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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... "
The Elements of Euclid, containing the first six books, with a selection of ... - Side 6
av Euclides - 1874
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The Collected Works of Dugald Stewart, Volum 3

Dugald Stewart - 1854
...Euclid's Elements. When it is asserted, for example, that " if one straight line falls on two other straight lines, so as to make the two interior angles on the same side together equal to two right angles, these two straight lines, though indefinitely produced, will never...
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The Collected Works of Dugald Stewart, Esq., F.R.SS., ...: Elements of the ...

Dugald Stewart - 1854
...Euclid's Elements. When it is asserted, for example, that " if one straight line falls on two other straight lines, so as to make the two interior angles on the same side together equal to two right angles, these two straight lines, though indefinitely produced, will never...
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1855
...at X. Two straight Unes cannot enclose a space. XI. All right angles are equal to one another. XII. If a straight line meets two straight lines, \ so...being \ continually produced, shall at length meet ' V ' 'L upon that side on which are the angles -which \ are less than two right angles. It H admitted...
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Elements of Geometry: Containing the First Six Books of Euclid with a ...

John Playfair - 1855 - 318 sider
...self-evident propositions. It is therefore removed from among the Axioms. The 12th Axiom of Euclid is, that " if a straight line meets two straight lines, so as...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 - 1856 - 318 sider
...self-evident propositions. It is therefore removed from among the Axioms. The 12th Axiom of Euclid is, that " if a straight line meets two straight lines, so as...' 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
...X. Two straight lines cannot inclose a space. XI. All right angles are equal to one another. xn. " If a straight line meets two straight lines, so as...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
...must be equal ; and consequently the angles measured by those equals must themselves be equal. 12. If a straight line meets two straight lines, so as...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 Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1860 - 361 sider
...part. X. Two straight lines cannot enclose a space. XI. All right angles are equal to one another. XII. If a straight line meets two straight lines, so as...are the angles which are less than two right angles. PROPOSITION I. PROBLEM. To describe an equilateral triangle upon a given finite straight line. Let...
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The Elements of Euclid with Many Additional Propositions and Explanatory Notes

Eucleides - 1860
...opposite angle upon the same side, And also the two internal angles on the . same side, together equal to two right ^ angles. These straight lines being continually...that side on which are the angles which are less than tiro right angles. f They are equidistant. They are parallel to each other. They are themselves equal...
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Euclid's plane geometry, books iii.-vi., practically applied; or, Gradations ...

Euclides - 1861
...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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