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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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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 317 páginas
...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...line AL has been drawn equal to the given straight line1 BC. Which was to be done. PROP. III. PROB. From the greater of two given straight lines to cut...
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Elements of algebra, compiled from Garnier's French translation of L. Euler ...

Charles Tayler - 1824
...will be as follows ; viz. From the first equation, x=.°~ -^ From the second x ~ -~ ^ . a' Now since things that are equal to the same are equal to one another, these two values of x are equal ; and we have therefore this new equation ; c— by __d— b'y, ~a~...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - 1825 - 372 páginas
...is equal to the remainder (3 Ax.) BG : But it has oeen shown, that BC is equal to BG ; wherefore AL and BC are each of them equal to BG ; and things that...AL is equal to BC. Wherefore from the given point À a straight line AL has been drawn equal to the given straight Une BC. • Which was to be done....
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - 1826 - 320 páginas
...remainder (3. Ax.) BG : But it has been shewn that BC is equal to BG : wherefore AL and BC are eaeh B of them equal to BG ; and things that are equal to...has been drawn equal to the given straight line BC. Whieh was to be done. PROP. III. PROB. From the greater of two given straight lines to eut off a part...
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Euclid's Elements of geometry, transl. To which are added, algebraic ...

Euclides - 1826
...EBA, ABC. But it was shown that the angles CBE, EBD, are equal to the same three, and things which are equal to the same are equal to one another; therefore the angles CBE, EBD, are equal to DBA, ABC; but CBE, EBD, are two right angles; therefore the angles DBA,...
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Elements of Geometry, Containing the First Six Books of Euclid

Euclid - 1826 - 180 páginas
...EBA, ABC. But it was shown that the angles CBE, BBD, are equal to the same three, and things which are equal to the same are equal to one another; therefore the angles CBE, EBD, are equal to DBA, ABC; but CBE, EBD, are two right angles ; therefore the angles DBA,...
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - 1827 - 513 páginas
...1 Ax. '2.1. ' 3 Post. t 15 Def. t Constr. •1Ax. that BC is equal to BG ; wherefore AL nnd BC nre 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. Wherefore from the...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - 1832 - 333 páginas
...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 same are equal to one another;thereforethestraight line AL is equal to BC. Wherefore, from the given point A, a straight...
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The Millennial Harbinger, Volumen3

Alexander Campbell, Charles Louis Loos - 1832
...effect of the Spirit mean the same thing, for water means the Spirit and the effect of the Spirit: and things that are equal to the same are equal to one another! What does not the phrase ''born of water" mean? It is equal to born ofjire, born of like as of Jire,...
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The American Monthly Magazine, Volumen6

1835
...argument to prove, that a dog runs on four feet : and so a cat is like a fox, and a dog is like a fox, and things that are equal to the same are equal to one another ; and so a cat is a dog, and a dog is a cat ; and so, your Honours, I trust I have established my defence,...
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