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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. "
Euclid's Elements of Geometry: The Six First Books. To which are Added ... - Page 96
by Rev. John Allen - 1822 - 494 pages
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The Elements of Euclid for the Use of Schools and Colleges: With Notes, an ...

Isaac Todhunter - Euclid's Elements - 1880 - 426 pages
...right angles. Wherefore, the opposite angles &c. QED 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 he possible, on the same straight line AD, and on the same side of it, let there...
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Military examinations. Mathematical examination papers, set at entrance to ...

Sandhurst roy. military coll - 1880 - 68 pages
...to a given line not greater than the diameter of the circle. 3. 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. 4. Inscribe an equilateral and equiangular pentagon in a given circle. 5. Define similar,...
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Ten years' Queen's scholarship questions, 1870-9, with answers to arithmetic ...

Education Ministry of - 1880 - 248 pages
...numbers, must be used in the diagrams. Not more than ten questions to bo answered. 1. On the same straight line, and on the same side of it, there cannot be two triangles which have their sides terminated in one extremity of the base equal to one another, and...
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The Practical Teacher, Volume 1, Issue 1

Education - 1882 - 676 pages
...this it is 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...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...
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University local half-hour examination papers

John Robertson (LL.D., of Upton Park sch.) - Examinations - 1882 - 152 pages
...BOOKS III., 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...
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Twelve years' Queen's scholarship questions

Education Ministry of - 1882 - 292 pages
...numbers, must bo used in tho diagrams. Not more than ten questions to be answered. 1. On the same straight line, and on the same side of it, there cannot be two triangles which have their sides terminated in one extremity of the base equal to one another, and...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1883 - 428 pages
...right angles. 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...
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The Elements of Euclid, books i. to vi., with deductions, appendices and ...

Euclides - 1884 - 434 pages
...A,Z,0, 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...
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The text of Euclid's geometry, book 1, uniformly and systematically arranged ...

Euclides - 1884 - 214 pages
...bisects an angle, he also, by the same construction, bisects a straight line. (108) On the same straight line, and on the same side of it, there cannot be two equilateral triangles not coincident with one another. (109) Find a point equally distant from each...
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Examinations Papers

1885 - 522 pages
...internally 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...
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