| Henry Longueville Mansel - 1851 - 320 Seiten
...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
...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 - 1853
...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 - 1853 - 136 Seiten
...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 - 1854
...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
...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
...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
...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 - 1855 - 318 Seiten
...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 - 1856 - 318 Seiten
...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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