 | Euclides, James Hamblin Smith - 1872 - 376 σελίδες
...the radius. PROPOSITION XXXI. THEOREM. In a circle, the angle in a semicircle is a right angle ; and the angle in a segment greater than a semicircle is...than a semicircle is greater than a right angle. Let ABC be a © , O its centre, and BC a diameter. Draw AC, dividing the © into the segments ABC, ADC.... | |
 | Robert Johnston (F.R.G.S.) - 1872 - 212 σελίδες
...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... | |
 | Euclid - 1872 - 284 σελίδες
...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... | |
 | Euclides - 1872 - 102 σελίδες
...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.... | |
 | Henry Major - 1873 - 592 σελίδες
...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... | |
 | Edward Atkins - 1874 - 424 σελίδες
...cor.); Therefore the arc AD is equal to the arc DB. Therefore, the given arc is bisected in DQJE.F. Proposition 31. — Theorem. In a circle, the angle...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... | |
 | Francis Cuthbertson - 1874 - 400 σελίδες
...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...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 segments... | |
 | Edward Atkins - 1874 - 428 σελίδες
...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... | |
 | Euclid, James Bryce, David Munn (F.R.S.E.) - 1874 - 234 σελίδες
...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... | |
 | Edward J. Cowling Welch - 1875 - 244 σελίδες
...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... | |
| |
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. 
