The Doctrine of Proportion Clearly Developed: On a Comprehensive, Original, and Very Easy System; Or, The Fifth Book of Euclid SimplifiedJ. Williams, 1841 - 98 sider |
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Resultat 1-5 av 10
Side x
... incommensurable , seems well known to Mr. Leslie ; but that those magnitudes should also be homogeneous is altogether neglected by the learned professor . Mr. Keith , desirous of applying a new demonstra- tion to Proposition XVIII , in ...
... incommensurable , seems well known to Mr. Leslie ; but that those magnitudes should also be homogeneous is altogether neglected by the learned professor . Mr. Keith , desirous of applying a new demonstra- tion to Proposition XVIII , in ...
Side xii
... incommensurable . " When this simple fact is known , what is to be understood by the term cannot be misconstrued , although we do allow that in many cases the exact ratio of one magnitude to another of the same kind cannot be expressed ...
... incommensurable . " When this simple fact is known , what is to be understood by the term cannot be misconstrued , although we do allow that in many cases the exact ratio of one magnitude to another of the same kind cannot be expressed ...
Side xiv
... incommensurable or not , we must question the whole of our beautiful system of analysis , which is just as certain in its results as plane geometry , and much more extensive in its application . Nor do we defend the system of showing ...
... incommensurable or not , we must question the whole of our beautiful system of analysis , which is just as certain in its results as plane geometry , and much more extensive in its application . Nor do we defend the system of showing ...
Side 70
... incommensurable or not . This may be shown as follows : - : - Let m be contained in A more than p times , and less than p + 1 times ; therefore A is greater than pm , and less than ( p + 1 ) m ; and let m be con- tained in B , q times ...
... incommensurable or not . This may be shown as follows : - : - Let m be contained in A more than p times , and less than p + 1 times ; therefore A is greater than pm , and less than ( p + 1 ) m ; and let m be con- tained in B , q times ...
Side 84
... ~ B :: C + D : C ~ D ; n A or , if p B n C p D m q m Չ we may infer A2 : B2 :: C2 : D2 ; or any other property respecting four proportionals . SUPPLEMENT I. ON COMMENSURABLE AND INCOMMENSURABLE MAGNITUDES . MAGNITUDES which 84.
... ~ B :: C + D : C ~ D ; n A or , if p B n C p D m q m Չ we may infer A2 : B2 :: C2 : D2 ; or any other property respecting four proportionals . SUPPLEMENT I. ON COMMENSURABLE AND INCOMMENSURABLE MAGNITUDES . MAGNITUDES which 84.
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The Doctrine of Proportion Clearly Developed: On a Comprehensive, Original ... Oliver Byrne Uten tilgangsbegrensning - 1841 |
The Doctrine of Proportion Clearly Developed: On a Comprehensive, Original ... Oliver Byrne Uten tilgangsbegrensning - 1841 |
The Doctrine of Proportion Clearly Developed: On a Comprehensive, Original ... Oliver Byrne Ingen forhåndsvisning tilgjengelig - 2014 |
Vanlige uttrykk og setninger
2nd edition 6d Reports Algebraical Exposition antecedent ar³ Arches Architect Arithmetical Illustration BILL OF QUANTITIES Birmingham Birmingham Railway 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 engraved equal equimultiples ex æquali ex f expressed by numbers fifth definition folio four magnitudes four proportionals fraction Fx G geometrical proportion geometry gonal greater ratio half-bound incommensurable india paper infer inversely Keith's Thos last remainder Let A B C D London London Bridge magnitude taken magnitudes are proportionals Mechanics Nicholson's North Midland Railway North Shields number of magnitudes plates Practical Treatise prime PROP quantities Railway Bill ratio compounded remaining ratio second and fourth seventh definition SIR JOHN RENNIE sixth Spilsby Steam Steam-Engine term ratio THEO three magnitudes tion tiple Wilson Lowry ㅁㅁ
Populære avsnitt
Side 10 - The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any...
Side 2 - 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.
Side 58 - 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
Side 62 - 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,
Side 18 - 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...
Side 32 - 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.
Side 21 - 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...
Side 55 - 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...
Side 14 - 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.
Side 73 - L : and the same thing is to be understood when it is more briefly expressed, by saying A has to D the ratio compounded of the ratios of E to F, G to H, and K to L. In like manner, the same things being supposed, if M has to N the same ratio which A has to D ; then, for shortness...