## Euclidian Geometry |

### From inside the book

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Page 14

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

... Thus 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

... space , which is impossible . .. AR is not 1 to BC .

... space , which is impossible . .. AR is not 1 to BC .

**Similarly**it may be proved that no other straight line besides AQ , drawn from A to BC , is 1 to it . INEQUALITIES . PROPOSITION XIII . If a side of a RIGHT ANGLES . 21. Page 22

... ; LACD is the EAB ; i.e. △ CAB .

... ; LACD is the EAB ; i.e. △ CAB .

**Similarly**it may be shewn , if AC be produced to G ; that BCG is > the ABC . But ACD is = L BCG ; ( 1. 6 ) ☀ . △ ACD 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 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

Algebra base Cambridge centre chord circumference cloth Conic Sections Crown 8vo Describe a circle diagonals diameter divided draw a straight ELEMENTARY TREATISE English equiangular equilateral Euclid Examples Extra fcap fcap GEOMETRY given angle given circle given point given straight line Grammar greater H Let Hence inscribed intersecting isosceles triangle Latin Let ABC line bisecting locus Mathematical meet opposite angles Owens College parallel parallelogram perimeter perpendicular plane polygon PROBLEM produced Professor proportional PROPOSITION ratio rect rectangle rectangle contained rectilineal figure regular polygon respectively revised rhombus right angles Schools Second Edition segment similar Similarly squares on AC straight line drawn straight line joining tangent THEOREM TRIGONOMETRY twice rectangle twice the squares vertex