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" BG; and things that are equal to the same are equal to one another; therefore the straight line AL is equal to BC. Wherefore from the given point A a straight line AL has been drawn equal to the given straight line BC. "
Elements of Geometry: Containing the First Six Books of Euclid, with a ... - Side 19
av Euclid, John Playfair - 1826 - 320 sider
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Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ...

Euclides - 1860
...the remainder BG (Ax. 3). But it has been shewn that BC is equal to BG ; wherefore AL and BC are each of them equal to BG ; and things that are equal to...equal to one another; therefore the straight line to BC. Wherefore from the given AL shall line AL BC. AL is equal point A a straight has been drawn...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1860 - 361 sider
...the remainder BG; (ax. 3.) but it has been shewn that BCia equal to BG, wherefore AL and BC are each of them equal to BG ; and things that are equal to the same thing are equal to one another ; therefore the straight line AL is equal to BC. (ax. 1.) Wherefore...
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The Philosophical Works of Francis Bacon, with Prefaces and Notes ..., Volum 4

Francis Bacon - 1861
...distributive, if unequals be not given VOL. IV. Z to unequals there is the greatest injustice.1 Again " things that are equal to the same are equal to one another," is likewise a rule of mathematics ; but it is at the same time so potent in logic as to be the basis...
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DISCUSSIONS ON PHILOSOPHY AND LITERATURE, EDUCATION AND UNIVERSITY REFORM

SIR WILLIAM HAMILTON - 1861
...Induction, than in establishing his own. 1 " It is by induction that all axioms are known, such as : — * Things that are equal to the same are equal to one another ;' * A whole is greater than its parts ;' and all other mathematical axioms." Huyshe, p. 132. The same...
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Euclid's Elements of geometry, books i. ii. iii. iv

Euclides - 1862
...same thing are equal to one another, therefore AL is equal to BC. (ax. 1.) Conclusion. — Therefore from the given point A a straight line AL has been drawn equal to the given straight line BC. Which was to be done. PROPOSITION 3.— PROBLEM. From the greater of two given straight lines to cat...
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The school Euclid: comprising the first four books, by A.K. Isbister

Euclides - 1862
...BG ; wherefore AL and BC are each of them equal to BG ; and things which are equal to the same thing are equal to one another ; therefore the straight line Al Is equal to BC. (ax. 1.) Wherefore from the given point A a straight line AL has been drawn equal to the given straight...
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The Danville Quarterly Review, Volum 2

1862
...demonstration, the idea of a First Cause becomes as intuitive as that all the parts are equal to the whole, or things that are equal to the same are equal to one another. Facts that may seem to conflict with this may be easily accounted for from the determination of the...
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The elements of plane geometry; or, The first six books of Euclid, ed. by W ...

Euclides - 1863
...3) to the remainder BG. But it has been shown that BC is equal to BG. Wherefore AL and BC are each of them equal to BG. And things that are equal to the same thing are (Ax. 1) equal to one another. Therefore the straight line AL is equal to the straight line...
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The Works of Thomas Reid, D.D.: Now Fully Collected, with Selections from ...

Thomas Reid - 1863
...certainly than through demonstration, that we know in a. common notion.' .... Such common notions are — ' Things that are equal to the same are equal to one another,' — ' If equals be taken from equals the remainders are equal,' — ' Everything must be either affirmed...
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The school edition. Euclid's Elements of geometry, the first six books, by R ...

Euclides - 1864
...the remainder BG; (ax. 3.) but it has been shewn that BC is equal to BG, wherefore AL and B Care each of them equal to BG; and things that are equal to the same thing are equal to one another ; therefore the straight line AL is equal to BC. (ax. 1.) Wherefore...
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