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 TrigonometryE. Duyckinck, and George Long, 1824 - 333 σελίδες |
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Σελίδα 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 . 1. THEOR . One part of a straight line cannot be in a plane and another part it . about If it be possible ...
... 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 . 1. THEOR . One part of a straight line cannot be in a plane and another part it . about If it be possible ...
Σελίδα 192
... solid angle be contained by three plane angles , any two of these , angles are greater than the third . 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 . D If the ...
... solid angle be contained by three plane angles , any two of these , angles are greater than the third . 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 . D If the ...
Σελίδα 193
... solid angle at B is contained by three plane angles CBA , ABF , FBC , of which any two are greater ( 20. 2. Sup . ) than the third , the angles CBA , ABF are great- er than the angle FBC : For the same reason , the two plane angles at ...
... solid angle at B is contained by three plane angles CBA , ABF , FBC , of which any two are greater ( 20. 2. Sup . ) than the third , the angles CBA , ABF are great- er than the angle FBC : For the same reason , the two plane angles at ...
Σελίδα 194
... solid angle , any two are great- er than the third , S7 ; and therefore X4R ; that is , the sum of the plane angles which contain the solid angle at A is less than four right angles . Q , E. D. SCHOLIUM . It is evident , that when any ...
... solid angle , any two are great- er than the third , S7 ; and therefore X4R ; that is , the sum of the plane angles which contain the solid angle at A is less than four right angles . Q , E. D. SCHOLIUM . It is evident , that when any ...
Σελίδα 196
... solid figure described 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 triangle revolves ...
... solid figure described 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 triangle 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 multiple opposite angle parallel parallelepipeds parallelogram perpendicular polygon prism PROB produced proportionals 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 parallelepipeds spherical angle spherical triangle straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore