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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 ... - Pągina 19
per Euclid, John Playfair - 1826 - 320 pągines
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## The Metaphysics of the School: Book 4. Principles of being; Book 5. Causes ...

Thomas Harper - 1881 - 414 pągines
...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 pągines
...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, Part I: Being a Familiar ...

Stephen Thomas Hawtrey - 1880 - 155 pągines
...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,...
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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 pągines
...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
...equal 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 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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## An introduction to geometry, consisting of Euclid's Elements, book ..., Volum 1

Euclides - 1884
...EBA, ABD. But the angles CBE, EBD have been proved equal to the same three angles ; and things which are equal to the same are equal to one another ; therefore the angles CBA, ABD are equal to the angles CBE, EBD. ' (Ax. 1) But CBE, EBD are two right angles. (Constr.)...
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## Studies and Exercises in Formal Logic: Including a Generalisation of Logical ...

John Neville Keynes - 1884 - 414 pągines
...I should say the same in reference to Hansel's remark (Prolegomena Logica, p. i03), that the Axiom "things that are equal to the same are equal to one another" is only another statement of the Principle of Identity. CHAPTER II. SIMPLE EXERCISES ON THE SYLLOGISM....
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## Essays and Speeches of Jeremiah S. Black

Jeremiah Sullivan Black - 1885 - 621 pągines
...and the white men, and therefore yon can not distinguish between the white men themselves, because things that are equal to the same are equal to one another. Is not that as certain as mathematics ? If a State Constitution would provide for a Supreme Court,...
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