Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle, and the Geometry of Solids ; to which are Added, Elements of Plane and Spherical TrigonometryW.E. Dean, 1839 - 318 páginas |
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Página 181
... solid angle is an angle made by the meeting of more than two plane angles , which are not in the same plane in one point . PROP . I. THEOR . One part of a straight line cannot be in a plane and another part about it . C If it be ...
... solid angle is an angle made by the meeting of more than two plane angles , which are not in the same plane in one point . PROP . I. THEOR . One part of a straight line cannot be in a plane and another part about it . C If it be ...
Página 192
... solid angle be contained by three plane angles , any two of these angles are greater than the third . D. Let the solid angle at A be contained by the three plane angles BAC , CAD , DAB . Any two of them are greater than the third . If the ...
... solid angle be contained by three plane angles , any two of these angles are greater than the third . D. Let the solid angle at A be contained by the three plane angles BAC , CAD , DAB . Any two of them are greater than the third . If the ...
Página 193
... angles DAB , DAC ; therefore BAC , with either of them , is greater than the other . Wherefore , if a solid angle , & c . Q. E. D. PROP . XXI . THEOR . The plane angles which contain any solid angle are together less than four right angles ...
... angles DAB , DAC ; therefore BAC , with either of them , is greater than the other . Wherefore , if a solid angle , & c . Q. E. D. PROP . XXI . THEOR . The plane angles which contain any solid angle are together less than four right angles ...
Página 194
... angles as there are sides of the same figure ; therefore S + X = x + 4R . But because of the three plane angles which contain a solid angle , any two are greater than the third , S > ; and therefore X4R ; that is , the sum of the plane ...
... angles as there are sides of the same figure ; therefore S + X = x + 4R . But because of the three plane angles which contain a solid angle , any two are greater than the third , S > ; and therefore X4R ; that is , the sum of the plane ...
Página 196
... solid figure deseribed by the revolution of a right angled triangle about one of the sides containing the right angle , which side remains fixed . XII . The axis of a cone is the fixed straight line about which the trian- gle revolves ...
... solid figure deseribed by the revolution of a right angled triangle about one of the sides containing the right angle , which side remains fixed . XII . The axis of a cone is the fixed straight line about which the trian- gle revolves ...
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ABC is equal ABCD altitude angle ABC angle ACB angle BAC angle EDF arch AC base BC bisected centre circle ABC circumference cosine cylinder demonstrated diameter draw equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater hypotenuse inscribed join less Let ABC Let the straight line BC magnitudes meet opposite angle parallel parallelogram parallelopipeds perpendicular polygon prism PROB produced proportional proposition Q. E. D. COR Q. E. D. PROP radius ratio rectangle contained rectilineal figure remaining angle segment semicircle shewn side BC sine solid angle solid parallelopipeds spherical angle spherical triangle square straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore