## Euclidian Geometry |

### From inside the book

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Page 160

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**similar**manner it may be proved that straight lines have to one another the same ratio as s or △ s of equal altitude described upon them . DEFINITION . Magnitudes which have the same ratio are called 160 PROPORTION . Page 164

... = or < b . PROPOSITION IX . If a : b as c : d , then a is > = or < c , according as b is > = or < d . This follows in a

... = or < b . PROPOSITION IX . If a : b as c : d , then a is > = or < c , according as b is > = or < d . This follows in a

**similar**manner to the preceding demonstration . PROPOSITION X. If a b as c : d , 1644 PROPORTION . Page 176

... the secant XPQ becomes a tan- gent , and rectangle XP , XQ becomes the square on XQ ; ... rectangle XR , XS = square on XQ . DEFINITION .

... the secant XPQ becomes a tan- gent , and rectangle XP , XQ becomes the square on XQ ; ... rectangle XR , XS = square on XQ . DEFINITION .

**Similar**rectilineal figures are those which have their 176. COMPARISON OF STRAIGHT LINES . Page 181

Francis Cuthbertson (M.A.). COMPARISON OF AREAS OF

Francis Cuthbertson (M.A.). COMPARISON OF AREAS OF

**SIMILAR**RECTILINEAL FIGURES . PROPOSITION VII .**Similar**triangles are to one another as the squares on their corresponding sides . K A H B IX E Let ABC , AHK be**similar**as ; Then △ ABC ... Page 186

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**similar**to another given rectilineal figure . M N P R T Let it be required to describe a rectilineal figure**similar**to ABCFG and equal to H. Describe squares MS , PK ...**Similar**polygons inscribed in circles are to 186**SIMILAR**figures .### 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