A Treatise On the Valuation of Life Contingencies Arranged for the Use of Students
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In our eReader you can find the full English version of the book. Read A Treatise On the Valuation of Life Contingencies Arranged for the Use of Students Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book A Treatise On the Valuation of Life Contingencies Arranged for the Use of Students
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Having found log P -log Q = log N, we enter the table with this as an argument, and opposite to it find log (1 + -^) or log (1 - -j^), according as we have to do with the sum or with the difference : this added to Log P gives log{P+ Q) or log{P- Q). Tables of this kind are to be found in several Logarithmic and Trigonometrical collections.
The ordinary trigonometrical tables can be made use of in this calcula- tion ; thus we have sec a^ = 1 + tan a? . If, then, we assume a such that tan a^ = -^... we shall obtain P+ Q = P .seca^. To apply this to our pre- sent problem we make the subtraction LogQ-LogP, and halving this difference we find «, such that Log tana = ^ {Log Q - Log P) , then taking out from the page which is already open, the arithmetical complement of log cos a, or log sec a if it be given, we have Log{P+Q) = Log P + 2 Log sec a .
Similarly 1 - sin a^ = cos a^, wherefore if we obtain an angle a such that log sin a = ^ {log Q - log P), we shall have Log {P - Q) = Log P + 2 log cos a, .
What to read after A Treatise On the Valuation of Life Contingencies Arranged for the Use of Students?
You can find similar books in the "Read Also" column, or choose other free books by Sang, Edward, 1805-1890 to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
Having found log P -log Q = log N, we enter the table with this as an argument, and opposite to it find log (1 + -^) or log (1 - -j^), according as we have to do with the sum or with the difference : this added to Log P gives log{P+ Q) or log{P- Q). Tables of this kind are to be found in several Logarithmic and Trigonometrical collections.
The ordinary trigonometrical tables can be made use of in this calcula- tion ; thus we have sec a^ = 1 + tan a? . If, then, we assume a such that tan a^ = -^... we shall obtain P+ Q = P .seca^. To apply this to our pre- sent problem we make the subtraction LogQ-LogP, and halving this difference we find «, such that Log tana = ^ {Log Q - Log P) , then taking out from the page which is already open, the arithmetical complement of log cos a, or log sec a if it be given, we have Log{P+Q) = Log P + 2 Log sec a .
Similarly 1 - sin a^ = cos a^, wherefore if we obtain an angle a such that log sin a = ^ {log Q - log P), we shall have Log {P - Q) = Log P + 2 log cos a, .
What to read after A Treatise On the Valuation of Life Contingencies Arranged for the Use of Students?
You can find similar books in the "Read Also" column, or choose other free books by Sang, Edward, 1805-1890 to read onlineMoreLess
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