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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 geometry, by T. S. Davies. Conic sections, by Stephen Fenwick - Seite 19
von Royal Military Academy, Woolwich - 1853
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid - 1837 - 410 Seiten
...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...them, make the interior angles on the same side less that two right angles, meet together, if continually produced ; therefore the straight lines AB, CD,...
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Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838 - 264 Seiten
...angles BGH, GBD: 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...line falling upon them, make the interior angles on nt . the same side less than two right angles, will meet* '- *' together if continually prolonged ;...
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - 1838 - 434 Seiten
...two right angles: but straight lines which with another straight line make the interior angles upon the same side less than two right angles do 'meet (12. Ax.) if produced far enough : therefore EB, FD shall meet, if produced towards B, D: let them meet in G,...
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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - 1841 - 378 Seiten
...* is. 1. the angles AGH, BGH are together equal* to two right angles; therefore the angles BGH, GHD are less than two right angles; but those straight...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...
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Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842 - 320 Seiten
...&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...
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845 - 544 Seiten
...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 ; but those straight...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...
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The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1845 - 380 Seiten
...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,...
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Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - 1845 - 218 Seiten
...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...
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The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846 - 292 Seiten
...it together less than two right angles, these straight lines, being produced, shall meet (Ax. 12) ; therefore the straight lines AB, CD, if produced far...meet — but they never meet, since they are parallel (Hyp.) : Therefore the angle AGH is not unequal to the angle GHD, that is, it is equal to it : But...
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The first three books of Euclid's Elements of geometry, with theorems and ...

Euclid, Thomas Tate - 1849 - 120 Seiten
...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 those straight...the same side less than two right angles, do meet (Ax. 12.) together if continually produced; therefore the straight lines AB, CD, if produced far enough,...
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