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" If a straight line meet two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles... "
Elements of Geometry: With Notes - Page 172
by John Radford Young - 1827 - 208 pages
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Elements of Geometry: Containing the First Six Books of Euclid with a ...

John Playfair - Geometry - 1855 - 334 pages
...therefore removed from among the Axioms. The 12th Axiom of Euclid is, that " if a straight line meets two straight lines, so as to make the two interior angles on the same side of it taken " which are less than two right angles." Instead of this proposition, which, though true, is by no...
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Elements of Geometry: Containing the First Six Books of Euclid with a ...

John Playfair - Euclid's Elements - 1856 - 346 pages
...therefore removed from among the Axioms. The 12th Axiom of Euclid is, that " if a straight line meets two straight lines, so as to make the two interior...' produced, shall at length meet upon that side on w^^^ <• the angle* " which are less than two right angles." Instead of this proposition, which,...
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Mensuration of Lines, Areas, Surfaces, and Volumes ...

Robert Rawson - 1856 - 178 pages
...cannot inclose a space. XI. All right angles are equal to one another. xn. " If a straight line meets two straight lines, so as to make the two interior angles on the same side of it taken together lesi than two right angles, these straight lines being continually produced, shall at length meet upon...
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Gradations in Euclid : books i. and ii., with an explanatory preface [&c ...

Euclides - 1858 - 248 pages
...consequently the angles measured by those equals must themselves be equal. 12. If a straight line meets two straight lines, so as to make the two interior angles on the same side of it taken C ^\ t^JD together less than two right angles, these two straight lines, being continually produced,...
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Euclid's plane geometry, books iii.-vi., practically applied; or, Gradations ...

Euclides - 1861 - 464 pages
...to make the two int. _a on the same side of it taken together less than two rt. s, these two st. lines, being continually produced, shall at length meet upon that side on which the s are less than two rt. _a. Dof. 10, I. When a st. line standing on another st. line makes...
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Euclid's Elements of geometry, books i. ii. iii. iv

Euclides - 1862 - 140 pages
...part. 10. Two straight lines cannot inclose a space. 11. All right angles are equal to one another. 12. If a straight line meet two straight lines, so as...lines being continually produced, shall at length meet on that side on which are the angles which are less than two right angles. EXPLANATION OF TERMS. A...
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Euclid's plane geometry, practically applied; book i, with explanatory notes ...

Euclides - 1863 - 74 pages
...angles measured by those equals must themselves be equal. 12. If a straight line meets two skaight lines, so as to make the two interior angles on the...it taken together less than two right angles, these two straight lines, being continually produced, shall at length meet upon that side on which the angles...
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The elements of plane geometry; or, The first six books of Euclid, ed. by W ...

Euclides - 1863 - 122 pages
...part. j 11. All right angles are equal to one another. | 10. Two straight lines cannot enclose a space to make the two interior angles on the same side of it, \ 12. If a straight line meets two straight lines, so as straight lines, being continually produced,...
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The College Euclid: Comprising the First Six and the Parts of the Eleventh ...

Euclides - 1865 - 402 pages
...Enclid gets over the difficulty by assuming the following as an axiom : — ' If a straight line meets two straight lines, so as to make the two interior...right angles ; these straight lines being continually prodnced, shall at length meet upon that side on which are the angles which are less than two right...
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - Geometry - 1855 - 350 pages
...therefore removed from among the Axioms. The 12th Axiom of Euclid is, that " if a straight line meets two straight lines, so as to make the two interior...produced, shall at length meet upon that side on which are th*i angles "which ire less than two right angles." Instead of this proposition, which, though true,...
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