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" AB; but things which are equal to the same are equal to one another... "
Elements of Geometry: Containing the First Six Books of Euclid : with a ... - Side 12
av John Playfair - 1837 - 318 sider
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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - 1841 - 378 sider
...AB; and because the point B is the Bullion. centre O f tn e c i rc i e ACE, BC is equal to BA: hut it has been proved that CA is equal to AB; therefore CA, CB, are each of them equal to AB; but things * 1st which are equal to the same thing are equal* to one Axiom. anot her; therefore CA...
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The Works of Francis Bacon, Lord Chancellor of England, Volum 3

Francis Bacon - 1841 - 616 sider
...similar to that of music termed the declining of a cadence. 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....
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The Dublin Review, Volum 11

Nicholas Patrick Wiseman - 1841 - 618 sider
...arrangement, how can the celebrated demand in the theory of parallels rank under the same head as that " things which are equal to the same are equal to one another." The misplacement of this axiom about parallels has cost many a trial at this old difficulty, and procured...
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Works, Volum 3

Francis Bacon - 1841 - 616 sider
...similar to that of music termed the declining of a cadence. 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....
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Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842 - 316 sider
...shall at length meet upon that side on which are the angles less than two right angles. AXIOMS. I. THINGS which are equal to the same are equal to one another. II. If equals be added to equals, the wholes are equal. III. If equals be taken from equals, the remainders...
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Nuces Philosophical

Sir Edward Johnson - 1842 - 622 sider
...word which is equivalent to any one of them, must, therefore, also be equivalent to the others, since things which are equal to the same, are equal to one another. I have said that when we wish to convert a noun into a verb, we do so by prefixing the word to. Thus,...
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Lectures on the Principles of Demonstrative Mathematics

Philip Kelland - 1843 - 168 sider
...I propose to take up the same subject, and inquire, for the sake of precision, whether the truth, " things which are equal to the same are equal to one another," is demonstrable or not. If it be an immediate consequence of our conception of equality, then is it...
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Ancient Egypt: Her Monuments, Hieroglyphics, History and Archæology, and ...

George Robins Gliddon - 1844 - 92 sider
...Africans, but Asiatics, the utter destruction of all biblical chronology by thia process would be another. Now, " things which are equal to •the same are equal to one another." If they are anterior to Shoopho's pyramid in Egypt, then Weroe must have been occupied in the earliest...
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Novum Organum: Or, True Suggestions for the Interpretation of Nature

Francis Bacon - 1844 - 348 sider
...similar to that of music termed the declining of a cadence. 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....
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The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1845 - 382 sider
...30) to AB; and because the point B is the centre of the circle ACE, BC is equal (I. def. 30) to BA. But it has been proved that CA is equal to AB ; therefore, CA, CB are each of them equal to AB : but things which are equal to the same are equal (I. axiom 1) to one another; therefore CA is equal...
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