## Euclidian Geometry |

### From inside the book

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Page 14

... the arms of A would fall along the former positions of the arms of B ; .. the angles A , B are equal to one another . "

... the arms of A would fall along the former positions of the arms of B ; .. the angles A , B are equal to one another . "

**Similarly**the angles H , K may be proved equal . COR . If DEF be any angle , the adjacent ( 14 ) Page 21

... would inclose a space , which is impossible . AR is not to BC .

... would inclose a space , which is impossible . AR is not to BC .

**Similarly**it may be proved that no other straight line besides AQ , drawn from A to BC , is to it . INEQUALITIES . PROPOSITION XIII . If a side of a RIGHT ANGLES . 21. Page 22

... LACD is > the EAB ; i.e. △ CAB . ( 1. 6 ) ( I. I )

... LACD is > the EAB ; i.e. △ CAB . ( 1. 6 ) ( I. I )

**Similarly**it may be shewn , if AC be produced to G , that BCG is the ABC . But ACD is = LBCG ; ( 1. 6 ) LACD is the ABC . Hence it follows that Any two angles of a triangle ( 22 ) Page 35

...

...

**Similarly**all points in BC are equidistant from RS . Again , if any line be drawn through A other than RAS , and points taken along that part of it which is on the R S Q B σ same side of RAS as BC is , farther and farther from A , their ... Page 36

... ( I. 13 ) .. PQ , RS do not meet when produced towards Q , S.

... ( I. 13 ) .. PQ , RS do not meet when produced towards Q , S.

**Similarly**it may be proved that they will not meet if produced towards P , R. ... they are parallel . Hence are easily deduced the following Theorems : If a 36 · PARALLELS :### Other editions - View all

### Common terms and phrases

applied base bisect Cambridge centre chapter chord circle circumference cloth College common complete contained Crown 8vo DEFINITION describe diameter difference divided double draw drawn Edition elementary English equal equiangular Examination Examples extremities fall fcap figure Find former four GEOMETRY given point given straight line Grammar greater Hence illustrations impossible inscribed introduction Join language Latin less magnitudes Master Mathematical meet method Notes opposite parallel parallelogram pass perpendicular plane polygon possible present principles PROBLEM produced Professor proportional PROPOSITION prove ratio reader rect rectangle rectilineal respectively revised right angles Schools Second Edition segment selected sides similar Similarly square taken tangent THEOREM third touch TREATISE triangle twice University volume whole