Some General Theorems of Considerable Use in the Higher Parts of Mathematics

Cover Some General Theorems of Considerable Use in the Higher Parts of Mathematics
Some General Theorems of Considerable Use in the Higher Parts of Mathematics
Pre-1801 Imprint Collection (Library of Congress) Dlc
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Jjef there he any number greater than two cf right lines inter jeBing each other in a pointy and making all the angjki round the point of interfeSion equals and from any point let there he drawn perpendiculars to the right lines ^ and Ukewife let there be drawn a right line to the point of interfeBion ; 8 times the fum of the fourth powers of the perpendicu^ lars drawn to the right lines^ will be equal to 3 times the multiple of the fourth power of the line drawn to the point of inter feElion b
...y the number of the ri^t lines.
Let the number of the tines be three ; and iihe theorem will be as follows.
Let there be three right lines interieding tfach other in a pointy and makmg all the anglea M 2 round I 9> ] round the point of interie£tion equal, and from iny point let there be drawn perpendiculars ta^ the right lines^ and likewife let there be drawn a right line to the point of interfedion ; 8 timei the fum of the fourth powers of the perpendi- culars, will be equal to 9 times the fourth powet of the line drawn to the point of intcr- fe£tion» Again, Let the number of the lines be fivt> and the theorem will be as follows.


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