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" The opposite angles of any quadrilateral figure described in a circle, are toe/ether equal to two right angles. Let ABCD be a quadrilateral figure in the circle ABCD : any two of its opposite angles are together equal to two right angles. "
Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ... - Page 71
by Euclid - 1845 - 199 pages
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The essentials of geometry, plane and solid, as taught in French and German ...

John Reynell Morell - Geometry - 1871 - 156 pages
...quadrilateral is divided into two triangles, whose angles form those of the quadrilateral ; and as the three angles of every triangle are equal to two right angles or 180, the angles of the quadrilateral must be equal to four right angles or 300. From this it...
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Spirit and mind polarity, or The disentanglement of ideas

Arthur Young - Meditation - 1873 - 222 pages
...it is compelled to affirm, and does affirm this, with the same confidence as the propositition that the three angles of every triangle are equal to two right angles, or that two bodies cannot occupy the same space. Even this, notwithstanding it lies at the foundation...
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The Elements of Euclid, containing the first six books, with a selection of ...

Euclides - 1874 - 342 pages
...22. — Theorem. The opposite angles of any quadrilateral figure inscribed, in a circle, are together equal to two right angles. Let ABCD be a quadrilateral figure in the circle ABCD. Then any two of its opposite angles shall together be equal to two right angles. Construction. Join...
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Elements of Euclid Adapted to Modern Methods in Geometry

Euclid, James Bryce, David Munn (F.R.S.E.) - Geometry - 1874 - 234 pages
...angles are together equal to two right angles. Let ABCD be a quadrilateral figure inscribed in a circle, any two of its opposite angles are together equal to two right angles. Join the centre 0 to B and D. Then in both cases, the two angles at 0 are together double of the angle A...
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Pure mathematics, Volume 1

Edward Atkins - 1874 - 428 pages
...a semicircle, is less than a right angle. And, because ABCD is a quadrilateral figure in a circle, any two of its opposite angles are together equal to two right angles (III. 22); Therefore the angles ABC, ADC are together equal to two right angles. But the angle ABC...
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Designing Valve Gearing

Edward J. Cowling Welch - Steam-engines - 1875 - 244 pages
...than a semicircle, is less than a right angle. And because ABCD is a quadrilateral figure in a circle, any two of its opposite angles are together equal to two right angles (Euc. III. 22) ; therefore the angles ABC, ADC are together equal to two right angles. But the angle...
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Elements of geometry, based on Euclid, books i-iii

Edward Atkins - 1876 - 130 pages
...a semicircle, is less than a right angle. And, because ABCD is a quadrilateral figure in a circle, any two of its opposite angles are together equal to two right angles (III. 22); Therefore the angles ABC, ADC are together equal to two right angles. But the angle ABC...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - Geometry, Plane - 1876 - 446 pages
...THEOREM. The opposite angles of any quadrilateral figure inscribed in a circle, art together equal to twu right angles. Let ABCD be a quadrilateral figure in the circle ABCD. Then any two of its opposite angles shall together be equal to two right angles. Join ^ C, BD. And...
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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - Conic sections - 1877 - 458 pages
...is the sixth part of four right angles (Pr. 2, Sch. 1), or the third part of two right angles. Also, because the three angles of every triangle are equal to two right angles, the two angles OAB, OBA are together equal to two thirds of two right angles ; and since AO is equal to...
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The elements of plane geometry, from the Sansk. text of Ayra Bhatta, ed. by ...

Āryabhaṭa - 1878 - 100 pages
...right angles, a circle can be described about it. First let ABCD be a quadrilateral figure inscribed iu the circle ABCD. Any two of its opposite angles are together equal to two right angles. Because the angle ADB is equal to the angle ACB (P. 36) and the angle DCA to the angle DBA (P. 30)....
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