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 sider |
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Side 22
... wherefore CA , AB , CB are equal to one another ; and the triangle ABC is therefore equilateral , and it is described upon the given straight line AB . Which was required to be done . PROP . II . PROB . From a given point to draw a ...
... wherefore CA , AB , CB are equal to one another ; and the triangle ABC is therefore equilateral , and it is described upon the given straight line AB . Which was required to be done . PROP . II . PROB . From a given point to draw a ...
Side 23
... wherefore AL and BC are each of them equal to BG ; and things that are equal to the same are equal to one another ; therefore the straight line AL is equal to BC . Where- fore , from the given point A , a straight line AL has been drawn ...
... wherefore AL and BC are each of them equal to BG ; and things that are equal to the same are equal to one another ; therefore the straight line AL is equal to BC . Where- fore , from the given point A , a straight line AL has been drawn ...
Side 24
... wherefore also the point C shall coincide with the point F , because AC is equal to DF : But the point B coincides with the point E ; wherefore the base BC shall coincide with the base EF ( cor . def . 3. ) , and shall be equal to it ...
... wherefore also the point C shall coincide with the point F , because AC is equal to DF : But the point B coincides with the point E ; wherefore the base BC shall coincide with the base EF ( cor . def . 3. ) , and shall be equal to it ...
Side 25
... wherefore the triangles BFC , CGB are equal ( 3.1 . ) and their remaining angles are equal , to which the equal sides are opposite ; therefore the angle FBC is equal to the angle GCB , and the angle BCF to the angle CBG . Now , since it ...
... wherefore the triangles BFC , CGB are equal ( 3.1 . ) and their remaining angles are equal , to which the equal sides are opposite ; therefore the angle FBC is equal to the angle GCB , and the angle BCF to the angle CBG . Now , since it ...
Side 27
... wherefore likewise the angle BAC coincides with the angle EDF , and is equal ( 8. Ax . ) to it . Therefore if two triangles , & c . Q. E. D. • PROP . IX . PROB . To bisect a given rectilineal angle , that is to divide it into two equal ...
... wherefore likewise the angle BAC coincides with the angle EDF , and is equal ( 8. Ax . ) to it . Therefore if two triangles , & c . Q. E. D. • PROP . IX . PROB . To bisect a given rectilineal angle , that is to divide it into two equal ...
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Vanlige uttrykk og setninger
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