 | Henry Longueville Mansel - Logic - 1851 - 350 pages
...character, analogous to the geometrical principles, " two straight lines cannot enclose a space," or, " if a straight line meets two straight lines, so as to make the two interior angles on the same side together less than two right angles, the two straight lines will meet if produced." As a matter of... | |
 | Euclides - 1852 - 48 pages
...inclose a space. 11. All right angles are equal to one another. 12. If a right line meet two other right lines, so as to make the two interior angles on the...it taken together less than two right angles, these two right lines being continually induced, shall at length meet on that side on which are the angles,... | |
 | Euclides - Geometry - 1853 - 334 pages
...parallel to FG; but both cannot. »^^F/ — 1 5- jf" * 3. — To BK. I. PEOP. A. If a straight line cut two straight lines, so as to make the two interior angles on the same side of it together less than two right angles : then these two straight lines, being continually produced, shall... | |
 | Euclid - Geometry - 1853 - 176 pages
...internal an£;^' '\ the same side, fS6g..£ ''• ' ^uol to two right I. 29, theor. . . I. 29, cor. . . If a straight line meets two straight lines so as to make the two internal angles on the same side together less than two right angles. {These '' stralgnt lines being... | |
 | William Somerville Orr - Science - 1854 - 534 pages
...crossed shall be meeting-lines. This is the twelfth axiom, and is thus expressed in Euclid : — AXIOM XII. — If a straight line meets two straight lines,...than two right angles, these straight lines, being prolonged, shall at length meet upon that side on which are the angles that are less than two right... | |
 | Dugald Stewart - 1854 - 454 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 - 1854 - 452 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... | |
 | Euclides - 1855 - 270 pages
...axiom, another, viz. , th " the whole is equal to all its parts taken together." at X. Two straight Unes cannot enclose a space. XI. All right angles are equal...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... | |
 | John Playfair - Geometry - 1855 - 334 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...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... | |
 | John Playfair - Euclid's Elements - 1856 - 346 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...' 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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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... 
