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A Description of the Admirable Table of Logarithms

(Page 7)

 

CHAP. II.
Of the Propositions of Logarithmes.

 

Proposition 1.

The Logarithmes of Proportionall numbers and quantities are equally differing.
 

 

As for example. The Logarithmes of the proportionall sines, namely cz which is to ez, as hz is to kz, are respectiuely the numbers defining AC, AE, AH, AK, (as is manifest by the 6 Definition.) Now AC, and AE differ by the difference CE, and AH and AK by the difference HK. But by the first definition and his Corolarie CE and HK, are equall: therefore the Logarithmes of the foresaid proportional sines are equally differing. And so in all proportionals.
For what affections and symtomes the Logarithmes haue gotten in their first beginning and generation, the same must they needes retaine and keepe afterwards.
But in their beginning and generation, they are indued with this affection, and this law is prescribed vnto them, that they bee equally differing, when their sines or quantities are proportionall (as it appeareth by the definition of a Logarithme, and of both motions, and shall hereafter more fully appeare in the making of the Logarithmes.) Therefore the Logarithmes of proportional quantities are equally differing.
 

Proposition 2.

Of the Logarithmes of three proportionals, the double of the second or meane, made lesse by the first, is equall to the third.
 

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