 | 1835 - 684 pages
...magnitudes between one and two, two and three, three and four, &c. quadrants. PROP. 14. (Euc.iii. 20.) The angle at the centre of a circle is double of the...that is, upon the same part of the circumference. Let А С В be any angle at the centre С of the circle А В D, and let ADB be an angle at the circumference... | |
 | John Playfair - 1836 - 148 pages
...the centre ; that is, the centre is in CA. Therefore, if a straight line, &c. QED B PROP. XII. THEOR. The angle at the centre of a circle is double of the...that is, upon the same part of the circumference. Let ABC be a circle, and BEC an angle at the centre, and BAC an angle at the circumference, which have... | |
 | John Playfair - 1836 - 488 pages
...the centre; that is, the centre i$ in CA, Therefore, if a straight line, &c. QE Di PROP. XX. THEOR. The angle at the centre of a circle is double of the...the circumference, upon the same base, that is, upon thc.same part of the circumference. First, let D," the centre of the circle, be within the . angle... | |
 | Schoolmaster - 1836 - 926 pages
...of A and B is double of the sum or difference of C and D. It can thence be immediately proved that the angle at the centre of a circle is double of the angle at the circumference, and that all the angles in the same segment are equal. These we suppose to be also known facts, our... | |
 | 1836 - 502 pages
...of A and B is double of the sum or difference of C and D. It can thence be immediately proved that the angle at the centre of a circle is double of the angle at the circumference, and that all the angles in the same segment are equal. These we suppose to be also known facts, our... | |
 | 1836 - 488 pages
...touching line, the centre of the circle is in that line. XX. The angle at the centre of a circle is double the angle at the circumference, upon the same base, that is, upon the same point of the circumference. XXI. The angles in the same segment of a circle are equal to one another.... | |
 | Andrew Bell - 1837 - 290 pages
...the point of contact — if a line fulfil two, it also fulfils the third. PROPOSITION XX. THEOREM. The angle at the centre of a circle is double of the...circumference, upon the same base, that is, upon the same arc. arc BC for their base ; the angle BDC is double of the angle BAG. First, let D, the centre of... | |
 | Great Britain. Committee on Education - 1850 - 790 pages
...circle to the middle point of any chord in the circle, is perpendicular to that chord. 2. Show that the angle at the centre of a circle is double of the angle at the circumference upon the same base. 3. If two straight lines cut one another within a circle, the rectangle contained by the segments of... | |
 | Great Britain. Committee on Education - 1850 - 904 pages
...base and the straight line intercepted between the perpendicular and the obtuse angle. Section 2. 1 . The angle at the centre of a circle is double of the angle at the circumference. 2. To inscribe a circle in a given triangle. 3. If two straight lines cut one another in a circle,... | |
 | Euclides - 1840 - 82 pages
...of contact perpendicular to the tangent, passes through the centre of the circle. PROP. XX. THEOR. The angle at the centre of a circle, is double of the angle at the circumference, standing on the same arch. PROP. XXI. THEOR. All angles in the same segment of a circle are equal to... | |
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The angle at the centre of a circle is double of the angle at the circumference, upon the same base, that is, upon the same part of the circumference. 
