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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
Πλήρης προβολή - Σχετικά με αυτό το βιβλίο

Solid Geometry

Charles Austin Hobbs - 1921 - 216 σελίδες
...corresponding angles equal, the two lines are parallel. Prop. 41. If two lines are cut by a transversal so as to make the two interior angles on the same side of the transversal supplementary, the lines are parallel. Prop. 41, Cor. II. Two lines respectively perpendicular...

Tufts College Graduate, Τόμοι 1-2

1901
...far from "self-evident" it is the reader may judge for himself. "If a straight line meets two other straight lines so as to make the two interior angles...it taken together less than two right angles, these sides being continually produced shall at length meet on that side on which are the angles which are...

Popular Science Monthly, Τόμος 68

1906
...can not enclose a space. 11. All right angles are equal to one another. 12. 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. Modern objections to these...

Non-Euclidean Geometry: A Critical and Historical Study of Its Development

Roberto Bonola - 1955 - 452 σελίδες
...make equal alternate angles, he hrings m the unwieldly postulate or axiom: " If a straight line meet two straight lines, so as to make the two interior...less than two right angles, these straight lines, heing continually produced, shall at length meet on that side on which are the angles which are less...
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Research in Educational Administration: Cooperative Research Project No. F-2

University Council for Educational Administration - 1962 - 548 σελίδες
...primitive terms, for example, "point"; defined terms, for example, "triangle"; axioms, for example, "If a straight line meets two straight lines, so as to make two interior angles on the same side of it taken together less than two right angles, these straight...

Matters Mathematical

I. N. Herstein, Irving Kaplansky - 1978 - 246 σελίδες
...one another. But nothing up to this point has prepared us for the astonishing final axiom. AXIOM 12. If a straight line meets two straight lines, so as...lines, being continually produced, shall at length meet on that side on which are the angles which are less than two right angles. The axiom is illustrated...
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George Boole: Selected Manuscripts on Logic and its Philosophy

Ivor Grattan-Guinness, Gerard Bornet - 1997 - 236 σελίδες
...4. And that all right angles are equal to one another. 5. And that if a straight line meet two other straight lines so as to make the two interior angles...these straight lines being continually produced shall meet on that side on which are the angles which are less than two right angles. 6. And that two straight...
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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...than two right angles, these straight lines being I continually produced shall at length meet upon that side on which are the angles which are less than...

The American Mathematical Monthly: Devoted to the Interests of ..., Τόμοι 3-4

1896
...the two angles AKH and CfJK equal to two right angles. QED PROPOSITION XI. If a straight line meet two straight lines so as to make the two interior angles on the same side of it taken tdgethcr less than two light angles, these straight lines, being continually produced, shall at length...

Atti del V Congresso internazionale di filosofia, Napoli 5-9 maggio 1924 ...

Guido Della Valle - 1925 - 1183 σελίδες
...line. The furst runs as follows: « Two straight lines cannot enclose a space », and the second: « If a « straight line meets two straight lines, so as to make the two interior « angles on one side of it together less than two right angles, these strai« ght lines meet, if continually produced,...




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