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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; viz. the first six books, together with the eleventh ...

Euclides - 1814
...is them, are equal; therefore the remainder AL is equal to equal to BG; wherefore'AL and BC are each of them equal to BG; and things that are equal to...has been drawn equal to the given straight line BC. Which was to-be done. PROP. HI. PROB. FR0M the greater of two given straight lines to cut off a part...
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An Easy Introduction to the Mathematics: In which the Theory and ..., Volum 2

Charles Butler - 1814
...an inference that two and two, and three and one, are equal to the same (viz. to four) : now, since things that are equal to the same are equal to one another, it follows as a further inference, that two and two are equal to three and one. 42. This example will...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 528 sider
...f3Ar. the remainder* BG; But it has been shown, that BC is equal to BG ; wherefore AL and BG are each of them equal to BG; and things that are equal to...straight line AL has been drawn equal to the given s^raigfrf line , BC. Which was to be done. ai PROP. III. PROB. ^ > FROM the greater of two given straight...
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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 sider
...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 are equal to...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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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 sider
...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 sider
...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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The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - 1829 - 516 sider
...equal to G, wherefore AL and BC are each of them equal to BG ; and things that are equal to the came are equal to one another ; therefore the straight...has been drawn equal to the given straight line BC. Which was to be done. PROP. III. PROB. FROM the greater of two given straight lines to cut off a part...
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The Millennial Harbinger, Volum 3

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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