## Euclidian Geometry |

### From inside the book

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**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

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**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 : d ... Page 163

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**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

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**proportional**, then a cas b : d . For a bas c : d ; . : rect . ( a , d ) = rect . ( b , c ) ; ... a : c . as 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

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**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 c : d , and B : H as d : k , then A : H as c : k . For , if be any ...### 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 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 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