| John Playfair - 1846 - 317 sider
...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...has been drawn equal to the given straight line BC.** PROP. III. PROB. From the greater of two given straight lines to cut off a part equal to the less.... | |
| Euclides - 1846
...angles DBE, EBA, ABC : But the angles CBE, EBD have been shewn to be equal to the same three angles ; **and things that are equal to the same are equal to one another ; therefore the** angles CBE, EBD arc equal to the angles DBA, ABC : But CBE, EBD are two right angles ; therefore DBA,... | |
| Euclides, Thomas Tate - 1849 - 108 sider
...remainder BG (Ax. 3.) : But it has been shown that BC is 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. III. PROB. From the greater of two given straight lines to cut off a part... | |
| Maria Georgina Shirreff Grey, Emily Anne Eliza Shirreff - 1851 - 464 sider
...above given, or it may contain a self-evident maxim, requiring no proof, as in the following : — **Things that are equal to the same, are equal to one another** ; A and B are each equal to C ; Therefore, A is equal to B. But in either case the process by which... | |
| Euclides - 1852
...equal to the remainder f BG. But it has been shown 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** h i Ax. another h ; therefore the straight line AL is equal to BC. Wherefore, from the given point... | |
| Euclides - 1853 - 147 sider
...the remainder (3 ax) bg; but it has been shewn that bc is equal to bg; wherefore a1 and bc are each **of them equal to bg ; and things that are equal to...equal to one another; therefore the straight line** a1 is equal to bc. Wherefore from the given point aa straight line a1 has been drawn equal to the given... | |
| Euclides - 1853
...equal to the remainder BG. But it has been shown 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 ; therefore** 4. The straight line AL is equal to BC. Wherefore from the given point A a straight line AL has been... | |
| Euclides - 1853
...that are equal to the same thing are equal to one another (Ax. i) ; therefore AL is equal to BC. Hence **from the given point A a straight line AL has been drawn equal to the given straight line BC.** Which was to be done. PEOP. III. PEOB. From the greater of two given straight lines to cut off a part... | |
| Royal Military Academy, Woolwich - 1853
...remainder (3 Ax.) BG ; But it has been shown, 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** (1 Ax.) to one another ; therefore the straight line AL is equal to BC. Wherefore from the given point... | |
| 1854
...rank of intellectual and moral agents, is to me as plain and evident as the mathematical axiom, " that **things that are equal to the same, are equal to one another."** The word happiness, however, is far from being generally understood. It is not applicable to inanimate... | |
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