 | Edward Mann Langley, W. Seys Phillips - 1890 - 538 σελίδες
...the angles are equal, or which contain equal angles. PROPOSITION 23. THEOREM. Upon the same straight line, and on the same side of it, there cannot be...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 - 1890 - 144 σελίδες
...Describe a 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... | |
 | John Fry Heather - 1890 - 252 σελίδες
...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... | |
 | Euclid, Henry Sinclair Hall, Frederick Haller Stevens - 1900 - 330 σελίδες
...are those 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... | |
 | University of St. Andrews - 1902 - 740 σελίδες
...intersection of SA and RP. 9. What is meant by similar segments of circles ? Prove that on the same straight line and on the same side of it there cannot be two similar segments not coinciding with one another. ABC are three points in a straight line. On AB and BC and on the same... | |
 | Euclid - 1904 - 488 σελίδες
...those 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... | |
 | Trinity College (Dublin, Ireland) - 1909 - 546 σελίδες
...touch another circle. 6. When are Uvo segments of circles said to be similar? Upon the same straight line and on the same side of it there cannot be two similar segments of circles not coinciding with one another ? 7. State Euclid's tests for determining whether four magnitudes were proportionals or... | |
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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. 
