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" AB; but things which are equal to the same are equal to one another... "
The synoptical Euclid; being the first four books of Euclid's Elements of ... - Side 7
av Euclides - 1853
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The First Two Books of the Elements of Euclid ... with Additional Figures ...

Euclides - 1852
...the circle ACE, BC is equal to BA. But it has been proved that AC is equal to AB ; therefore AC, BC are each of them equal to AB ; but things which are equal to the same are equal to one 4 I Axiom. another d therefore AC is equal to BC ; wherefore AC, AB, BC are equal to one another; and...
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The New quarterly review, and digest of current literature, Volum 7

1858
...have a gayer or gladder aspect. Mr. Smith's only justification here is a mathematical one : that as things which are equal to the same are equal to one another, and both blossoms and tears have been likened to a shower of rain, therefore blossoms may always be...
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The Elements of Euclid [book 1] for beginners, by J. Lowres

Euclides - 1852
...a circle may be described from any centre, with any distance from that centre as radius. AXIOMS. 1. Things which are equal to the same, are equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be taken from equals, the remainders...
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The British Millennial Harbinger

1852
..."Yes." " And the three baskets three days too?" "Yes." Well, thought I, if it be a true axiom that things which are equal to the same are equal to one another, then a grape vine and a basket are identical ! So, finding the rabbinical logic of this poor deluded...
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The first six books of the Elements of Euclid, with numerous exercises

Euclides - 1853 - 147 sider
...circle bСd, aС is equal (15 def.) to ab; and because the point b is the centre of the circle ace, bc is equal to ba : but it has been proved that ca...which are equal to the same are equal to one another (1 ax.); therefore ca is equal to cb; wherefore ca, ab, bc are equal to one another; and the triangle...
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The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

Royal Military Academy, Woolwich - 1853
...BCD, AC is equal (15 Definition) to AB; and because the point B is the centre of the circle ACE, EC is equal to BA : But it has been proved that CA is...which are equal to the same are equal to one another (1 Axiom) ; therefore CA is equal to CB ; wherefore CA, AB, BC are equal to one another; and the triangle...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1868 - 410 sider
...CE, therefore .BCis equal to AB; but it has been proved that AC is equal to AB ; therefore AC, .BC are each of them equal to AB ; but things "which are equal to the same thing are equal to one another ; therefore .4 C is equal to BC; (ax. 1.) wherefore AB, BC, CA are equal...
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The Victor in the Conflict: Sermons Preached During the Season of Lent, 1867 ...

1868 - 216 sider
...: it must always have been true that " truth is a virtue," as it must always have been true that " things which are equal to the same are equal to one another." And if moral or mathematical truth is thus co-eternal with God, it cannot be something independent...
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Report of the Mildmay park conference

Mildmay conference - 1880 - 2062 sider
...another. I would remind you of an expression which I made use of in prayer on this platform this week — "Things which are equal to the same are equal to one another." If then we are equally like Jesus, we shall be like one another. Thus shall we learn to love one another,...
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New theories and the old faith, a course of lectures

James Allanson Picton - 1870
...must owe something to each of these. Let it be granted for instance that the universal judgment, " things which are equal to the same are equal to one another," is not merely suggested but learned by experience. Still, the fact that experience takes this form...
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