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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 2
των Euclides - 1853 - 147 σελίδες
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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 - 488 σελίδες
...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...

Studies and Exercises in Formal Logic: Including a Generalisation of Logical ...

John Neville Keynes - 1928 - 580 σελίδες
...proposition and its contrapositive ; for example, between Euclid's twelfth 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 that are less than two right angles," and the second part of the...

Manuel de kingwana: le dialecte occidental de swahili

John Whitehead, L. F. Whitehead - 1928 - 514 σελίδες
...lines cannot enclose a space Ii. AU right angles are equal to one another. I2. If a straight line meet two straight lines, so as to make the two interior...it taken together less than two right angles, these two straight lines being continually produced shall at length meet on that side on which are tht angles...

Condensed Encyclopedia of Engineering: A Compact Work of Reference ...

Franklin D. Jones - 1928 - 1256 σελίδες
...a space, n. All right angles are equal to one another. 12. If a straight line intersects two other straight lines, so as to make the two interior angles...side of it taken together less than two right angles, then these straight lines, if continually produced, must meet upon the side on which the angles are...

Popular Science Monthly, Τόμος 68

1906 - 600 σελίδες
...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 - 580 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 - 256 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 - 310 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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