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" DL is equal to DG, and DA, DB, parts of them, are equal ; therefore the remainder 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 Elements of Euclid; viz. the first six books, together with the eleventh ... - Página 8
por Euclides - 1814
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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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Elements of Geometry: Containing the First Six Books of Euclid with a ...

John Playfair - 1855 - 318 páginas
...from the centre D, at the distance DG, describe the circle GKL, AL is equal to BC. to the same arc equal to one another; therefore the straight line...has been drawn equal to the given straight line BC. PROP. HI. PROB. From the greater of two given straight lines to cut off a part equal to the less. Let...
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Elements of Geometry: Containing the First Six Books of Euclid with a ...

John Playfair - 1855 - 318 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...equal to one another ; therefore the straight line AL ia equal to BC. Wherefore, from the given point A, a straight line AL has been drawn equal to the given...
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1855
...are equal (Ax. 1) to one another. Therefore the straight line AL is equal to the straight line B С. Wherefore from the given point A, a straight line AL has been drawn equal to the given straight line B С. QEF The construction of this problem might be improved thus:— Join AB. Upon AB describe the...
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Notes to Aristotle's Ethics

William Edward Jelf - 1856 - 231 páginas
...¿v pавiц1атiкois fo-^arov тpiyшvov,) hence termed aHrÖijo-is ; such as in mathematics, " Things that are equal to the same are equal to one another." In morals, apart, of course, from religion, the generalised facts thus perceived are, from our inability...
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Trees and Their Nature: Or, The Bud and Its Attributes: in a Series of ...

Alexander Harvey - 1856 - 236 páginas
...generation possible ne sont point encore parvenus a en faire voir une seule instance." — BABON CUTIEB. " Things that are equal to the same are equal to one another." — EUCLID. June 2, 1855. MY DEAR SONS, 1. I had not space in the preceding letter to consider the...
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A second letter to the archbishop of Canterbury, being an exposure of W ...

Charles Stephen Grueber - 1856
..."outward sign" are equivalent to the " outward part," and therefore to one another, by the common axiom, " Things that are equal to the same are equal to one another." It is true that the term was improperly used by Romanists, as also was " Sign," but it is equally true...
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Milner refuted; or, Pious frauds exemplified in dr. Milner's 'End of ...

Charles Hastings Collette - 1856
...us in our last agonies," and that we may expire in peace with them ! In theology, as in mathematics, "things that are equal to the same are equal to one another." Mary and Joseph are placed in our affection on a level with Jesus, the second person of the Holy Trinity;...
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The Christian remembrancer; or, The Churchman's Biblical ..., Volumen33

1857
...illustration of this, we ask the reader to compare together his two views of the following truths: — Things that are equal to the same are equal to one another ; and — the force of gravity varies inversely as the square of the distance. Mr. Solly, in treating...
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The Works of Francis Bacon, Volumen4

Francis Bacon - 1858
...distributive, if unequals be not given VOL. IV. z to unequals there is the greatest injustice.1 Again " things that are equal to the same are equal to one another," is likewise a rule of mathematics ; but it is at the same time so potent in logic as to be the basis...
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