 | Education - 1882 - 676 pages
...manifest that the required locus is a circle whose centre is O. 29. On the same straight line, and on the same side of it, there cannot be two similar segments of circles not coinciding with each other. (18) Euclid in. 23. 30. Let two equal parallelograms ABCD and AEFG, with their angles at A equal, be... | |
 | John Robertson (LL.D., of Upton Park sch.) - Examinations - 1882 - 152 pages
...IV., AXT> VI. 5. Define similar segments of circles : and prove that on the same straight line, and on the same side of it, there cannot be two similar segments of circles, not coinciding with one another. 6. Describe a circle about a given triangle. 7. Triangles of the same altitude are to... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1883 - 428 pages
...Wherefore, t/te opposite angles &c. Q.KD. PROPOSITION 23. THEOREM. On the same straight line, and on the same side of it, there cannot be two similar segments of circles, not coinciding with one another. If it be possible, on the same straight line AB, and on the same side of it, let there... | |
 | Euclides - 1884 - 434 pages
...Y; B,X,0,Z; C, Y,0,X; A,B,X, Y; B,C, Y,Z; C,A,Z,X. PROPOSITION 23. THEOREM. On the same chord and on the same side of it there cannot be two similar segments of circles not coinciding with one another. JO If it be possible, on the same chord AB, and on the same side of it, let there be two... | |
 | 1885 - 522 pages
...at C. Shew that the straight line BA produced passes through C. 8. On the same straight line and on the same side of it there cannot be two similar segments of circles not coinciding. 9. A is a point without a circle. Straight lines ABC, ADE are drawn cutting the circle in B, C and... | |
 | John Fry Heather - Geometry, Modern - 1890 - 252 pages
...CHAPTER V. ON AEC8 AND SEGMENTS OF CIRCLES. THEOREMS. 173. THEOR. 26. — Upon the same straight line and upon the same side of it, there cannot be two similar segments of circles not coinciding with one another. (Eu. III. 23.) 174. THEOR. 27. — In equal circles, equal angles, whether they be at... | |
 | Edward Mann Langley, W. Seys Phillips - 1890 - 538 pages
...equal, or which contain equal angles. PROPOSITION 23. THEOREM. Upon the same straight line, and on the same side of it, there cannot be two similar segments of circles not coinciding with each other. Let ADB, ACB be two segments of 0s upon the same st. line AB, and not coinciding with each other, then... | |
 | Royal Military College, Sandhurst - Mathematics - 1890 - 144 pages
...square that shall be equal to a given rectilineal figure. 3. Show that on the same straight line and on the same side of it, there cannot be two similar segments of circles, not coinciding with one another. 4. Prove that the angle at the centre of a circle is double of the angle at the circumference... | |
 | Euclid, Henry Sinclair Hall, Frederick Haller Stevens - Euclid's Elements - 1900 - 330 pages
...which contain equal angles. [Book in., Def. 10.] PROPOSITION 23. THEOREM. On the same chord and on the same side of it, there cannot be two similar segments of circles, not coinciding with one another. If possible, on the same chord AB, and on the same side of it, let there be two similar... | |
 | Euclid - Euclid's Elements - 1904 - 488 pages
...which contain equal angles. [Book III., Def. 10.] PROPOSITION 23. THEOREM. On the same chord and on the same side of it, there cannot be two similar segments of circles, not coinciding with one another. If possible, on the same chord AB, and on the same side of it, let there be two similar... | |
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Upon the same straight line, and upon the same side of it, there cannot be two similar segments of circles, not coinciding with one another. If it be possible. let the two similar segments of circles, viz. ACB' ADB be upon the same side of the same straight... 
