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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. "
Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ... - Page 26
by Euclides - 1845
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Trigonometry - 1806 - 518 pages
...the angles BGH, GHD ; but the angles AGH, BGH are equal a to two right angles ; therefore a 13. 1. the angles BGH, GHD are less than two right angles...angles on the same side less than two right angles, do meet* together if continually produced ; therefore • 12. •. the straight lines AB, CD, if...
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1814 - 558 pages
...angles ; therefore the . 13. i. angles BGH, GHD, are less than two right angles; but those straight hnes which, with another straight line falling upon them,...angles on the same side less than two right angles, do meet* together it' continually * 12 Ax. produced ; therefore the straight lines AB, CD, if produced...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 528 pages
...angles BGH, GHD; but the angles AGH, BGH, are equal a to two right angles ; therefore the • 13. 1. angles BGH, GHD, are less than two right angles ;...angles on the same side less than two right angles, do meet* together if continually * ig AX.' produced; therefore the straight lines AB, CD, if produced...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - Mathematics - 1825 - 372 pages
...are less than two right angles ; but those straight lines which, with another straight line tilling upon them, make the interior angles on the same side less than two right angles, do meet (12. Ax.) together if continually produced; therefore the straight lines AB, CD, if produced...
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - Trigonometry - 1827 - 513 pages
...are greater f than the angles BGH, GHD : but the angles AGH, BGH are equal * to two right angles ; therefore the angles BGH, GHD are less than two right...angles, will meet * together if continually produced; therefore the straight lines AB, CD, if produced far enough, will meet : but they never meet, since...
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The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - Geometry - 1829 - 516 pages
...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...angles on the same side less than two right angles, do meet (12. ax.)* together if continually produced ; therefore the straight lines AB, CD, if produced...
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1834 - 518 pages
...the angles BGH, GHD : but the angles t AGH, BGH are equal * to two right angles ; therefore the * IS. angles BG.H, GHD are less than two right angles :...angles, will meet * together if continually produced; * 12 A*, therefore the straight lines AB, CD, if produced far enough, See lhe \ will meet : but they...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 540 pages
...greater than the angles BGH, GHD; but the angles AGH, a 13. 1. BGH are equal a to two right angles ; therefore the angles BGH, GHD are less than two right...angles on the same side less than two right angles, * 12. ax. do meet * together if continually produced ; therefore the se the straight lines AB, CD,...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1836 - 359 pages
...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...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid - Geometry - 1837 - 410 pages
...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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