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" If a straight line meets two straight lines, so as to " make the two interior angles on the same side of it taken " together less than two right angles... "
Euclid's Elements of geometry, books i. ii. iii. iv - Seite 4
von Euclides - 1862
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The Popular Science Monthly, Band 17

1880
...his six al-ijiiara (requests) Euclid says : "Let it be granted that if a straight line meet two other straight lines, so as to make the two interior angles...lines being continually produced shall at length meet upon that side on which are the angles, which are together less than two right angles." This somewhat...
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First principles of Euclid: an introduction to the study of the first book ...

T S. Taylor - 1880
...produced to any length, still remain ev(.ry where the same distance apart. Euclid's twelfth Axiom. If a straight line meet two straight lines, so as...side of it taken together less than two right angles, those straight lines being continually produced, shall at length meet on that side on which are the...
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Studies in Deductive Logic: A Manual for Students

William Stanley Jevons - 1880 - 304 Seiten
...Give the logical opposites, converse and contrapositive, of Euclid's (so-called) twelfth axiom — If a straight line meet two straight lines, so as to make the interior angles on the same side of it taken together less than two right angles, those straight lines...
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The Cambridge Examiner, Band 1

1881
...and explain the difficulty of assuming as an axiom (Euclid's axiom xn.) that if a straight line meets two straight lines so as to make the two interior...angles on the same side of it taken together less than right angles these straight lines continually produced shall meet. Explain what is meant by exterior,...
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Elements of Geometry, After Legendre: With a Selection of ..., Teil 2

Charles Scott Venable - 1881 - 366 Seiten
...then, since EFD + HFD = two right angles, we must have GEB — EFD. Therefore (3) AB is parallel to CD. lines so as to make the two interior angles on the same side of it less than two right angles, these straight lines being continually produced will meet on the side on...
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1881
...another. xn If a straight line meets two straight lines, no as to make the two interior angles on thr same side of it, taken together, less than two right angles, these straight lines, oeing continually produced, shall at length meet T upon that side on which are the angles which \ are...
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Class lessons on Euclid

Marianne Nops - 1882
...together equal to two right Zs .'. the Zs BGH, GHD are together less than two right ZB (I. 13). But if a straight line meet two straight lines, so as to make the two interior Z a on the same side of it, taken together, less than two rt. Z s, these straight lines being produced...
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Moffatt's pupil teachers' course (ed. by T. Page). Candidates, 2nd ..., Band 3

Moffatt and Paige - 1883
...(1. 13), therefore the angles BGH, GHD are less than two right angles. But if a straight line meets two straight lines so as to make the two interior...than two right angles, these straight lines, being continuallyproduced, shall at length meet on that side on which are the angles that are less than two...
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Science, Band 20

John Michels (Journalist) - 1892
...at least one which is not axiomatic.3 This is the axiom of parallels, which reads as follows : — " If a straight line meet two straight lines so as to...on the same side of it taken together less than two right-angles, these straight lines, being continually produced, shall at length meet on that side on...
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The Practical Teacher; with which is Incorporated the Practical ..., Band 2

Joseph Hughes - 1883
...; and also the two interior angles on the same side toeether equal to two right angles. Axiom xii. If a straight line meet two straight lines so as to...on the same side of it taken together less than two ri^ht angles, these straight lines being continually produced, îhall at length meet on that side on...
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