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Seeing that by the first propos. the difference of the
Logarithmes of the first and second, is equall to the
difference of the Logarithmes of the second and the third, that
is, the second made lesse by the first, is equall to the third, lesse
by the second: therefore the second being added to both sides of the
equation twice, the second, or the double of the second made lesse by
the first, shall come forth equall to the third, which was to bee
proued.
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Proposition 3. |
Of the Logarithmes of three proportionals, the
double of the second, or middle one, is equall to the summe of the
extremes.
By the second Proposition next going before, the
double of the second, made lesse by the first, is equall to the third.
To both the equall sides adde the first, and there shall arise the
double of the second equall to the first and the third, that is, the
summe of the extremes, which was to bee demonstrated.
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Proposition 4. |
Of the Logarithmes of foure proportionals, the
summe of the second and third, made lesse by the first, is equall to
the fourth.
Seeing by the first Proposition of the Logarithmes of 4
proportionals, the second made lesse by the first, is equall to the
fourth lesse by the third: adde the third to both sides of the
equality, and the second and third made lesse by the first, shall bee
made equall to the fourth, which was propounded.
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Proposition 5. |
Of the Logarithmes of foure proportionals, the
summe of the middle ones, that is, of the second and third, is equall
to the Logarithme of the extreames, that is to say, the first and
fourth.
By the 4 proposition going afore the 2 & third
made lesse by the first, were equall to the fourth: to both sides of
the equality adde the first, and the second more by the third shall
bee made equall to the fourth, more by the first, which was to be
demonstrated.
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