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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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The Elements of Euclid for the Use of Schools and Colleges: With Notes, an ...

Isaac Todhunter - 1880 - 400 sider
...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,...
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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 sider
...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 sider
...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 sider
...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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The First Six Books of the Elements of Euclid: And Propositions I-XXI of ...

Euclid, John Casey - 1885 - 312 sider
...sum of the angles CBE, EBD is equal to the sum of the three angles CBE, EBA, ABD. And things which are equal to the same are equal to one another. Therefore the sum of the angles CBA, ABD is equal to the sum of the angles CBE, EBD ; but CBE, EBD are right angles...
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