...— c : c, or b : b—a: : d : d — c, &c. 7. Adding and subtracting, o+6: 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,...

...not be of the same kind as those in the other set. PROPOSITION XVIII.— THEOREM. In any proportion the sum of the first two terms is to their difference as the sum of the other two is to their difference. Let A : В . . С : D ; then A + В : АсяВ::С + О:С^ D. For...

...the last two, as the difference of the first two terms is to the 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. If we had taken proportion (2) in (x), we might have obtained from it 6 + а: d-\-c = b —...

...— 1> : : d : d — с, etc. 7. Adding and subtracting, a -\- b : a — b : : с -\- d : с — 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=l, we have b-\-a: b — a:: d-\- c: d — c, a proportion which may he enunciated thus, The sum of the first two terms is to their difference, as the sum of the last two is to their differencc. 165. The proportion a : b : : c : d may be written thus, a: c : : b : d, we...

...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...

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

...the last two, as the difference of the first two terms is to the 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. If we had taken proportion (2) in (x), we might have obtained from it b-\-a:d-\-c=.b — a:...

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

...the difference o> the first two terms is to the difference of the last two in th» same ratio ; also the sum of the first two terms is to their difference as the sum of the laft two is to their difference Proof. The proportion • A : C = B : D ; from which we obtain, by...