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 TrigonometryB. & S. Collins; W. E. Dean, printer, 1836 - 311 páginas |
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Página 73
... similar ( 12 . def . 3. ) to the segment EDF ; and they are upon equal straight lines BC , EF ; but similar segments of circles upon equal straight lines are equal ( 24. 3. ) to one another , therefore the segment BAC is equal to the ...
... similar ( 12 . def . 3. ) to the segment EDF ; and they are upon equal straight lines BC , EF ; but similar segments of circles upon equal straight lines are equal ( 24. 3. ) to one another , therefore the segment BAC is equal to the ...
Página 114
... similar . For , let A = mC , and B = nC ; A + B = ( m + n ) C , and A - B = ( m - n ) C . COR . If C measure B , and also A - B , or A + B , it must measure A , for the sum of B and A - B is A , and the difference of B and A + B is also ...
... similar . For , let A = mC , and B = nC ; A + B = ( m + n ) C , and A - B = ( m - n ) C . COR . If C measure B , and also A - B , or A + B , it must measure A , for the sum of B and A - B is A , and the difference of B and A + B is also ...
Página 115
... SIMILAR rectilineal figures are those which have their several angles equal , each to each , and the sides about the equal angles proportionals . In two similar figures , the sides which lie adjacent to equal angles , are called ...
... SIMILAR rectilineal figures are those which have their several angles equal , each to each , and the sides about the equal angles proportionals . In two similar figures , the sides which lie adjacent to equal angles , are called ...
Página 123
... similar ( def . 1. 6. ) . In like manner , it may be demonstrated , that the triangle ADC is equiangular and similar to the triangle ABC : and the triangles ABD , ADC , being each equi- angular and similar to ABC , and equiangular and ...
... similar ( def . 1. 6. ) . In like manner , it may be demonstrated , that the triangle ADC is equiangular and similar to the triangle ABC : and the triangles ABD , ADC , being each equi- angular and similar to ABC , and equiangular and ...
Página 128
... similar , and similarly situated to a given rectilineal figure . Let AB be the given straight line , and CDEF the given rectilineal figure of four sides ; it is required upon the given straight line AB to describe a rectilineal figure ...
... similar , and similarly situated to a given rectilineal figure . Let AB be the given straight line , and CDEF the given rectilineal figure of four sides ; it is required upon the given straight line AB to describe a rectilineal figure ...
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ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC angles equal base BC bisected centre chord circle ABC circumference cosine cylinder demonstrated diameter divided equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater Hence hypotenuse inscribed join less Let ABC Let the straight magnitudes meet multiple opposite angle parallel parallelogram parallelopiped perpendicular polygon prism PROP proposition quadrilateral radius ratio rectangle contained rectilineal figure remaining angle right angled triangle SCHOLIUM segment semicircle shewn side BC sine solid angle solid parallelopiped spherical angle spherical triangle square straight line BC THEOR third touches the circle triangle ABC triangle DEF wherefore