...is to the first, as the excess of the third above the fourth to the fourth. 70. If four quantities be proportionals, the sum of the first and second...their difference, as the sum of the third and fourth to their difference. Let a : b :: c : d, then will a+b : a—b : : c+d : c—d; for u + li c 4 </ a...

...inversely, a : a—b :: c : c — d., (182.) When four quantities are proportionals, the sum of the Jirst and second is to their difference, as the sum of the third and fourth, to their difference. Let a : b :: c : d ; then, ' + b : ab :: c + d: «— d. G Ey ac , If possible,...

..., that is, ab : a :: cd : c; and inversely, a : ab :: с : c — d. (182.) When four quantities are proportionals, the sum of the first and second is...their difference, as the sum of the third and fourth, to their difference. Let a : b :: с : d; then, a + b : a — b :: c + d : c—d. By Art. 179, °—...

...— d, and, therefore, by again alternating, a: a — b::c:c — rf. 116. When four quantities are proportionals, the sum of the first and second is...their difference, as the sum of the third and fourth to their difference. This readily appears from Nos. 114 and 115. For, (No. 114.) a+b:b::c+d : d, therefore,...

...а с ас a^-bc^-d For T=-d-'- b^=^1' or —=Т' Or, a*rb : b : : c~rd : d. 64. If four quantities be proportionals, the sum of the first and second is to their difterence,.as the sum of the third and fourth is to their difference. * The terms are similarly designated...

...other fraction equal to j whose terms are not equimultiples of a and b. 232. When four quantities are proportionals, the sum of the first and second is...their difference as the sum of the third and fourth to their difference. 234. Express a + b . Jl]. and log, (a + 6 v'~) in the c + « v __ l form A -|-...

...to its excess above the second, as the third is to its excess above the fourth. 27- By mixing, when the sum of the first and second, is to their difference, as the sum of the third and fourth to their difference. 28. By equality, when there is any number of magnitudes more than two, and as...

...is to the secoml, as the excess of the third above the fourth to the fourth ; (332.) By mixing, when the sum of the first and second is to their difference, as the sum of the third and fourth to their difference ; (333.) By direct equality, when there are several analogies, and two homologous...

....-. inversely a : a±» :: c : c±d. TH. 8. " If four quantities be proportional, then the sum of Ihe first and second is to their difference as the sum of the third arid fourth is to their difference." For by TH. 6, — =— = — 5- , and od a — bc — d . , ,...

...similar triangles it may be proved that of any three of the consecutive circles, the sum of the radii of the first and second, is to their difference, as the sum of the radii of the second and third, is to their difference. HINTS, &c. TO THE THEOREMS. BOOK VI. 3. THIS...