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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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Manual

1903 - 898 pages
...number of such quadrilateiuls can be drawn. 2. Show that an angle in a semicircle is a right angle, an angle in a segment greater than a semicircle is less than a light angle, and an angle in a segment less than a semicircle is greater than a right angle. Two fixed...
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A Text-book of Euclid's Elements for the Use of Schools, Book 1

Euclid - Euclid's Elements - 1904 - 488 pages
...into three, four, or six equal parts. PROPOSITION 31. THEOREM. The angle in a semicircle is a right angle. The angle in a segment greater than a semicircle is less than a right angle. The angle in a segment less than a semicircle is greater than a right angle. F, Let ABCD be a circle,...
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The Educational Ideas of Pestalozzi

John Alfred Green - Education - 1905 - 266 pages
...ANGULAR PROPERTIES. THEOREM [ AC.4J. — (i) Any angle In a semi-circle In a right angle, (ii) Any angle in a segment greater than a semicircle is less than a right angle, (iii) Any angle in a segment less than a semi-circle is greater than a right angle. In Figs. 290, 291,...
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Calendar, Part 1

University of Calcutta - Universities and colleges - 1907 - 458 pages
...points on the same side of it, the four points lie on a circle. The angle in a semi-circle is a right angle ; the angle in a segment greater than a semi-circle...than a semi-circle is greater than a right angle. The opposite angles of any quadrilateral inscribed in a circle are supplementary ; and the converse....
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Calendar

University of Allahabad - 1907 - 528 pages
...points on the same side of it, the four points lie on a circle. The angle in a semi-circle is a right angle, the angle in a segment greater than a semi-circle...less than a semicircle is greater than a right angle. The opposite angles of any quadrilateral inscribed in a circle are supplementary ; and the converse....
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Calendar, Part 3

University of Calcutta - 1907 - 446 pages
...draw the least possible chord. 4 6. In a circle the angle in a semicircle is a right angle, bnt the 8 angle in a segment greater than a semicircle is less...less than a semicircle is greater than a right angle. AB is a fixed diameter of a given circle, and PQ a variable chord of 7 length eqnal to the radius:...
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Calendar

University of Allahabad - 1908 - 566 pages
...points on the same side of it, the four points lie on a circle. . 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 the ancrle in a segment less than a semicircle is greater than a light angle. The opposite angles of any...
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The Practice of Navigation and Nautical Astronomy

Henry Raper - Nautical astronomy - 1908 - 1020 pages
...the arc BDC, that is, by a quantity less than half 180 (No. 140), is less than a right angle. 143. The angle in a segment less than a semicircle is greater than a right angle. The segment BAG being less than a semicircle, the segment BDC must be greater than a semicircle, and...
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Intermediate Geometry: Being Sections V and VI of "geometry, Theoretical and ...

Walter Percy Workman - Geometry - 1908 - 228 pages
...vertices are concyclic . . 258 AC. 4. — (i) Any angle in a semicircle is a right angle, (ii) Any angle in a segment greater than a semicircle is less than a right angle, (iii) Any angle in a segment less than a semicircle is greater than a right angle .... (Euc. III. 31)...
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Atti Del ... Congresso Internazionale Dei Matematici ...

Mathematics - 1909 - 605 pages
...points on the same side of it, the four points lie on a circle. The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle...less than a semicircle is greater than a right angle. The opposite angles of any quadrilateral inscribed in a circle are supplementary; and the converse....
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