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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 Works of Dugald Stewart: Elements of the philosophy of the human mind

Dugald Stewart - 1829
...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 Works of Dugald Stewart: Elements of the philosophy of the human mind

Dugald Stewart - 1829
...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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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - 1832 - 333 sider
...before the llth is accounted the 10th. The 12th Axiom of Euclid is, that " if a straight line meet two " straight lines, so as to make the two interior...the angles which are less than two right angles." Instead of this proposition, which, though true, is by no means selfevident; another that appeared...
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Elements of Geometry with Notes

John Radford Young - 1833 - 216 sider
...proposition Legendre is enabled to demonstrate Euclid's twelfth axiom, viz. ; If a straight line meet two straight lines so as to make the two interior angles on the same side \T> HAUM T> of it, taken together, less than two right angles, these straight lines being continually...
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The First Six Books of the Elements of Euclid: With Notes

Euclid - 1833 - 183 sider
...equal to one another. 12. If a right line meet two right lines, so as to make See N. .the two internal angles on the same side of it taken together less than two right angles ; these right lines, being continually produced, shall at length meet upon that side on which are the angles,...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 513 sider
...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...the angles which are less than two right " angles. See the notes on Prop. 29. of Book I." PROPOSITION I. PROBLEM. To describe an equilateral triangle...
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The Elements of Euclid: viz. the first six books, together with the eleventh ...

Robert Simson - 1835 - 513 sider
...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...the angles which are less than two right " angles. See the notes on Prop. 29. of Book I." PROPOSITION I. PROBLEM. To describe an equilateral triangle...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1835 - 316 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 to make the two interior angles on the•same side of it taken " together less than two right angles, these straight lines being continually...
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The Element of Geometry

John Playfair - 1836 - 114 sider
...same distance from each other (Cor. 11. 2.), BC will then meet AB. Therefore, if a straight line meet two straight lines, so as to make the two interior...that side on which are the angles, which are less thau two right angles. Which was to be proved. i PROP. XIV. THEOR. Parallelograms of equal base and...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1836 - 311 sider
...Axioms, and that which was before the llth, is accounted the 10th. The 12th Axiom of Euclid is, that " if a straight line " meets two straight lines, so as to make the two inte" rior angles on the same side of it taken together less " than two right angles, these straight...
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