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" Again ; the mathematical postulate, that " things which are equal to the same are equal to one another," is similar to the form of the syllogism in logic, which unites things agreeing in the middle term. "
The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... - Page 306
by Euclid - 1835 - 513 pages
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God's Week of Work: Being an Examination of the Mosaic Six Days in Relation ...

Evan Lewis - Creation - 1865 - 150 pages
...Euclid are felt to be true in every age, and among every people : "The whole is greater than its part." "Things which are equal to the same, are equal to one another." There may be truths which reason can neither discover nor comprehend; but nothing can be true which...
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An Examination of Mr. J.S. Mill's Philosophy: Being a Defence of Fundamental ...

James McCosh - Philosophy - 1866 - 424 pages
...principle in all such cases is either, ' Things are the same which are the same with a third,' or ' things which are equal to the same are equal to one another.' Much confusion is avoided by allotting reasoning of this description to a separate head. As there is...
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Biography: Or, Third Division of "The English Encyclopedia", Volume 1

Charles Knight - Biography - 1866 - 552 pages
...mentions that Apollonius attempted to prove the axioms, and cites his investigation of the theorem, that things which are equal to the same are equal to one another, in which, as may be supposed, propositions are assumed not more obvious than the theorem itself. Vitruvius...
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An outline of logic

Francis Garden - 1867 - 222 pages
...affections of the thing thought about, not of our thought about it. PART III. ON SYLLOGISM. 1. AXIOMS. I. THINGS which are equal to the same are equal to one another. II. A part of a part is a part of the whole. III. A predicate of a predicate is a predicate of the...
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Journal of the Transactions of the Victoria Institute, Or ..., Volume 1

Religion and science - 1867 - 524 pages
...science. The man who tells me that he cannot believe that " the whole is greater than the part," or " that things which are equal to the same are equal to one another," cannot step over the very threshold of geometry. Nor are these axioms confined to self-evident truths....
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The Victor in the Conflict: Sermons Preached During the Season of Lent, 1867 ...

Lenten sermons - 1868 - 254 pages
...: it must always have been true that " truth is a virtue," as it must always have been true that " things which are equal to the same are equal to one another." And if moral or mathematical truth is thus co-eternal with God, it cannot be something independent...
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Report of the Mildmay park conference

Mildmay conference - 1880 - 274 pages
...another. I would remind you of an expression which I made use of in prayer on this platform this week — "Things which are equal to the same are equal to one another." If then we are equally like Jesus, we shall be like one another. Thus shall we learn to love one another,...
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New theories and the old faith, a course of lectures

James Allanson Picton - 1870 - 250 pages
...must owe something to each of these. Let it be granted for instance that the universal judgment, " things which are equal to the same are equal to one another," is not merely suggested but learned by experience. Still, the fact that experience takes this form is...
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New Theories and the Old Faith: A Course of Lectures on Religious Topiecs of ...

James Allanson Picton - Theology - 1870 - 248 pages
...must owe something to each of these. Let it be granted for instance that the universal judgment, " things which are equal to the same are equal to one another," is not merely suggested but learned by experience. Still, the fact that experience takes this form is...
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The Contemporary Review, Volume 15

Great Britain - 1870 - 688 pages
...properties as emotion we shall not only have established points of resemblance between the two (for things which are equal to the same are equal to one another), but we shall have actually reached the common ground, or kind of border-land, upon which internal emotion...
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