then
a + b + c = m(a′ + b′ + c′).
Prop. 2. If
| a = mb, and c = md, e = nb, and f = nd, |
then a + e is the same multiple of b as c + f is of d, viz.:—
a + e = (m + n)b, and c + f = (m + n)d.
Prop. 3. If a = mb, c = md, then is na the same multiple of b that nc is of d, viz. na = nmb, nc = nmd.
Prop. 4. If
a : b :: c : d,
then