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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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Civil service guide

Robert Johnston (F.R.G.S.) - Civil service - 1872 - 178 pages
...in a semicircle is a right angle; but the an?le in a segment greater than a semicircle is less tban a right angle ; and the angle in a segment less than a semicircle is greater than a right angle. ALGEBRA. I. Specimen Paper. (Time, 3 hours.) 1. Find (1) the sum, (2) the difference, of the two expressions...
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Euclid's Elements of Geometry

Euclid - Geometry - 1872 - 261 pages
...Prop. 21. B. 3), and therefore the angle ABC is also less than a right angle. PART 3.— The angle ABC in a segment less than a semicircle is greater than a right angle. For assume in the opposite circumference any point D, and draw DA and DC. semicircle, is less than...
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Elements of geometry, containing the first two (third and fourth ..., Part 2

Euclides - 1872
...angle in a semicircle is a right anglt and the angle in a segment greater than a semicircle is fe^ than a right angle; and the angle in a segment less than < semicircle is greater than a right angle. Let ABC be a , of which O is the centre and BC diameter....
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The Acting Teacher's and Student's in Training Guide and Text Book for ...

Henry Major - Student teachers - 1873
...DC, if produced, passes through the centre: therefore the arc AD is equal to the arc DB. XXXI. — In a circle the angle in a semicircle is a right angle...than a semicircle is greater than a right angle. Let BC be a diameter, and the centre E, and draw CA, dividing the circle into the segments ABC, ADO Join...
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The Elements of Euclid, containing the first six books, with a selection of ...

Euclides - 1874
...equal to the arc DB. Therefore the given arc ADJB 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 A BCD be a circle, of which the diameter is BC, and centre E ; and let CA be drawn, dividing the circle...
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Pure mathematics, Volume 1

Edward Atkins - 1874
...is equal to the arc DB. Therefore, the given arc is bisected in DQJE.F. 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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Euclidian Geometry

Francis Cuthbertson - Euclid's Elements - 1874 - 349 pages
...three / s of &AFB, and .-. = two right angles. (i. 24) Similarly it may be proved that PROPOSITION XVI. In a circle, the angle in a semicircle is a right...than a semicircle is greater than a right angle. Let A PB be a of which C is the centre, ACB a diameter, and AP a chord dividing the APB into the...
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Pure mathematics, Volume 1

Edward Atkins - 1874
...DQEF Proposition 31. — Theorem. In a circle, the angle in a semicircle is a right angle; but t/ie angle in a segment greater than a semicircle is less...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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Elements of Euclid [selections from book 1-6] adapted to modern methods in ...

Euclides - 1874
...is a right angle, an angle in a segment less than a semicircle is greater than a right angle, and an angle in a segment greater than a semicircle is less than a right angle. For the angle AOB at the centre may be increased till it becomes two right angles (I. Def. 9), then...
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Designing Valve Gearing

Edward J. Cowling Welch - Steam-engines - 1875 - 283 pages
...3ist Proposition of the 3rd Book of Euclid's Elements, and stated in the enunciation to be, that " in a circle the angle in a semicircle is a right angle...less 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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