...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;...

...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...

...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, and as the first term is to the third, or as the second is to the fourth. Likewise, the sum of the first two terms is to their difference, 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...

...of the last two, or as the first term is to the third, or as the second is to the fourth. Likewise, the sum of the first two terms is to their difference, as the sum of the last two is to their difference. Moreover, in finding these sums and differences, both the antecedents may be...

...of the last two, or as the first term is to the third, or as the second is to the fourth. Likewise, the sum of the first two terms is to their difference, as the sum of the last two is to their difference. Moreover, in finding these sums and differences, both the antecedents may be...

...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,...sum of the last two terms is to their difference. Remark. It is manifest that the last two proportions might be written thus : a-\-b :c-\-d=a — b:c...

...c; changing the means, b-\-a:b — a = d-\-c:d — c. From the last two proportions, we infer, that, In any proportion, the sum of the first two terms is to the sum of the last two, as the difference of the first two terms is to the difference of the last...

...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,...

...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 :...