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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 ... - Side 318
av Euclid, Robert Simson - 1821 - 516 sider
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Faith and Thought, Volum 1

1867
...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 ...

1868 - 216 sider
...: 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 - 2062 sider
...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
...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 - 1870 - 227 sider
...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, Volum 15

1870
...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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The Principles of Psychology: Special analysis. General analysis. Corollaries

Herbert Spencer - 1872
...knowledge beyond that of the coexistence of an indefinite number of things ; any more than the axiom — "Things which are equal to the same are equal to one another," can, by multiplied application, do more than establish the equality of some series of magnitudes. But...
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Faith and Free Thought: A Second Course of Lectures Delivered at the Request ...

Christian evidence society, Samuel Wilberforce - 1872 - 468 sider
...things, this maxim we apply to the actual material of this world. Did we apply, eg, the axiom that things which are equal to the same are equal to one another to actual things, we should first have to ascertain the fact that the two things were exactly equal,...
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Euclid's Elements of Geometry

Euclid - 1872 - 261 sider
...3. That a circle can be described from any centre, with any radius. COMMON NOTIONS, OR AXIOMS. 1 . Things which are equal to the same are equal to one another. 2. If equals be added to equals, the wholes will be equal. 4. If to unequals, equals be added, the...
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The Mystery of Matter, and Other Essays

James Allanson Picton - 1873 - 492 sider
...believes the axioms of Euclid, but simply because of the impossibility of thinking the contrary. That " things which are equal to the same are equal to one another " is a truth clear at once to any mind capable of understanding its terms, without the slightest necessity...
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