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" ... therefore the angle ACB is equal to the angle CBD. And because the straight line BC meets the two straight lines AC, BD, and makes the alternate angles ACB, CBD equal to one another, AC is parallel to BD. "
Elements of Geometry, Conic Sections, and Plane Trigonometry - Page 34
by Elias Loomis - 1871 - 58 pages
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Mathematics - 1806 - 320 pages
...other anglesb, each to each, to which the equal sides are opposite ; therefore the angle ACB is equal to the angle CBD ; and because the straight line BC meets the two straight lines AC, BD, and makes the alternate angles ACB, CBD equal to one another, AC is parallel0 to BD ; and it was shown...
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 354 pages
...angles (4. 1.), each to each, to which the equal sides are opposite ; therefore the angle ACB is equal to the angle CBD ; and because the straight line BC meets the two straight lines AC, BD, and makes the alternate angles ACB, CBD equal to ofie another, AC is parallel (27. 1.) to BD ; and...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - Geometry - 1821 - 514 pages
...angles, (4. I.) each to each, to which the equal sides are opposite: therefore the angle ACBis equal to the angle CBD; and because the straight line BC meets the two straight lines AC, BD, and makes the alternate angles ACB, CBD equal to one another, AC is parallel (_7. 1.) to BD; and it...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - Mathematics - 1825 - 1046 pages
...angles, (4. 1 .) each to each, to which the equal sides are opposite ; therefore the angle ACB is equal to the angle CBD ; and because the straight line BC meets the two straight lines AC, BD, and makes the alternate angles ACB, CBD, equal to one another, AC is parallel (17. 1 .) to BD -, and...
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - Trigonometry - 1827 - 546 pages
...angles*, each to each, to *4. 1. which the equal sides are opposite : therefore the angle ACB is equal to the angle CBD : and because the straight line BC meets the two straight lines AC, BD, and makes the alternate angles ACB, CBD equal to one another, AC is parallel * to BD : and it was shewn...
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Geometry Without Axioms; Or the First Book of Euclid's Elements. With ...

Thomas Perronet Thompson - Euclid's Elements - 1833 - 168 pages
...wherefore the J *• 4> third side AC isj equal to the third side DB, and the angle ACB to the angle DBC. And because the straight line BC meets the two straight lines AC, BD, and the alternate angles ACB, DBC *I.27.Cor.l. are equal to one another ; AC is* parallel to BD. And...
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The Elements of Euclid: viz. the first six books, together with the eleventh ...

Robert Simson - Trigonometry - 1835 - 544 pages
...sides are Book I. opposite : therefore the angle ACB is equal to the angle CBD ; v— •/•»•• and because the straight line BC meets the two straight lines AC, BD, and makes the alternate angles ACB, CBD equal c 27. 1. to one another, AC is parallel0 to BD; and it...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 540 pages
...equal sides are Book I. opposite : therefore the angle ACB is equal to the angle CBD ; v-— Y"*-' and because the straight line BC meets the two straight lines AC, BD, and makes the alternate angles ACB, CBD equal c 27. l. to one another, AC is parallel c to BD ; and...
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Elements of Plane Geometry According to Euclid

Andrew Bell - Euclid's Elements - 1837 - 290 pages
...other angles, each to each, to which the equal sides are opposite ; therefore the angle ACB is equal to the angle CBD ; and because the straight line BC meets the two straight lines AC, BD, and makes the alternate angles ACB, CBD, equal to one another, AC is parallel to BD (I. 27) j and it...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1837 - 410 pages
...therefore the base AC is equal (I. 4. part 1.) to the base BD, and (I. 4. part 3.) the angle ACB to CBD; and because the straight line BC meets the two straight lines AC, BD, and makes the alternate angles ACB, CBD equal, AC is parallel (I. 27.) to BD ; and it has been shown...
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