## Euclidian Geometry |

### From inside the book

Results 1-5 of 19

Page 161

...

...

**proportional**then any others which have the same ratio as the first and second are**proportional**to any others which have the same ratio as the third and fourth . For the test expressed by the definition is satisfied . PROPOSITION IV ... Page 162

...

...

**proportional**. Then rect . ( a , d ) is = rect . ( b , c ) . On a , b construct rectangles , the altitude of each being equal to c , and on c , d construct rectangles , the altitude of each being equal to a . By hypothesis a : b as c ... Page 163

...

...

**proportional**. Hence , if three straight lines are**proportional**the rect- angle contained by the extremes is equal to the square on the mean : and conversely . Hence may be easily established the following Pro- positions : II - 2 ... Page 164

...

...

**proportional**, then a cas b : d . For a bas c : d ; ... rect . ( a , d ) = rect . ( b , c ) ; a : cas b : d . PROPOSITION VII . If a bas c : d , then ba as d : c . For rect . ( a , d ) = rect . ( b , c ) , and .. b : a as d : c ... Page 167

...

...

**proportional**to certain straight lines and angles to certain arcs . Moreover PROPOSITION XIII . If A , B , H be areas and c , d , k straight lines , such that A B as cd , and B : H as d : k , then A : Has c : k . For , if be any ...### 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