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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 94
by Euclides - 1841 - 351 pages
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Euclid's Elements of Geometry

Euclid - Geometry - 1872 - 284 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 - 102 pages
...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 - 592 pages
...arc AD is equal to the arc DB. XXXI. — In a circle the angle in a semicircle is a right angle ; but the angle in a segment greater than a semicircle is...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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Pure mathematics, Volume 1

Edward Atkins - 1874 - 424 pages
...in DQJE.F. Proposition 31. — Theorem. In a circle, the angle in a semicircle is a right angle; but the angle in a segment greater than a semicircle is...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 - 400 pages
...it may be proved that PROPOSITION XVI. In a circle, the angle in a semicircle is a right angle; but the angle in a segment greater than a semicircle is...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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The Elements of Euclid, containing the first six books, with a selection of ...

Euclides - 1874 - 342 pages
...in DQEF PROPOSITION 31. — Theorem. In a circle, the angle in a semicircle is a right angle ; but the angle in a segment greater than a semicircle is...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 - 428 pages
...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 Adapted to Modern Methods in Geometry

Euclid, James Bryce, David Munn (F.R.S.E.) - Geometry - 1874 - 234 pages
...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 - 244 pages
...stated in the enunciation to be, that " in a circle the angle in a semicircle is a right angle ; but the angle in a segment greater than a semicircle is...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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Elements of geometry, based on Euclid, books i-iii

Edward Atkins - 1876 - 130 pages
...bisected in DQEF Proposition 31. — Theorem. In a circle, the angle in a semicircle is a right angle; but the angle in a segment greater than a semicircle is...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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