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" The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle. "
The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... - Page 79
by Euclides - 1816 - 528 pages
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Designing Valve Gearing

Edward J. Cowling Welch - Steam-engines - 1875 - 283 pages
...Elements, and stated in the enunciation to be, that "in a circle the angle in a semicircle is a rig/lit angle ; but the angle in a segment greater than a...than a semicircle is greater than a right angle," is the basis upon which the system, applied in the following pages, is directly founded : and it is...
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Elements of geometry, based on Euclid, books i-iii

Edward Atkins - 1876 - 119 pages
...AD is equal to the arc DB. Therefore, the given arc is bisected in DQEF Proposition 31. — Theorem. In a circle, the angle in a semicircle is a right...than a semicircle is greater than a right angle. Let ABC be a circle, of which BC is a diameter, and E the centre; and draw CA, dividing the circle into...
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Examination Christmas,1875

Education Department,London - 1876
...inscribed quadrilateral and the opposite exterior angle meet in the circumference. SECTION III. 1. In a circle, the angle in a semicircle is a right...less than a semicircle is greater than a right angle. The greatest rectangle that can be inscribed in a circle is a square. Divide a circle into two segments,...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - Geometry, Plane - 1876 - 403 pages
...the angle in a lemicircle i3 a right angle ; but the angle in a segment greater than a semicircle ii less than a right angle ; and the angle in a segment...angle. Let ABCD be a circle, of which the diameter isBC, and center E, and let CA be drawn, dividing the circle into the segments ABC, ADC. Join BA, AD,...
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Annual Report

1876
...Give the algebraical equivalent of this proposition. 6. The angle in a semi-circle is a right angle, the angle in a segment greater than a semi-circle is less than a right angle, and in a segment less than a semi-circle it is greater than a right angle. Show how this follows from the...
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Modern geometry [ed.] with an appendix by W.B. Jack

Richard Wormell - 1876
...is a right angle ; the angle in a segment less than a semicircle is greater than a right angle ; and the angle in a segment greater than a semicircle is less than a right angle. Let А В be a diameter and А С a chord of a circle, ADBE ; then Л А С В in the semicircle AC...
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Report of Her Majesty's Civil Service Commissioners: Together ..., Volume 21

1877
...points, and touching a given circle. 7. In any circle, the angle in a semicircle is a right angle, and the angle in a segment greater than a semicircle is...less than a semicircle is greater than a right angle. The sides of two acute-angled triangles inscribed in the same circle cannot intersect in fewer than...
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Mathematical Exercises ...: Examples in Pure Mathematics, Statics, Dynamics ...

Samuel H. Winter - 1877 - 413 pages
...Prove by means of the equation to a circle that the angle in a semicircle is a right angle, and that the angle in a segment greater than a semicircle is less than a right angle. 13. Find the equation to the tangent of an ellipse; prove that from a given point two tangents can...
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The elements of plane geometry, from the Sansk. text of Ayra Bhatta, ed. by ...

Āryabhaṭa - 1878
...if the centre falls without the triangle, the angle opposite to the side beyond which it is, being in a segment less than a semicircle, is greater than a right angle (24. cor.}. Conversely, if the given trwngle le acute-angled, tht centre of the circle falls within...
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Examination Papers: Moderations

University of Oxford - Education, Higher - 1879
...circumference 011 the same base, that is, on the same arc. 7. Inscribe a circle in a given square. 8. In a circle the angle in a semicircle is a right angle...less than a semicircle is greater than a right angle. 9. Draw a straight line from a given point, either without or in the circumference, which shall touch...
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