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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 Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... - Page 23
by Euclides - 1816 - 528 pages
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The Elements of Euclid: viz. the first six books, together with the eleventh ...

Euclid, Robert Simson - Euclid's Elements - 1806 - 518 pages
...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 ; but...two right angles, do meet* together if continually produced ; therefore • 12. •. the straight lines AB, CD, if produced far enough, shall meet ;...
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1814
...the angles BGH, GHD; but the angles AGH, BGH, are equal3 to two right 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, make the interior angles on the same side...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - Mathematics, Greek - 1821 - 516 pages
...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; but...upon them, make the interior angles on the same side leas than two right angles, do meet (12 ax.)* together if continually produced; therefore the straight...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - Mathematics - 1825 - 372 pages
...BGH, GHD ; but the angles AGH, BGH are equal (13. 1.) to two right angles ; therefore the angles HGH, GHD ; 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....
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - Trigonometry - 1827 - 513 pages
...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 : but...angles on the same side less than two right angles, will meet * together if continually produced; therefore the straight lines AB, CD, if produced far...
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The Elements of Euclid: viz, the first six books, together with the eleventh ...

Euclid, Robert Simson - Geometry - 1829 - 516 pages
...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; but...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...
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1834
...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 on the same side less than two right angles, will meet * together if continually produced; * 12 A*, 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 ...

Euclid, John Davidson - 1835 - 513 pages
...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 ; but...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 - 1837 - 390 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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