Euclidian Geometry |
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Page 72
... squares on AC , CD . = F G K H We shall first describe a square twice the squares on AC , CD . Draw CF and = AC ; join AF . Then ACF is a right - angled isosceles △ , and square on AF twice the square on AC . = ( I. 35 ) Join FH ; draw ...
... squares on AC , CD . = F G K H We shall first describe a square twice the squares on AC , CD . Draw CF and = AC ; join AF . Then ACF is a right - angled isosceles △ , and square on AF twice the square on AC . = ( I. 35 ) Join FH ; draw ...
Page 73
... squares on AK , KH = twice the squares on AC , CK . For the squares on AD , DH = twice the squares on AC , CD ; .. the squares on AD , DH and twice the square on DK = twice the square on AC and twice the squares on CD , DK ; i.e. the ...
... squares on AK , KH = twice the squares on AC , CK . For the squares on AD , DH = twice the squares on AC , CD ; .. the squares on AD , DH and twice the square on DK = twice the square on AC and twice the squares on CD , DK ; i.e. the ...
Page 81
... AC , CB describe squares XC , YC . Then ACE , BCD are straight lines equal and to one another . -- = Complete the ... squares on AC , CB + four as each equal to △ ABC square XY ; = .. square on AB squares on AC , CB . C. G. 6 BOOK ...
... AC , CB describe squares XC , YC . Then ACE , BCD are straight lines equal and to one another . -- = Complete the ... squares on AC , CB + four as each equal to △ ABC square XY ; = .. square on AB squares on AC , CB . C. G. 6 BOOK ...
Page 86
... AC produced . Then shall the square on AB be > the squares on AC , CB by twice the rectangle AC , CK . For AK is the sum of AC and CK ; ... square on AK is = squares on AC , CK .. squares on AK , KB are but squares on AK , + twice rectangle ...
... AC produced . Then shall the square on AB be > the squares on AC , CB by twice the rectangle AC , CK . For AK is the sum of AC and CK ; ... square on AK is = squares on AC , CK .. squares on AK , KB are but squares on AK , + twice rectangle ...
Page 87
... square on AB be < the squares on AC , CB by twice the rectangle AC , CK . For should the fall within or without the △ ABC , in either case AK is the difference between AC and CK . = .. square on AK + twice rectangle AC , CK is on AC , CK .
... square on AB be < the squares on AC , CB by twice the rectangle AC , CK . For should the fall within or without the △ ABC , in either case AK is the difference between AC and CK . = .. square on AK + twice rectangle AC , CK is on AC , CK .
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Common terms and phrases
Algebra Arithmetic base BEGINNERS Cambridge centre chord Christ's College circumference cloth Conic Sections Crown 8vo Describe a circle diagonals diameter divided ELEMENTARY TREATISE English equiangular equilateral Euclid Examples Extra fcap GEOMETRY given angle given circle given point given straight line Grammar greater H Let Hence inscribed intersecting isosceles triangle John's College Latin Let ABC line bisecting locus magnitudes Mathematical meet Owens College parallel parallelogram perimeter perpendicular plane PROBLEM produced Professor proportional PROPOSITION radius ratio rect rectangle rectangle contained rectilineal figure regular polygon render respectively revised rhombus right angles Schools Second Edition segment Similarly squares on AC straight line joining student tangent THEOREM TRIGONOMETRY twice rectangle twice the squares Uppingham School vertex
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Page 157 - The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever of the second and fourth ; if the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth...
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