...we make m = 1, we have simply 6 -f- a: b — a : : d + c : d — c, which may be enunciated thus ; The sum of the first two terms is to their difference...as the sum of the last two is to their difference. 225. The proportion a : b : : c : d may be written thus ; a : c : : b : d; we have then < c _, d ....

...whence making ro= 1, we have b-\- a:b — a:;d + c:d — c a proportion which may be enunciated thus The sum of the first two terms is to their difference,...as the sum of the last two is to their difference. 180. The proportion n : l::c : d may be written thus, a : c::b : d, we have then e , d_ from which...

...we make m •=. I, we have simply b + a ib — ai id -\- c id — c, which may be enunciated thus ; The sum of the first two terms is to their difference as the sum of th» last two is to their difference. 225. The proportion aib ncid may be written thus ; aici ib id;...

...of the last two, as the difference of the first two terms is to the difference of the last two, and as the first term is to the third, or as the second...as the sum of the last two is to their difference. Two proportions, as A :B = CD and E : F = G '. Hy may evidently be multiplied together term by term,...

...andthe difference of the first two terms is to the difference of the last two in the same ratio ; also the sum of the first two terms is to their difference...as the sum of the last two is to their difference. Proof. The proportion A: B= C :D gives, by transposing the means, A : C = JB : D ; from which we obtain,...

...the last two, as the difference of the first two terms is to thf. difference of the last two ; also, the sum of the first two terms is to their difference, as the sum of the last two terms is to their difference. Remark. It is manifest that the last two proportions might be written...

...: C — D = mA — nB:mC — nD and A + B : A — B = C+ D : C— D mA-\-nB:mA — nB = mC + nD:mC that is, the sum of the first two terms of a proportion...both the consequents may be multiplied by any number. 98. Two proportions, as A: B = C : D and Ratio of Reciprocals. may evidently be multiplied together,...

...b : b — a : : d : d — c, &c. 7. Adding and subtracting, a-\-b:a — b::c-\-d:c — d. That is, the sum of the first two terms, is to their difference, as the sum of the last two, to their difference. Cor. If any compound quantities, arranged as in the preceding examples, are proportional,...

...whence making m = 1, we have b-\-a:b — a::d-\-c:d — c, a proportion which may be enunciated thus, The sum of the first two terms is to their difference, as the sum of the last turn is to their difference. 165. The proportion a : b : : c : d may be written thus, a : c : : b :...

...the difference of the first two terms is to the difference of the last two in the same ratio ; also the sum of the first two terms is to their difference as the sum of the last lilo is to their difference. Proof. The proportion A:B= C : D gives, by transposing the means, A :...