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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Side xvii
... four magnitudes were proportional or not ; and seldom con- ceives that the conditions of the definition require to be fulfilled with every set of equimultiples that might be selected . This test for proportionals has been regarded by ...
... four magnitudes were proportional or not ; and seldom con- ceives that the conditions of the definition require to be fulfilled with every set of equimultiples that might be selected . This test for proportionals has been regarded by ...
Side 1
... four times exactly ; the same may be said with respect to other numbers and magnitudes . II . A greater magnitude is said to be a multiple of a less , when the greater is measured by the less ; that is , when the greater contains the ...
... four times exactly ; the same may be said with respect to other numbers and magnitudes . II . A greater magnitude is said to be a multiple of a less , when the greater is measured by the less ; that is , when the greater contains the ...
Side 8
... four magnitudes be the same multiple of the second that the third is of the fourth , and if any equimultiples whatever of the first and third be taken , those shall be equimultiples ; one of the second , and the other of the fourth ...
... four magnitudes be the same multiple of the second that the third is of the fourth , and if any equimultiples whatever of the first and third be taken , those shall be equimultiples ; one of the second , and the other of the fourth ...
Side 9
... fourth , for 132 is 12 times 11 , and 96 is 12 times 8 . Algebraical Exposition . Let the four magnitudes be m a , a , m b , and b , take equimultiples of the first and third , as , n times the first , and n times the third ; then it is ...
... fourth , for 132 is 12 times 11 , and 96 is 12 times 8 . Algebraical Exposition . Let the four magnitudes be m a , a , m b , and b , take equimultiples of the first and third , as , n times the first , and n times the third ; then it is ...
Side 10
... four magnitudes , taken in the same manner . Euclid expresses this definition as follows : - The first of four magnitudes is said to have the same ratio to the second , which the third has to the fourth , when any equimul- tiples ...
... four magnitudes , taken in the same manner . Euclid expresses this definition as follows : - The first of four magnitudes is said to have the same ratio to the second , which the third has to the fourth , when any equimul- tiples ...
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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...