 | Dugald Stewart - 1829 - 418 pages
...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... | |
 | Dugald Stewart - 1829 - 442 pages
...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... | |
 | John Playfair - Euclid's Elements - 1832 - 358 pages
...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... | |
 | Euclid - Euclid's Elements - 1833 - 216 pages
...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,... | |
 | John Radford Young - Geometry, Modern - 1833 - 240 pages
...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... | |
 | Robert Simson - Trigonometry - 1835 - 544 pages
...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... | |
 | Euclid - 1835 - 540 pages
...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... | |
 | John Playfair - Euclid's Elements - 1835 - 336 pages
...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... | |
 | John Playfair - Geometry - 1836 - 148 pages
...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... | |
 | John Playfair - Euclid's Elements - 1836 - 488 pages
...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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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... 
