 | War office - 1861 - 714 pages
...contained by the whole and each of the parts are together equal to the square on the whole line. 4. In a circle the angle in a semi-circle is a right...than a semi-circle is greater than a right angle. ALGEBRA. 1 . Multiply a3 — a V + az6 - a;9 by a + x3. 2. Add together (ax*-by*f and (ay* + bx*)*,... | |
 | Woolwich roy. military acad - 1861 - 572 pages
...fourth converging fraction to VJI . • 7. In a circle the angle in a semicircle is a right angle, the angle in a segment greater than a semicircle is...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
...is equal to the square on the straight line which is made up of the half and the part produced. 3. In a circle the angle in a semicircle is a right angle,...greater than a semicircle is less than a right angle. 4. To describe an equilateral and equiangular hexagon in a given circle. 5. If two triangles have one... | |
 | Euclides - 1862 - 140 pages
...arc DB. Conclusion. — Therefore, the given arc is bisected in D. QEF PROPOSITION 31.— THEOREM. In a circle, the angle in a semicircle is a right...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
...in c, d. Shew that abed is a parallelogram of which two sides are parallel to two sides of AB CD. 4. In a circle, the angle in a semicircle is a right...less 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... | |
 | Euclides - 1863 - 122 pages
...(THEouEM.)—In a circle (ABCD), the angle in a semicircle (BAC) is a right angle; 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... | |
 | Euclides - 1864 - 262 pages
...is equal to the arc DB. Therefore the given arc ADB is bisected in DQEF PROPOSITION XXXI. THEOREM. In a circle, the angle in a semicircle is a right...ABCD be a circle, of which the diameter is BC, and center E, and let CA be drawn, dividing the circle into the segments ABC, ADC. Join BA, AD, DC. Then... | |
 | Euclides - 1864 - 448 pages
...given arc ADB is bisected in DQEF PROPOSITION XXXI. THEOREM. In a circle, the angle in a semicircte is a right angle ; but the angle in a segment greater...ABCD be a circle, of which the diameter is BC, and eenter E. and let CA be drawn, dividing the circle into the segments ABC, ADC. Join BA, AD, DC. Then... | |
 | Henry White - 1864 - 156 pages
...line from a given point, either without or in the circumference, which shall touch a given circle. 7. In a circle, the angle in a semicircle is a right...less than a semicircle is greater than a right angle. • ALGEBRA. Set to candidates for the Admiralty who selected Algebra as a subject of Examination.... | |
 | Euclides, James Hamblin Smith - Geometry - 1872 - 376 pages
...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.... | |
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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. 
