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" An angle in a segment is greater than, equal to, or less than, a right angle, according as the segment is less than, equal to, or greater than, a semicircle. "
New Plane Geometry - Page 131
by Wooster Woodruff Beman, David Eugene Smith - 1899 - 252 pages
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Calendar of the University of Sydney

University of Sydney - 1853 - 810 pages
...drawn through a given point in one of the sides. 8. Prove that the angle in a segment of a circle is greater than, equal to, or less than a right angle, according as the segment is less than a semicircle, actually a semicircle, or greater than a semicircle. A is a fixed point on the circumference...
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The Elements of Euclid: With Many Additional Propositions ..., Part 1

Euclid - Geometry - 1853 - 176 pages
...substituted for the tedious one given by Euclid, who divides this proposition into three cases, namely, when the segment is less than, equal to, or greater than a semicircle. PROPOSITION XXVI. THEOREM. — If equal angles (BAC and EDF, or BGC and EHF) are in equal circles (ABC...
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The Calendar of Owens college, Manchester

Manchester univ - 1872 - 380 pages
...opposite sides, show that the parallelogram is a rhombus. 6. The angle in a segment of a circle is greater than, equal to, or less than a right angle,...less than, equal to, or greater than a semicircle. triangle ABC, and another AE perpendicular to the side BC, meeting BC in D, E; AD is bisected in F...
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Elements of Euclid Adapted to Modern Methods in Geometry

Euclid, James Bryce, David Munn (F.R.S.E.) - Geometry - 1874 - 236 pages
...less thau the squares on BA and AC. But DAC is a right angle ; (Const.) therefore the angle BAC is greater than, equal to, or less than a right angle, according as the square on BC is greater than, equal to, or less than the squares on BA and AC. QED APPENDIX TO BOOK...
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Elementary geometry

James Maurice Wilson - 1878 - 450 pages
...line subtends a constant angle is an arc of a circle of which that line is the chord. THEOREM 15. The angle in a segment is greater than, equal to, or less...angle, according as the segment is less than, equal tci, or greater than a semicircle*. ELEMENTARY GEOMETRY. Part. En. Let AB be a diameter of a circle,...
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Syllabus of plane geometry, books 1-3, corresponding to Euclid, books 1-4 ...

Mathematical association - 1883 - 86 pages
...which that line subtends a constant angle is an arc of which that line is the chord. THEOR. 15. The angle in a segment is greater than, equal to, or less...less than, equal to, or greater than a semicircle. [By Theor. 13.] THEOR. 16. A segment is less than, equal to, or greater than a semicircle, according...
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The Elements of Geometry

George Bruce Halsted - Geometry - 1885 - 389 pages
...quadrilateral are supplemental.) From hypothesis, .*. ^ A = ^ F, .'. A is on the arc DFB. THEOREM XIX. 383. The angle in a segment is greater than, equal to, or less than, a right angle, according as the arc of the segment is less than, equal to, or greater than, a semicircle. HYPOTHESIS. Lei AD 60 a diameter...
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The Elements of Geometry

George Bruce Halsted - Geometry - 1886 - 394 pages
...are supplemental.) From hypothesis, .-. £ A = £ F, .: A is on the arc DFB. THEOREM XIX. 383. The angle in a segment is greater than, equal to, or less than, a right angle, according as the arc of the segment is less than, equal to, or greater than, a semicircle. HYPOTHESIS. Let AD be a diameter...
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Plane and Solid Geometry

Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 344 pages
...fixed points is an arc. Let the student state the converse in full, and give the proof. Theorem 12. An angle in a segment is greater than, equal to, or...greater than, equal to, less than a right angle. Proof. Draw OB, OD ; then 1. ZAED>rt. Z, -.- it = £ reflex Z AOD. Th. 11 2. ZAEC = rt. Z, " " st. ZAOC. Why?...
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Plane and Solid Geometry

Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 346 pages
...sectors, the greater has the greater angle. Law of Converse, from th. 1, cors. 1, 2. 2. A central angle is greater than, equal to, or less than a right angle, according as the arc on which it stands is greater than, equal to, or less than a quadrant. (Why ?) Section 2. — Chords...
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