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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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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

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....
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The Elements of Euclid, the parts read in the University of Cambridge [book ...

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,...
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The first three books of Euclid's Elements of geometry, with theorems and ...

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...
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Thoughts on Self-culture, Addressed to Women

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...
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The first two books of the Elements of Euclid, with additional figures ...

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...
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The first six books of the Elements of Euclid, with numerous exercises

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...
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The synoptical Euclid; being the first four books of Euclid's Elements of ...

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...
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The Elements of Euclid, books i-vi; xi. 1-21; xii. 1,2; ed. by H.J. Hose, Bok 1

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...
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The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

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...
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The British Millennial Harbinger

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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