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" DL is equal to DG, and DA, DB, parts of them, are equal ; therefore the remainder AL is equal to the remainder (3. Ax.) BG : 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... "
The Elements of Euclid; viz. the first six books, together with the eleventh ... - Página 8
por Euclides - 1814
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The elements of plane geometry; or, The first six books of Euclid, ed. by W ...

Euclides - 1863
...AL is equal (Ax. 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
...to 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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Euclid's Elements of geometry, the first four books, by R. Potts. Corrected ...

Euclides - 1864
...to the remainder BG ; (ax. 3.) but it has been shewn that BCis equal to BG, wherefore AL and .BCare 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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Works, Volumen8

Francis Bacon - 1864
...whereas in distributive, if unequals be not given 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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The college Euclid: comprising the first six and the parts of the eleventh ...

Euclides - 1865
...the same thing are equal to one another ; therefore tne straight line AI. is equal to BC. (ax. 1.) Wherefore from the given point A a straight line AL...drawn equal to the given straight line BC. Which was to be done. PROP. III.— PROBLEM. From the greater of two given straight lines to cut off a part equal...
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1855 - 317 páginas
...; and things that are equal to the same are equal to one another ; therefore the straight line AL u equal to BC. Wherefore, from the given point A, a straight line AL haj been drawn equal to the given straight line BC. a part equal to tht PROP. III. PROB. From the greater...
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Philosophy of Sir William Hamilton, Bart: Professor of Logic and Metaphysics ...

Sir William Hamilton - 1866 - 530 páginas
...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,'—' Every thing must be either affirmed or...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - 1867 - 400 páginas
...to BG. But things which are equal to the same thing are equal to one another. [Axiom 1 . Therefore AL is equal to BC. "Wherefore from, the given point...has been drawn equal to the given straight line BC. QEF PROPOSITION 3. PROBLEM. From the greater of two given straight lines to cut off a part equal to...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - 1867 - 400 páginas
...equal to BG. But things which are equal to the same thing are equal to one another. [Axiom 1. Therefore AL is equal to BC. Wherefore from the given point A a straight line AI, has been drawn equal to the given straight line BC. QEP PROPOSITION 3. PROBLEM. From the greater...
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