Euclidian Geometry |
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Page 72
... twice the squares on half the line and on the line between the points of section . - Let AH be divided into two ... the square on AC . = ( I. 35 ) Join FH ; draw DK || to CF ; KG || to AH ; join AK . Then it may be easily shewn ...
... twice the squares on half the line and on the line between the points of section . - Let AH be divided into two ... the square on AC . = ( I. 35 ) Join FH ; draw DK || to CF ; KG || to AH ; join AK . Then it may be easily shewn ...
Page 73
... squares on half the base and on the line joining the vertex and the middle point of the base . K D H From the vertex K of △ AKH draw KD 1 to AH . Bisect AH in C , and join CK . Then shall the squares on AK , KH = twice ... the square on ...
... squares on half the base and on the line joining the vertex and the middle point of the base . K D H From the vertex K of △ AKH draw KD 1 to AH . Bisect AH in C , and join CK . Then shall the squares on AK , KH = twice ... the square on ...
Page 84
... the square on.S is > the squares on A and B by 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 ...
... the square on.S is > the squares on A and B by 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 ...
Page 85
... square on D + twice rectangle A , B squares on A , B. COR . It follows from the proposition that squares on S , D + twice rectangle A , B = = twice squares on A , B + twice rectangle A , B ; ... squares on S , D = twice squares on A , B.
... square on D + twice rectangle A , B squares on A , B. COR . It follows from the proposition that squares on S , D + twice rectangle A , B = = twice squares on A , B + twice rectangle A , B ; ... squares on S , D = twice squares on A , B.
Page 86
... the square on the side opposite the obtuse angle is greater than the squares on the sides contain- ing it by twice ... 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 ...
... the square on the side opposite the obtuse angle is greater than the squares on the sides contain- ing it by twice ... 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 ...
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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...
Page 15 - ... and the principles on which the observations made with these instruments are treated for deduction of the distances and weights of the bo.iits of the Solar System, and of a few stars, omitting all minutiit of Elementary Class- Books — continued. formulcE, and all troublesome details of calculation.