , DA . Therefore , if two circumferences , & c . Schol . If two circumferences touch each other , externally or internally ...
... radii CA , DA ; and when they touch internally , the dis- tance CD is equal to the difference of the radii CA , DA . Therefore , if two circumferences , & c . Schol . If two circumferences touch each other , externally or internally ...
Términos y frases comunes
ABCD AC is equal allel altitude angle ABC angle ACB angle BAC base BCDEF bisected chord circle circumference cone 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 given angle greater Hence Prop hyperbola inscribed intersection join latus rectum less Let ABC lines AC major axis mean proportional measured by half meet 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 side BC similar similar triangles solid angle sphere spherical triangle square subtangent tangent THEOREM triangle ABC triangle DEF vertex vertices VIII
Pasajes populares
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 60 - Any two rectangles are to each other as the products of their bases by their altitudes.
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 101 - When you have proved that the three angles of every triangle are equal to two right angles...
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 37 - Proportional, when the ratio of the first to the second is equal to the ratio of the second to the third.
Página 32 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Página 15 - Wherefore, when a straight line, &c. QED PROP. XIV. THEOR. 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 30 - If a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles; and the three interior angles of every triangle are together equal to two right angles.