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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 Contemporary Review, Volumen33

1878
...axioms are verbal truths which verify themselves everywhere and always, independently of experience. " Things that are equal to the same are equal to one another," is verified by the meaning of the word equal, which admits no proper definition ; " the whole is greater...
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Euclid, books i. & ii., with notes, examples, and explanations, by a late ...

Euclides - 1879
...equal ; (def. 24) /. the rem. AL = the rem. BG ; (ax. 3) but it has been shown that BC = BG, -. AL and BC are each of them equal to BG ; and things that are equal to the same thing are equal to one another; (ax. 1) /. AL = BC. Wherefore, from the g1ven pt. A a st. line AL has...
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The Metaphysics of the School: Book4. Principles of being; Book 5. Causes of ...

Thomas Harper - 1881
...definition by D, according to the whole of extension, we shall have D = A, S = D, /. S = A ; that is to say, Things that are equal to the same are equal to one another. But, first of all, it should be remembered that, although the equality is logical, it is quite accidental...
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The Metaphysics of the School: Book 4. Principles of being; Book 5. Causes ...

Thomas Harper - 1881 - 6 páginas
...definition by D, according to the whole of extension, we shall have D = A, S = D, /. S = A ; that is to say, Things that are equal to the same are equal to one another. But, first of all, it should be remembered that, although the equality is logical, it is quite accidental...
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The Elements of Euclid for the Use of Schools and Colleges: With Notes, an ...

Isaac Todhunter - 1880 - 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 B'C. 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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An introduction to the Elements of Euclid, being a familiar explanation of ...

Stephen Thomas Hawtrey - 1880
...to the same thing, they are equal to one another. Therefore AL is equal to BC (Ax. 1). Wherefore i from the given point A, a straight line AL has been...drawn equal to the given straight line BC, which was to be done. Observe here the connection between the endings of the enunciation, construction, and demonstration,...
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First principles of Euclid: an introduction to the study of the first book ...

T S. Taylor - 1880
...equal to one another. BC (a) and AL (c) are each equal to C G. .-. AL is equal to B C. Result. — Wherefore from the given point A a straight line AL has been drawn equal to the given line B CQEF EXERCISES. — I. Let A be the A • given point and BC the given line, then draw a line...
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The pupil teachers' handy mathematical and grammatical question-book, with key

Pupil teachers - 1880
...CG, wherefore AL and CB are each of them equal to CG; and things which are equal to the same thing are equal to one another; therefore the straight line AL is equal to BC (ax. i). Wherefore from the given point A, a straight line AL has been drawn equal to the given straight...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - 1883 - 400 páginas
...which are equal to the same thing are equal to one another. [Axiom 1. Therefore AL is equal to BO. Wherefore from the given point A a straight line AL...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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Stewart's specific subjects. Euclid. [1st] (-3rd stage). [With 2 issues of ...

Stewart W. and co - 1884
...remainder AL, is equal to the remainder BG ; bnt it has been shown that BC is equal to BG ; wherefore AL and BC are each of them equal to BG ; and things that...equal to the same are equal to one another ; therefore AL is equal to BC. Wherefore from the given point A a straight line AL has been drawn equal to the...
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