Proposition V.17 — If magnitudes composed be proportional, they will also be pr…

Proof

(a + b) : b = (c + d) : d

, then subtracting the consequents from the antecedents using V.5 / V.6 gives

a : b = c : d

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Depends on (3)

V.5Proposition V.5If a magnitude be the same multiple of a magnitude that a subtracted part is of a subtracted part, the remainder also…
V.6Proposition V.6If two magnitudes be equimultiples of two magnitudes, and any magnitudes subtracted from them be equimultiples of the…
V.5Definition V.5Magnitudes are said to be in the same ratio, the first to the second and the third to the fourth, when, if any…

Required by (dependents) (2)

V.18Proposition V.18If magnitudes separated be proportional, they will also be proportional componendo.
V.19Proposition V.19If, as a whole is to a whole, so is a part subtracted to a part subtracted, the remainder will also be to the remainder…

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