| 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... | |
| 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... | |
| 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... | |
| 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 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.... | |
| 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 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,... | |
| 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... | |
| 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... | |
| 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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