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" That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles. "
The first six books of the Elements of Euclid, with numerous exercises - Σελίδα 21
των Euclides - 1853 - 147 σελίδες
Πλήρης προβολή - Σχετικά με αυτό το βιβλίο

Stewart's specific subjects. Euclid. [1st] (-3rd stage). [With 2 issues of ...

Stewart W. and co - 1884
...than BGH, GHD ; but the angles AGH, BGH, are equal to two right angles ; therefore the angles BGH GHD, are less than two right angles; but those straight...the same side less than two right angles, do meet together if continually "oduced ; therefore the straight lines AB, CD, if oduced far enough, shall...

An introduction to geometry, consisting of Euclid's Elements, book ..., Τόμος 1

Euclides - 1884
...than BGH&nd GHD. (Ax. 4) But AGH and BGH are equal to two right angles ; (1. 13) therefore BGH and GHD are less than two right angles ; "but those straight lines which, with another falling upon them, make the interior angles on the same side of it together less than two right angles,...

Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Adrien Marie Legendre, Charles Davies - 1885 - 512 σελίδες
...PROPOSITION XXI. THEOREM. // two straight lines intersect a third straight line, making the sum of the interior angles on the same side less than two right angles, the two lines will meet if sufficiently produced. Let the two lines CD, IL, meet the line EF, making...

Elements of Plane Geometry

Alan Sanders - 1901 - 247 σελίδες
...also bisected. PROPOSITION XX. THEOREM 127. If two lines are cut by a transversal, making the sum of the interior angles on the same side less than two right angles, the lines will meet if sufficiently produced. Let AB and CD be cut by EF, making Z 1 + Z 2 < 2 KA's....

The Monist, Τόμος 13

1903
...to prop up the argument that proves the equality of alternate angles on parallels, viz. , that — "those straight lines which, with another straight...the same side less than two right angles, do meet if continually produced." This is exactly the point to be proved, for it is only one form of the conception...

Introduction and books 1,2

Euclid - 1908
...right angles are equal to one another. \ 5. That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than...

Pure Mathematics

Leslie Leland Locke - 1909 - 324 σελίδες
...all right angles are equal to one another. 5. That if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than...

Monographs on Topics of Modern Mathematics: Relevant to the Elementary Field

Jacob William Albert Young - 1911 - 416 σελίδες
...fifth postulate of Euclid reads as follows: "If a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, the two lines, if produced indefinitely, meet on that side on which are the angles less than two right...

Monographs on Topics of Modern Mathematics: Relevant to the Elementary Field

Jacob William Albert Young - 1911 - 416 σελίδες
...by Euclid in his Postulate 5 as follows : " If a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than...

Memorabilia Mathematica; Or, The Philomath's Quotation-book

Robert Édouard Moritz - 1914 - 410 σελίδες
...2007. Euclid's Postulate 5 [The Parallel Axiom]. That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than...




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