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And keeping the same order continually (according to
the former definition) the number of AG shall be the
Logarithme of the sine gz. AH the
Logarithme of the sine hz. AI the
Logarithme of the sine iz. AK the
Logarithme of the sine kz, and so forth
infinitely,
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| A consequent |
Therefore the Logarithme of the whole sine
1000000 is nothing, or 0; and consequently the Logarithms of numbers
greater then the whole sine, ar lesse then nothing.
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For seeing it is manifest by the definition, that
the sines decreasing from the whole sine, the Logarithmes
increase from nothing: therfore contrariwise the numbers which yet
we call Sines, increasing vnto the whole sine, that is to 10000000,
the Logarithmes must needs decrease to 0 or nothing: and by
consequent the Logarithmes of numbers increasing aboue the
whole sine 10000000, which we call Secants, or Tangents,
and no more sines, shall be lesse then nothing.
Therefore we call the Logarithmes of the
sines Abounding, because they are always greater then nothing, and
set this marke + before them, or else none. But the Logarithmes
which are lesse then nothing, we cal Defectiue, or wanting, setting
this marke - before them.
It was indeed left at libertie in the beginning,
to attribute nothing, or 0. to any sine or quantitie for his
Logarithme: but it was best to fit it to the whole sine, that the
Addition or Substraction of that Logarithme which is most frequent
in all Calculations, might neuer after be any troubel to vs.
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