 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 - Pagina 246door Euclid - 1838 - 416 pagina’sVolledige weergave - Over dit boek
 | 1867 - 524 pagina’s
...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.... | |
 | Francis Garden - 1867 - 228 pagina’s
...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... | |
 | 1868 - 254 pagina’s
...: 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... | |
 | Mildmay conference - 1880 - 274 pagina’s
...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,... | |
 | James Allanson Picton - 1870 - 250 pagina’s
...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... | |
 | James Allanson Picton - 1870 - 248 pagina’s
...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... | |
 | 1870 - 688 pagina’s
...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... | |
 | Herbert Spencer - 1872 - 670 pagina’s
...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... | |
 | Euclid - 1872 - 284 pagina’s
...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... | |
 | 1875 - 884 pagina’s
...the same time be and not be ; 2. That if equals be added to equals, the wholes are equal ; 3. That things which are equal to the same are equal to one another. It so happens that each of these propositions which he has assumed to be true is, if true, much more... | |
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