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" The opposite angles of any quadrilateral figure inscribed in a circle, are together equal to two right angles. "
The figures of Euclid with the enunciations, as printed in Euclid's Elements ... - Page 40
by Euclides - 1840
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Guide to the army - competitive examinations

Alexander Hadden Hutchinson - 1861 - 128 pages
...of balls in an incomplete pile of 20 courses, with 44 balls in each side of the base. 5. Prove that the opposite angles of any quadrilateral figure inscribed...a circle, are together equal to two right angles. If AB, CD be the opposite sides of a quadrilateral circumscribing a circle whose centre is E, prove...
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Examination papers used at the examination of candidates for appointment to ...

War office - 1861 - 260 pages
...from the opposite angle. Prove this only when the triangle has an obtuse angle. 3. The opposite angle of any quadrilateral figure inscribed in a circle, are together equal to two right angles. 4. Triangles and parallelograms of the same altitude are to one another as their bases. 5. If two parallel...
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Euclid's Elements of geometry, books i. ii. iii. iv

Euclides - 1862 - 140 pages
...2.) Conclusion. — Therefore, the angles in the same segment, &c. QED PROPOSITION 22.— THEOREM. The opposite angles of any quadrilateral figure inscribed...a circle, are together equal to two right angles. (References— Prop. 1. 32; III. 21.) Hypothesis. — Let ABCD be a quadrilateral figure inscribed...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson ...

Robert Potts - 1865 - 528 pages
...whole angle BED. (ax. 2.) Wherefore the angles in the same segment, &c. QED PROPOSITION XXn. THEOREM. The opposite angles of any quadrilateral figure inscribed...a circle, are together equal to two right angles. Let ABCD be a quadrilateral figure in the circle AB CD. Then any two of its opposite angles shall together...
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The College Euclid: Comprising the First Six and the Parts of the Eleventh ...

Euclides - 1865 - 402 pages
...III. 20. 2. The angles in the same segment of a circle are equal to one another. ........ m. 21. 3. The opposite angles of any quadrilateral figure inscribed...in a circle, are together equal to two right angles . . . HI. 22. 4. In equal circles, equal angles stand upon equal arcs, whether the angles be at the...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...whole angle BED. [Axiom 2. Wherefore, the angles in the same segment &c. QED PROPOSITION 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 inscribed in the circle ABCD : any two of its opposite angles shall...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1868 - 434 pages
...angle BED. (ax. 2.) Wherefore the angles in the same segment, &c. QEI». PROPOSITION XXII. THEOREM. The opposite angles of any quadrilateral figure inscribed...a circle, are together equal to two right angles. Let AB CD be a quadrilateral figure in the circle A BCD. Then any two of its opposite angles shall...
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Elementary Geometry, Volume 2

James Maurice Wilson - Geometry - 1868 - 150 pages
.... 13 COR. 3. The angle in a semicircle is a right angle . . 13 COR. 4. The opposite angles of every quadrilateral figure inscribed in a circle are together equal to two right angles . 14 COR. 5. The locus of a point at which a given straight line subtends a constant angle is an arc...
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Modern Methods in Elementary Geometry

E. M. Reynolds - Geometry - 1868 - 172 pages
...= £ the convex angle A OS. Therefore ADS + ACS = ^{AOS + AOB], Therefore ADB + ACS = 2fi. COR. 1. The opposite angles of any quadrilateral figure inscribed in a circle are equal to 2R. COB. 2. The angle on a semicircumference or in a semicircle is a right angle. COR. 3....
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Minutes of the General Council of Medical Education & Registration ..., Volume 6

General Medical Council (Great Britain) - 1869 - 402 pages
...drawn from the centre to the point of contact is perpendicular to the line touching the circle. 8. The opposite angles of any quadrilateral figure inscribed...in a circle are together equal to two right angles. 9. From a given circle to cut off a segment which shall contain an angle equal to a given rectilineal...
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