 | Euclid, James Thomson - 1845 - 382 σελίδες
...things that are equal to the same are equal (I. ax. 1) to one another; therefore the straight line AF is equal to BC. Wherefore from the given point A a straight line AF has been drawn equal to the given straight line BC : which was to be done. PROP. III. PROB. —... | |
 | Euclid, John Playfair - 1846 - 334 σελίδες
...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 - 292 σελίδες
...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,... | |
 | Euclid, Thomas Tate - 1849 - 120 σελίδες
...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 - 496 σελίδες
...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 - 152 σελίδες
...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 - 176 σελίδες
...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 - 146 σελίδες
...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 - 334 σελίδες
...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 - 400 σελίδες
...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... | |
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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. 
