| 1883
...in this line. Hence show how to describe a circle of which a portion only is given. 62 7. Prove that **the angle at the centre of a circle is double the angle at the circumference** standing on the same arc. Deduce that the angle in a segment greater than a semicircle is less than... | |
| Isaac Sharpless - 1882 - 266 páginas
...right-angled triangles ; hence, AK is equal to AB. GEOMETRY.— BOOK III. Proposition 16. Theorem. — **The angle at the centre of a circle is double the angle at the circumference** upon the same base ; that is, upon the same part of the circumference. Let ABC be a circle, BDC the... | |
| 1882
...its sides, find the locus of its vertex, and state when the locus becomes impossible. 6. Prove that **the angle at the centre of a circle is double the angle at** its circumference. on the same arc. 7. AB is any chord of a circle, and AC is the tangent at the point... | |
| Dalhousie University - 1885
...BDa + BF2 = 2 D17 + 2 CB2. 3. One circle cannot touch another internally in more points than one. 4. **The angle at the centre of a circle is double the angle at the circumference** standing on the same arc. Prove this, in the case where the lines containing the second angle are on... | |
| Isaac Hammond Morris - 1890 - 260 páginas
...first triangle. (Art.) Note. — Bisect the sides, and find the centre for the circumscribing circle. **The angle at the centre of a circle is double the angle at the circumference,** standing upon the same base. (Eue. ш. 20.) 7. Draw a triangle, two of whose sides are 2'5" and 8"... | |
| Euclid - 1890 - 400 páginas
...part of the other, unless TB go through O. /. TB must go through O. Proposition 20. • THEOREM — **The angle at the centre of a circle is double the angle at the circumference,** standing on the same arc. A Let BC be an arc of a O, on which stand BOC at centre O, A and BAG at circumf.... | |
| Royal Institution of Naval Architects - 1897
...from the bisecting line the amount * X = Q sin 2 (q + 45" -«!•) = Q cos (2 g - 2 ,|,). (17) Because **the angle at the centre of a circle is double the angle at the circumference,** standing upon the same arc, $ X is therefore the varying factor in the second line of (9). For the... | |
| Sidney Herbert Wells - 1900
...the vertex of the triangle must be in this line. We now use the proof of Euclid iii., 20, which says **"the angle at the centre of a circle is double the angle at the circumference** on the same base," and we see that we ought to be able to draw a circle having AB for a chord, so that... | |
| Euclid, Micaiah John Muller Hill - 1900 - 143 páginas
...that expressed by Fig. 62. Hence the scale of CAD, EBF is the same as that of arc CD, arc EF. (ii) An **angle at the centre of a circle is double the angle at the circumference** standing on the same arc. Hence the scale of two angles at the centre of the same or of equal circles... | |
| 1901
...them, and its continuation to meet a perpendicular on it from the opposite angle. 4. Prove that tihe **angle at the centre of a circle is double the angle at the circumference** standing on the same arc. 5. Construct an isosceles triangle having each base angle double the vertical... | |
| |