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 páginas |
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Página 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 . Wherefore , 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 . Wherefore , from the given point A , a straight line AL has been drawn ...
Página 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 ...
Página 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 ...
... 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 ...
Página 26
... wherefore E F B the angle FDC is likewise greater than BCD ; much more then is the angle BDC greater than the angle BCD . Again , because CB is equal to DB , the angle BDC is equal ( 5. 1. ) to the angle BCD ; but BDC has been proved to ...
... wherefore E F B the angle FDC is likewise greater than BCD ; much more then is the angle BDC greater than the angle BCD . Again , because CB is equal to DB , the angle BDC is equal ( 5. 1. ) to the angle BCD ; but BDC has been proved to ...
Página 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 ...
... 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 ...
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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