Elements of Geometry; Containing the First Six Books of Euclid ...For Bell & Bradfute, 1814 - 461 Seiten |
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Seite 25
... 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 ...
Seite 26
... 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 a cor . def . 3. base EF , 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 a cor . def . 3. base EF , and shall be equal to it ...
Seite 28
... wherefore the triangles BFC , CGB are equal , and their remaining angles are equal , to which the equal sides are opposite ; therefore the an- gle FBC is equal to the angle GCB , and the angle BCF to the angle CBG . Now , since it has ...
... wherefore the triangles BFC , CGB are equal , and their remaining angles are equal , to which the equal sides are opposite ; therefore the an- gle FBC is equal to the angle GCB , and the angle BCF to the angle CBG . Now , since it has ...
Seite 29
... to one another , but the angle ECD is greater than the angle BCD ; wherefore the angle FDC is likewise greater than BCD ; much more then is the " Book Į . N. a 5. 1 , a Book I. angle BDC greater than the angle BCD OF GEOMETRY . 29.
... to one another , but the angle ECD is greater than the angle BCD ; wherefore the angle FDC is likewise greater than BCD ; much more then is the " Book Į . N. a 5. 1 , a Book I. angle BDC greater than the angle BCD OF GEOMETRY . 29.
Seite 31
... wherefore likewise the angle BAC coincides with the an- gle EDF , and is equal to it . Therefore if two trian- b 8. Az . gles , & c . Q. E. D. b PROP . IX . PROB . To bisect a given rectilineal angle , that is , to divide it into two ...
... wherefore likewise the angle BAC coincides with the an- gle EDF , and is equal to it . Therefore if two trian- b 8. Az . gles , & c . Q. E. D. b 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 arch AC base BC bisected Book centre circle ABC circumference cosine cylinder definition demonstrated described diameter draw drawn equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles GEOMETRY given straight line greater hypotenuse inscribed join less Let ABC Let the straight line BC magnitudes meet opposite angle parallel parallelogram perpendicular polygon prism PROB 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 parallelepipeds spherical angle spherical triangle SPHERICAL TRIGONOMETRY straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore