 | Henry Major - Student teachers - 1873 - 588 pages
...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 less than a right angle ; and the angle in a segment less than a semicircle is greater than a right angle. Let BC be a diameter,... | |
 | Euclid, James Bryce, David Munn (F.R.S.E.) - Geometry - 1874 - 236 pages
...semicircle 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... | |
 | Francis Cuthbertson - Euclid's Elements - 1874 - 400 pages
...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 less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle. Let A PB be a © of... | |
 | Euclides - 1874 - 342 pages
...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 less than a right angle ; and the angle in a segment less than a semicircle, is greater than a right angle. Let A BCD be a... | |
 | Edward Atkins - 1874 - 426 pages
...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 less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle. Let ABC be a circle,... | |
 | Edward J. Cowling Welch - Machine engineering - 1875 - 240 pages
...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 semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle," is the basis upon... | |
 | Education Department,London - 1876 - 1010 pages
...the circumference. SECTION III. 1. 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 right angle ; and the angle in a segment less than a semicircle is greater than a right angle. The greatest rectangle... | |
 | Richard Wormell - 1876 - 268 pages
...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... | |
 | Edward Atkins - 1876 - 130 pages
...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 less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle. Let ABC be a circle,... | |
 | 1876 - 710 pages
...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... | |
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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. 
