Euclidian Geometry |
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Page 49
... twice as many right 4s as the figure has sides ; but all the exteriors are = 4 rights ; .. all the interiors of the polygon together with four rights are = twice as many rights as the figures has sides . C. G. 4 PROBLEM H. To divide a ...
... twice as many right 4s as the figure has sides ; but all the exteriors are = 4 rights ; .. all the interiors of the polygon together with four rights are = twice as many rights as the figures has sides . C. G. 4 PROBLEM H. To divide a ...
Page 72
... 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 DK || to CF ; KG || to AH ; join AK . Then it may be easily ...
... 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 DK || to CF ; KG || to AH ; join AK . Then it may be easily ...
Page 73
... 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 ...
... 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 ...
Page 84
... twice the rect- angle A , B. Also , if A and B be unequal and D be their difference , the rectangle S , D is the difference between the squares on A , B ; and the square on D is < the squares on A and B by twice the rectangle A , B ...
... twice the rect- angle A , B. Also , if A and B be unequal and D be their difference , the rectangle S , D is the difference between the squares on A , B ; and the square on D is < the squares on A and B by twice the rectangle A , B ...
Page 85
... twice rectangle A , B = = twice squares on A , B + twice rectangle A , B ; ... squares on S , D = twice squares on A , B. Also that square on S = squares on A , B + twice rectangle A , B , and ... = square on D + four times rectangle A ...
... twice rectangle A , B = = twice squares on A , B + twice rectangle A , B ; ... squares on S , D = twice squares on A , B. Also that square on S = squares on A , B + twice rectangle A , B , and ... = square on D + four times rectangle A ...
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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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