| 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... | |
| 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~... | |
| 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.... | |
| 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... | |
| 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,... | |
| 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,... | |
| 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... | |
| 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... | |
| 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,... | |
| 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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