The Elements of Mathematical Analysis, Abridged: For the Use of Students. With Notes, Demonstrative and Explanatory, and a Synopsis of Book V. of Euclid

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Bell & Bradfute, J. Fairbairn, and Arch. Constable, Edinburgh; and F. Wingrave, London, 1798 - 170 Seiten
 

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Seite 8 - ... 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: or, if the multiple of the first be equal to that of the second, the multiple of the third is also equal to that of the fourth...
Seite 14 - IF any number of magnitudes be equimultiples of as many, each of each ; what multiple soever any one of them is of its part, the same multiple shall all the first magnitudes be of all the other.
Seite 9 - When of the equimultiples of four magnitudes (taken as in the fifth definition), the multiple of the first is greater than that of the second, but the multiple of the third is not greater than the multiple of the fourth ; then the first is said to have to the second a greater ratio than the third magnitude has to the fourth ; and, on the contrary, the third is said to have to the fourth a less ratio than the first has to the second. VIII. Analogy, or proportion, is the similitude of ratios.
Seite 19 - 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.
Seite 23 - If magnitudes, taken jointly, be proportionals, they shall also be proportionals when taken separately: that is, if two magnitudes together have to one of them, the same ratio which two others have to one of these, the remaining one of the first two shall have to the other the same ratio which the remaining one of the last two has to the other of these.
Seite 11 - When four magnitudes are continual proportionals, the first is said to have to the fourth the triplicate ratio of that which it has to the second, and so on, quadruplicate, &c., increasing the denomination still by unity, in any number of proportionals.
Seite 12 - 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...
Seite 20 - IF any number of magnitudes be proportionals, as one of the antecedents is to its consequent, so shall all the antecedents taken together be to all the consequents.

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