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" Let it be granted that a straight line may be drawn from any one point to any other point. "
The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ... - Side 8
av Euclid, Robert Simson - 1838 - 416 sider
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1842 - 317 sider
...other point. 2. That a terminated straight line may be produced to any length in a straight line. 3. And that a circle may be described from any centre, at any distance from that centre. AXIOMS. 1. THINGS which are equal to the same thing are equal to one another. 2. If equals be added to equals,...
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Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842
...other point. II. That a terminated straight line may be produced to any length in a straight line. III. That a circle may be described from any centre, at any distance from that centre. IV. [Ax. XI.] V. And that if a straight line meets two straight lines, so as to make the two interior...
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Lessons on the globes

T H. Howe - 1842
...point within the circle which is thus equally distant from the circumference, is called the Centre. HA Circle may be described from any centre, at any distance from that centre. Illustration. The sensible horizon, or circular boundary, which every individual, standing in a clear...
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Lectures on the Principles of Demonstrative Mathematics

Philip Kelland - 1843 - 147 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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Elements of Geometry: On the Basis of Dr. Brewster's Legendre : to which is ...

James Bates Thomson - 1844 - 237 sider
...point. 2. That a terminated straight line may be produced to any length in a straight line. 3. That any circle may be described from any centre, at any distance from that centre. PROBLEM XVI. When the given angle is acute, the segment will be greater than a semicircle ; and when...
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Novum Organum: Or, True Suggestions for the Interpretation of Nature

Francis Bacon - 1844 - 336 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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Ancient Egypt: Her Monuments, Hieroglyphics, History and Archæology, and ...

George Robins Gliddon - 1844 - 66 sider
...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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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845
...one point to any other point. II. That a terminated straight line may be produced to any length in a straight line. III. And that a circle may be described...centre. AXIOMS. I. THINGS which are equal to the same thing are equal to one another. II. If equals be added to equals, the wholes are equal. III. If equals...
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The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1845 - 352 sider
...point : f 2. That a terminated straight line may be produced to any length in a straight line : , 3. That a circle may be described from any centre, at any distance from that centre. J AXIOMS. 1. Things which are equal to the same, or to equals, are equal to one another. 2. If equals...
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Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - 1845 - 199 sider
...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 to one another || ; therefore CA is equal to CB ; wherefore CA, « i Axiom. AB, BC are equal to one another ; and...
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