## Trigonometry and Double Algebra |

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Accordingly algebra answer appears arithmetic axes axis base becomes begin calculation called chapter circle combination complete connexion Consequently considered contained cosC cose cosine coso definitions denote described diminishes direction distinct divide double equal equation expressed extended factors formulæ fraction function geometry given gives half Hence increase indicated instance integer length limit logarithms logometer magnitude meaning mode multiplication namely nearly negative notion nth roots operation opposite ordinary positive powers preceding problem proceed projections quantity question rectangle remembered represent result revolving right angle rules seen side significant sine sino solution square root student successive suppose symbols taken tangent tano theorem third triangle trigonometrical true twelfth root units unity whence write

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Page v - An attempt to rectify the inaccuracy of some logarithmic formulae.' (Read December 18, 1828.) Philosophical Transactions for 1829. John Warren. Consideration of the objections raised against the geometrical representation of the square roots of negative quantities.

Page 99 - ... which may hereafter become the grammar of a hundred distinct significant algebras. If any one were to assert that + and — might mean reward and punishment and A, B, C, etc., might stand for virtues and vices, the reader might believe him, or contradict him, as he pleases, but not out of this chapter. The one exception above noted, which has some share of meaning, is the sign placed between two symbols, as in A B. It indicates that the two symbols have the same resulting meaning, by whatever...

Page vi - O'Brien (Rev. M.) Treatise on Plane Coordinate Geometry ; or the Application of the Method of Coordinates to the Solution of Problems in Plane Geometry.

Page v - J.) on the objections against the geometrical representation of the square roots of negative quantities ii. 371 ; on the geometrical representation of the powers of quantities whose indices involve the square roots of negative quantities, ii.

Page 41 - Frend's papers, and dated November 16, 1801, distinctly lays it down that, in these matters, it is not the principles which prove the conclusions, but the truth of the conclusions which proves that there must, somewhere or other, be principles. " Whether or not," says he, " I have found a logic, by the rules of which operations with imaginary quantities are conducted, is not now the question ; but surely this is evident, that, since they lead to right conclusions, they must have a logic.