The Doctrine of Proportion Clearly Developed: On a Comprehensive, Original, and Very Easy System; Or, The Fifth Book of Euclid Simplified |
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The Doctrine of Proportion Clearly Developed: On a Comprehensive, Original ... Oliver Byrne No preview available - 2014 |
Common terms and phrases
2nd edition 6d Reports Algebraical Exposition antecedent ar² ar³ Arches Architect Arithmetical Illustration Birmingham Birmingham Railway Bloomsbury Bridge CIVIL ENGINEERS cloth bds common measure Complete Measurer compounded of ratios consequent contains continued proportionals course of mathematics cross order CX DX demonstrations ditto DOCTRINE OF PROPORTION dx ex f engraved equal equimultiples ex æquali ex fx g expressed by numbers fifth definition folio four magnitudes four proportionals fraction gonal greater ratio half-bound incommensurable india paper infer inversely Keith's Thos last remainder Let a b c d Library of Arts London London Bridge magnitude taken Mechanics Nicholson's North Midland Railway North Shields number of magnitudes plates Practical Treatise prime PROP quantities Railway Bill ratio compounded ratio of F remaining ratio Russell Street second and fourth seventh definition SIR JOHN RENNIE sixth Spilsby Steam Steam-Engine term ratio THEO three magnitudes tion tiple Wilson Lowry
Popular passages
Page 12 - The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any...
Page 4 - Ratio is the relation which one quantity bears to another of the same kind, the comparison being made by considering what multiple, part, or parts, one quantity is of the other.
Page 62 - IF there be any number of magnitudes, and as many others, which, taken two and two, in a cross order, have the same ratio; the first shall have to the last of the first magnitudes the same ratio which the first of the others has to the last. NB This is usually cited by the words
Page 66 - If there be any number of magnitudes, and as many others, which, taken two and two in order, have the same ratio ; the first shall have to the last of the first magnitudes, the same ratio which the first of the others has to the last. NB This is usually cited by the words "ex sequali,
Page 20 - IF the first be the same multiple of the second, or the same part of it, that the third is of the fourth ; the first is to the second, as the third is to the fourth...
Page 23 - IF the first be to the second as the third to the fourth, and if the first be a multiple, or part of the second; the third is the same multiple, or the same part of the fourth...
Page 34 - THAT magnitude which has a greater ratio than another has to the same magnitude, is the greater of the two : and that magnitude, to which the same has a greater ratio than it has to another magnitude, is the less of the two.
Page 59 - IF there be three magnitudes, and other three, which, taken two and two, have the same ratio ; if the first be greater than the third, the fourth shall be greater than the sixth ; and if equal, equal ; and if less, less...
Page 60 - ... If there be three magnitudes, and other three, which have the same ratio taken two and two, but in a cross order; then if the first magnitude be greater than the third, the fourth shall be greater than the sixth: and if equal, equal; and if less, less.
Page 16 - IF one magnitude be the same multiple of another, which a magnitude taken from the first is of a magnitude taken from the other ; the remainder shall be the same multiple of the remainder, that the whole is of the whole.