 | Adrien Marie Legendre - 1836 - 394 σελίδες
...angles. PROPOSITION XXI. THEOREM. If a straight line meet two other straight lines, making the sum of 'the interior angles on the same side less than two right angles, the two lines will meet if sufficiently produced. Letthe line EF meet the two lines CD, IH, making... | |
 | Euclid, James Thomson - 1837 - 410 σελίδες
...ax. 4.) than the angles BGH, GHD; but the angles AGH, BGH are equal (I. 13.) to two right angles ; therefore the angles BGH, GHD are less than two right angles. But (I. ax. 12.) those straight lines which, with another straight line falling upon them, make the interior... | |
 | Robert Simson - 1838 - 434 σελίδες
...greater than the angles BGH, GHD ; but the angles AGH, BGH are equal (13. 1.) to two right angles; therefore the angles BGH, GHD are less than two right...the same side less than two right angles, do meet (12. ax.) * together if continually produced ; therefore the straight lines AB, CD, if produced far... | |
 | Euclides - 1838 - 264 σελίδες
...are t4Ax greatert than the angles BGH, GBD: but the angles AGH, BGH are equal* to two right angles; ' therefore the angles BGH, GHD are less than two right...line falling upon them, make the interior angles on nt . the same side less than two right angles, will meet* '- *' together if continually prolonged ;... | |
 | Euclides - 1841 - 378 σελίδες
...than the angles BGH, GHD; but * is. 1. the angles AGH, BGH are together equal* to two right angles; therefore the angles BGH, GHD are less than two right...interior angles on the same side less than two right * 12 Ax. angles meet,* if far enough produced; therefore the straight lines AB, CD, if produced far... | |
 | Euclides - 1842 - 316 σελίδες
...&c. is made to depend upon an assumption that, if a line falling upon two other lines makes with them the interior angles on the same side less than two right angles, those lines must meet if produced. Now this is evidently a theorem which ought to have been previously... | |
 | Euclides - 1845 - 546 σελίδες
...than the angles BGH, GHD; fax. 4.) but the angles AGH, BGH are equal to two right angles ; (i. 13.) therefore the angles BGH, GHD are less than two right...angles on the same side less than two right angles, will meet together if continually produced ; (ax. 12.) therefore the straight lines AB, CD, if produced... | |
 | Euclid, James Thomson - 1845 - 382 σελίδες
...to two right angles : wherefore the angles BGH, GHD are less than two right angles. But (I. ax. 12) those straight lines, which with another straight...angles on the same side less than two right angles, meet together, if continually produced : therefore the straight fines AB, CD, if produced far enough,... | |
 | Euclid - 1845 - 218 σελίδες
...angle AGH is greater than the angle GHD, add to each of them the angle BGH ; therefore the angles AGH, falling upon them, make the interior angles on the same side less than two right angles, do meetJ together if con- I « AX. tinually produced ; therefore the straight lines AB, CD, if produced... | |
 | Euclides - 1846 - 292 σελίδες
...greater than the angles BGH, GHD : But the angles AGH, BGH, are equal to two right angles (1. 13) ; therefore the angles BGH, GHD, are less than two right angles : But if a straight line falls upon two straight lines, so as to make the two interior angles on the same... | |
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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. 
