 | John Michels (Journalist) - 1895 - 758 σελίδες
...his " eleventh axiom "). This postulate refers to two lines cut by a transversal, and states that if the sum of the interior angles on one side of the transversal be less than two right angles the lines will meet on this side if sufficiently produced. The numerous... | |
 | John Michels (Journalist) - 1895 - 818 σελίδες
...his " eleventh axiom "). This postulate refers to two lines cut by a transversal, and states that if the sum of the interior angles on one side of the transversal be less than two right angles the lines will meet on this side if sufficiently produced. The mimerons... | |
 | Florian Cajori - 1896 - 324 σελίδες
...CANTOR, I., 389, for the proofs. 2 Consult CANTOR, I:, p. 392 ; Gow, p. 297. is the assertion that, in case of parallelism, the sum of the interior angles...on one side of the transversal must be the same as their sum on the other side of the transversal. Ptolemy appears to be the first of a long line of geometers... | |
 | William Henry Chandler - 1898 - 630 σελίδες
...perpendicular to a third: or both parallel to a third: or make alternate interior angles equal, or the sum of the interior angles on one side of the transversal equal to two right angles, they are parallel. If the lines are given by their equations, they will... | |
 | 1917 - 906 σελίδες
...postulate, over which the controversy has raged., namely: If two lines are cut by a transversal, making the sum of the interior angles on one side of the transversal together less than two right angles, the lines if sufficiently produced will meet on the side on which... | |
 | Herbert Ellsworth Slaught, Nels Johann Lennes - 1910 - 300 σελίδες
...is true because its converse is true. 99. THEOREM. // two parallel lines are cut by a transversal, the sum of the interior angles on one side of the transversal is two right angles. Suggestion. Make use of the preced- - , / , - z. ing theorem and give the proof... | |
 | Herbert Ellsworth Slaught, Nels Johann Lennes - 1910 - 304 σελίδες
...Z 3 = Z 2. Z3 = Z1. (§74) .-. Zl =Z2. (Ax. IV) 93. THEOREM. // two lines cut by a transversal have the sum of the interior angles on one side of the transversal equal to two right angles, the lines are parallel. A -Z, Given l± and 72 cut by t so that Z4 + Z2=2rt.... | |
 | John Wesley Young, Albert John Schwartz - 1915 - 248 σελίδες
...4. .-.AB\\CD. Why? 165. COROLLARY. When two straight lines in a plane are cut by a transversal, if the sum of the interior angles on one side of the transversal is less than two right angles, the two straight lines must meet (§ 158). Exercise. When two straight... | |
 | Edith Long, William Charles Brenke - 1916 - 292 σελίδες
...Euclid assumed that, when two lines AB and CD are crossed by a transversal (see figure on page 42), if the sum of the interior angles on one side of the transversal is less than a straight angle, the lines AB and CD, if produced, will meet on that side of the transversal.... | |
 | Edith Long, William Charles Brenke - 1916 - 292 σελίδες
...Euclid assumed that, when two lines AB and CD are crossed by a transversal (see figure on page 42), if the sum of the interior angles on one side of the transversal is less than a straight angle, the lines AB and CD, if produced, mil meet on that side of the transversal.... | |
| |
CD are crossed by a transversal (see figure on page 42), if the sum of the interior angles on one side of the transversal is... 
