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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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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - Euclid's Elements - 1849 - 332 pages
...angles, cannot be inscribed in a circle. PROP. XXIII. THEOR. Upon the same straight line, and upon the same side of it, there cannot be two similar segments of circles, not coinciding viith one another. If it be possible, let the two similar segments of circles, viz. ACB, ADB, be upon...
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The first three books of Euclid's Elements of geometry, with theorems and ...

Euclid, Thomas Tate - 1849 - 120 pages
...the opposite angles, &c. QED PROP. XXHL THEOR. 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...
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The synoptical Euclid; being the first four books of Euclid's Elements of ...

Euclides - 1853 - 146 pages
...Therefore the opposite angles, &c. QED PROP. XXIII. — THEOREM. 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...
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The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...opposite angles, etc. <;. £. i). PROPOSITION XXIII. TIIEOR. 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...
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The first six books of the Elements of Euclid, with numerous exercises

Euclides - Geometry - 1853 - 178 pages
...Therefore the opposite angles, &c. QED PROPOSITION XXIII. — THEOREM. Upon the same straight line and wpon the same side of it, there cannot be two similar segments of circles not coinciding imth one another. IF it be possible, let the two similar segments of circles, viz. a С b, adb be upon...
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The Elements of Euclid, books i-vi; xi. 1-21; xii. 1,2; ed. by H.J. Hose, Book 1

Euclides - Geometry - 1853 - 334 pages
...and it has just been shewn to be equal to it : which is impossible. Therefore on the same straight line and on the same side of it, there cannot be two similar segments of a circle, not coinciding with one another. Which was to be proved. PEOP. XXIV. THEOE. Similar segments...
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Orr's Circle of the Sciences: Organic nature, vols. 1-3 (1854-1856)

William Somerville Orr - Science - 1854 - 534 pages
...interior and opposite angle (U). PROPOSITION XXIII.— THEOREM. Ujion the same straight line (AB), and on the same side of it, there cannot be two similar segments of circles not coinciding with one another. For if it be supposed possible, let ACB, ADB be two similar segments, not coinciding with...
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1855 - 262 pages
...triangle ACD is equal to its interior angle, which is impossible (I. 16). Therefore upon the same straight line, and on the same side of it there cannot be two similar segments of circles which do not coincide. QED Corollary. — If there be two segments of circlea on the same base or chord,...
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Examination papers used at the examinations for admission to the Royal ...

Sandhurst roy. military coll - 1859 - 672 pages
...square on the straight line which is made up of the half and the part produced. 3. 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. VOLUNTARY PORTION. 1. If two straight lines meeting one another be parallel to two others...
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Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ...

Euclides - 1860 - 288 pages
...Def. 8), the exterior to the interior, which is impossible (I. 16); therefore on the same straight line, and on the same side of it, there cannot be two similar segments of circles not coinciding. Similar segments of circles upon equal straight lines are equal to one another. Given AEB and CFD two...
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