The Elements of Mathematical Analysis, Abridged: For the Use of Students. With Notes, Demonstrative and Explanatory, and a Synopsis of Book V. of Euclid
Bell & Bradfute, J. Fairbairn, and Arch. Constable, Edinburgh; and F. Wingrave, London, 1798 - 170 pages
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The Elements of Mathematical Analysis, Abridged. for the Use of Students ...
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Page 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...
Page 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.
Page 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.
Page 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.
Page 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.
Page 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...