 | John Paxton Hall - 1860 - 186 pages
...circumference. PEOP. XXXI. — In a circle, the angle in a semicircle is a right angle ; but the angle is a segment greater than a semicircle is less than a...less than a semicircle is greater than a right angle. ABC is a triangle of which the angle A is acute ; show that the square of BC is less than the squares... | |
 | Horatio Nelson Robinson - Geometry - 1860 - 470 pages
...a right angle ; an angle in a segment greater than a semicircle is less than a right angle; and an angle in a segment less than a semicircle is greater than a right angle. (Th. 8) ; that is, one half of 180°, or 90°, which is the measure of a right angle. If the angle... | |
 | Euclides - 1860 - 288 pages
...if the centre falls without the triangle, the angle opposite to the side beyond which it is, being in a segment less than a semicircle, is greater than a right angle. Wherefore, if the given triangle be acute-angled, the centre of the circle falls within it ; if it... | |
 | Woolwich roy. military acad - 1861 - 572 pages
...form of a continued fraction, and find by this method the fourth converging fraction to VJI . • 7. In a circle the angle in a semicircle is a right angle,...less than a semicircle is greater than a right angle. If two chords AB, CD in a circle cut each other at right angles, the sum of the opposite arcs AC and... | |
 | War office - 1861 - 260 pages
...between the acute angle and the perpendicular let fall upon it from the opposite angle. 3. Show that the angle in a semicircle is a right angle, the angle...less than a semicircle is greater than a right angle. 4. Define similar rectilineal figures. If the sides of two triangles about each of their angles be... | |
 | Euclides - 1861 - 464 pages
...Euclid's Geometry. РROP. 31. — THEOR. 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. COTS. 10, I. Psts. 1 & 2. DEM. Def. 15, I. 5,1. Axs. 1, 2. Def. 10, 1. 22, Ш. 32, I. If a side of... | |
 | War office - 1861 - 714 pages
...nearer to the centre than the less. 2. 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. 10 DIRECT COMMISSIONS. VOLUNTAKY PORTION. 1. Similar triangles are to one another in the duplicate... | |
 | Euclides - 1862 - 140 pages
...in D. QEF 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 semicircle is greater than a right angle. (References— Prop. I. 5, 17, 32; III. 22.) Hypothesis. — Let ABC be a circle, of which BC is a... | |
 | Robert Potts - 1863 - 482 pages
...are parallel to two sides of AB CD. 4. 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. The circumferences of three unequal circles, whose centres are A, B, C, pass through a common point O,... | |
 | Euclides - 1863 - 122 pages
...theannlein a segment (ABC) greater than a semicircle is less than a right angle; and the angle (ADC) in a segment less than a semicircle is greater than a right emgle. Take any point Din the arc ADC, and join AB, AD, DC, and AC. Also join AE, and produce BA to... | |
| |
... a circle. 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. 
