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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... "
The first six books of the Elements of Euclid, with numerous exercises - Σελίδα 4
των Euclides - 1853 - 147 σελίδες
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The national encyclopædia. Libr. ed, Τόμος 2

National cyclopaedia - 1884
...as stated by Euclid it is not a true axiom. It runs thus — 44 If a straight line meets two other straight lines, so as to make the two interior angles on the same side of it, taken j together, less than two right angles ; these straight lines, being continually produced, shall at...

Mathematical Questions and Solutions, Τόμος 42

1885
...as stated, AB would coincide with EF ; and thus is it proved that all right angles are equal.* Axiom XII.: — " If a straight line meets two straight...together, less than two right angles, these straight linos being continually produced, shall at length meet upon that side on which are the angles which...

Transactions and Proceedings of the New Zealand Institute, Τόμος 18

New Zealand Institute - 1886
...equivalence of the three forms of the parallel-axiom mentioned in my paper. Form (a), (Euclid's) is : — " If a straight line meets two straight lines, so as to make the two interior angles on the same I side of it taken together less than two right angles, these straight lines being continually produced...

A Mathematical Solution Book Containing Systematic Solutions to Many of the ...

Benjamin Franklin Finkel - 1888 - 481 σελίδες
...so as to make the two interior angles *For definitions of geometrical magnitudes, see Mensuration. on the same side of it taken together less than two...lines being continually produced shall at length meet on that side< on which are the angles which are less than, two right angles. An axiom must possess...

Circular[s] of Information, Τεύχη 1-3

1890
...in what is generally called the twelfth, by some the eleventh " axiom :" " If a straight line meet two straight lines so as to make the two interior...on the same side of it taken together less than two right-angles, these straight lines, being continually produced, shall at length meet on that side on...

The Teaching and History of Mathematics in the United States, Τόμοι 890-893

Florian Cajori - 1890 - 400 σελίδες
...consists in what is generally called the twelfth, by some the eleventh "axiom :" " If a straight line meet two straight lines so as to make the two interior...on the same side of it taken together less than two right-angles, these straight lines, being continually produced, shall at length meet on that side on...

The Harpur Euclid: An Edition of Euclid's Elements

Edward Mann Langley, W. Seys Phillips - 1890 - 515 σελίδες
...— Prove this proposition independently of Prop. 27. Ax. 12. — If a straight line meet two other straight lines so as to make the two interior angles on the same side of it together less than two right angles, these two straight lines being continually produced shall at length...

The Elements of Plane and Solid Geometry ...

Edward Albert Bowser - 1890 - 393 σελίδες
...straight line cut two other straight lines, (1) so as to make the exterior-interior angles equal, or (2) so as to make the two interior angles on the same side together equal to two right angles, then the two straight lines are parallel. xE (1) Hyp. Let the st....

Geometrical Researches on the Theory of Parallels

Nikolaĭ Ivanovich Lobachevskiĭ - 1891 - 50 σελίδες
...make equal alternate angles, he brings in the un wieldly postulate or axiom: " If a straight line meet two straight lines, so as to make the two interior...lines, being continually produced, shall at length meet on that side on which are the angles which are less than two right angles." Do you wonder that succeeding...

Educational Review

Nicholas Murray Butler, Frank Pierrepont Graves, William McAndrew - 1892
...required for use before proposition 14 of his first book. Also the axiom, " If a straight line meet two straight lines, so as to make the two interior...lines, being continually produced, shall at length meet on that side on which are the angles which are less than two right angles," is not required till proposition...




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