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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