The Substitution of Similars: The True Principle of Reasoning, Derived from a Modification of Aristotle's Dictum |
From inside the book
Results 1-5 of 11
Page
... AXIOMS OF EQUALITY GENERAL FORMULA OF MATHEMATICAL INFERENCE INFERENCE BY INEQUALITIES . 15 19 20 SUBSTITUTION OF EQUALS OR SIMILARS 23 GENERAL FORMULA OF LOGICAL INFERENCE 24 EXAMPLES OF LOGICAL SUBSTITUTION . 25 MOODS OF THE SYLLOGISM ...
... AXIOMS OF EQUALITY GENERAL FORMULA OF MATHEMATICAL INFERENCE INFERENCE BY INEQUALITIES . 15 19 20 SUBSTITUTION OF EQUALS OR SIMILARS 23 GENERAL FORMULA OF LOGICAL INFERENCE 24 EXAMPLES OF LOGICAL SUBSTITUTION . 25 MOODS OF THE SYLLOGISM ...
Page 9
... axiom was perfectly adapted to this view . The so - called Dictum de omni is , in Latin phrase , as follows- Quicquid de omni valet , valet etiam de quibusdam et singulis . And the corresponding Dictum de nullo is similarly- Quicquid de ...
... axiom was perfectly adapted to this view . The so - called Dictum de omni is , in Latin phrase , as follows- Quicquid de omni valet , valet etiam de quibusdam et singulis . And the corresponding Dictum de nullo is similarly- Quicquid de ...
Page 15
... axiom of quantity ; and the force of the axiom may best be illustrated in the first place by looking at it in its mathematical aspect . 15. The axiom indeed with which Euclid begins to build presents at first sight little or no resem ...
... axiom of quantity ; and the force of the axiom may best be illustrated in the first place by looking at it in its mathematical aspect . 15. The axiom indeed with which Euclid begins to build presents at first sight little or no resem ...
Page 16
... axiom asserts that Things equal to the same thing are equal to each other . In symbols , a = = b = c gives a = c . Here two equations are apparently necessary in order that an inference may be evolved ; and there is something peculiar ...
... axiom asserts that Things equal to the same thing are equal to each other . In symbols , a = = b = c gives a = c . Here two equations are apparently necessary in order that an inference may be evolved ; and there is something peculiar ...
Page 17
... axiom of Euclid thus requires to be supplemented by two other axioms , which can only be expressed in somewhat awkward language , as follows : - If the first of three things be equal to the second , but the second be unequal to the ...
... axiom of Euclid thus requires to be supplemented by two other axioms , which can only be expressed in somewhat awkward language , as follows : - If the first of three things be equal to the second , but the second be unequal to the ...
Other editions - View all
Common terms and phrases
A B C D abacus ABCD affirmative proposition Algebra analogy applied Aristotle Aristotle's ARITHMETIC assert axiom BEGINNERS Bentham Boole Boole's BROOKE FOSS WESTCOTT CALCULUS Cambridge canon Christ's College Church Clifton College cloth combinations conclusion CONIC SECTIONS consists copula Crown 8vo denote dictum differs EDUCATIONAL Edward Thring ELEMENTARY TREATISE English equal Euclid Examination Papers Examples expression Extra fcap fallacy Fellow of St follows forms of reasoning formulæ GEOMETRY George Bentham Grammar Head Master hence HISTORY identity illustrated indirect induction inference Iron J. S. Mill John's College late Fellow Latin law of duality Laws of Thought ledge logicians Maps ment metals are elements method MIXED MATHEMATICS ordinary oxygen predicate premises problem quantification quantity reader represented resemblance Schools Second Edition self-evident self-luminous SHILLING BOOK slips student substitution of similars syllogism symbols System of Logic thing Third Edition tion triangle true undecomposable substance
Popular passages
Page 23 - A GENERAL SURVEY OF THE HISTORY OF THE CANON OF THE NEW TESTAMENT DURING THE fIRST FOUR CENTURIES. Fourth Edition. With Preface on "Supernatural Religion.
Page 6 - Thucydides. — THE SICILIAN EXPEDITION. Being Books VI. and VII. of Thucydides, with Notes. A New Edition, revised and enlarged, with a Map. By the Rev. PERCIVAL FROST, MA. late Fellow of St. John's College, Cambridge. Fcap. 8vo.
Page 13 - PUCKLE— AN ELEMENTARY TREATISE ON CONIC SECTIONS AND ALGEBRAIC GEOMETRY. With Numerous Examples and Hints for their Solution ; especially designed for the Use of Beginners. By GH PUCKLE, MA New Edition, revised and enlarged.
Page 10 - NM FERRERS, MA, Fellow and Tutor of Gonville and Caius College, Cambridge. AN ELEMENTARY TREATISE ON TRILINEAR ' CO-ORDINATES, the Method of Reciprocal Polars, and the Theory of Projectors.
Page 23 - WILSON— THE BIBLE STUDENT'S GUIDE to the more Correct Understanding of the English Translation of the Old Testament, by reference to the original Hebrew. By WILLIAM WILSON, DD, Canon of Winchester, late Fellow of Queen's College, Oxford. Second Edition, carefully revised. 4to. cloth. 25*. YONGE (CHARLOTTE M.)— SCRIPTURE READINGS FOR SCHOOLS AND FAMILIES. By CHARLOTTE M. YONGE, Author of "The Heir of Redclyffe.
Page 16 - New Edition. Crown 8vo. $s. KEY TO PLANE TRIGONOMETRY. Crown 8vo. los. 6d. A TREATISE ON SPHERICAL TRIGONOMETRY. New Edition, enlarged. Crown 8vo. 4-?. 6d. PLANE CO-ORDINATE GEOMETRY, as applied to the Straight Line and the Conic Sections. With numerous Examples.
Page 18 - ASTRONOMY. ELEMENTARY LESSONS IN ASTRONOMY. With Coloured Diagram of the Spectra of the Sun, Stars, and Nebulae, and numerous Illustrations. By J. NORMAN LOCKYER, FRS New Edition. Fcap. 8vo. 5*. 6d. "Full, clear, sound, and worthy of attention, not only as a popular exposition, but as a scientific • Index.
Page 12 - Prelector of St. John's College, Cambridge. AN ELEMENTARY TREATISE ON MECHANICS. For the Use of the Junior Classes at the University and the Higher Classes in Schools.
Page 11 - AN ELEMENTARY TREATISE on the LUNAR THEORY. With a brief Sketch of the Problem up to the time of Newton. By HUGH GODFRAY, MA Second Edition, revised. Crown 8vo. cloth.
Page 16 - ... obtaining all the information which he will require on this branch of Mathematics. Each chapter is followed by a set of Examples : those which- are entitled Miscellaneous Examples, together with a fe-w in some of the other sets, may be advantageously reserved by the sttident for exercise after he has made some progress in the subject.