 | Euclides - 1842 - 316 σελίδες
...That a circle may be described from any centre, at any distance from that centre. IV. [Ax. XI.] V. And that if a straight line meets two straight lines,...length meet upon that side on which are the angles less than two right angles. AXIOMS. I. THINGS which are equal to the same are equal to one another.... | |
 | James Bates Thomson - 1844 - 268 σελίδες
...the necessity of a new axiom. Euclid's axiom alluded to is this : " If a straight line meet two other 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 produced, will at length meet on the side on which... | |
 | Euclid, James Thomson - 1845 - 382 σελίδες
...to one another. |j 12. If a straight line meet two other straight lines which are in the same plane, so as to make the two interior angles on the same...together, less than two right angles, these straight lines shall at length meet upon that side, if they be continually produced.^ * ln this axiom and the following,... | |
 | Euclides - 1846 - 292 σελίδες
...to two right angles, and therefore the angles BEF, EFD are together less than two right angles : But If a straight line meets two straight lines, so as...make the two interior angles on the same side of it together less than two right angles, these straight lines, being continually produced, shall at length... | |
 | Dugald Stewart - 1847 - 666 σελίδες
...Euclid's Elements. When it is assorted, for example, that " if one straight line falls on two other straight lines, so as to make the two interior angles on the san»« side together equal to two right angles, these two straight lines, though indefinitely produced,... | |
 | Henry Longueville Mansel - 1851 - 350 σελίδες
...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 σελίδες
...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 - 334 σελίδες
...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 - 176 σελίδες
...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 - 534 σελίδες
...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, so as...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... | |
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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... 
