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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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Studies and Exercises in Formal Logic: Including a Generalisation of Logical ...

John Neville Keynes - 1884 - 414 páginas
...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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An introduction to geometry, consisting of Euclid's Elements, book ..., Volumen1

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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The First Six Books of the Elements of Euclid: And Propositions I-XXI of ...

Euclid, John Casey - 1885 - 312 páginas
...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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Essays and Speeches of Jeremiah S. Black

Jeremiah Sullivan Black - 1885 - 621 páginas
...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 ...

Euclides - 1885
...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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The Passenger from Scotland Yard

H. Freeman Wood - 1888 - 398 páginas
...each of them equal to BG. And as things which are equal to the same thing are equal to one another, AL is equal to BC; wherefore, from the given point...been drawn, equal to the given straight line BC." Inspector Byde surveyed his handiwork with approbation, and added, most conscientiously, "QEF" He also...
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The Midland Naturalist: The Journal of the "Midland Union of ..., Volúmenes11-12

Edward W. Badger, William Hillhouse - 1888
...what process of experiment do you proceed to prove an axiom such as that expressed by the words, " Things that are equal to the same are equal to one another ? " It cannot be done, as at every step of the proof it is taken for granted ; presuming that physical...
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The Prevention of Measles

C. Candler - 1889 - 381 páginas
...by inoculation •with the blood, it follows — if the proposition holds good in bacteriology that things that are equal to the same are equal to one another — that bacteroid forms occur in the organism after inoculation with straw fungi. I conceive that...
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The Hereafter: Sheol, Hades and Hell, the World to Come, and the Scripture ...

James Fyfe - 1890 - 407 páginas
...moment. They both derive all their force from their mother, aevum, ever ; and there is an old axiom : Things that are equal to the same are equal to one another. In early Greek, as in Attic still, alan> (aion) signifies the duration of human life, course or term...
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A new theory of parallels

Lewis Carroll - 1890
...Physiology rather than in Geometry. The 47th Proposition of Euclid is quite as true as the Axiom ' things that are equal to the same are equal to one another ' ; but the average human intellect, while accepting the latter without proof, does most certainly...
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