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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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Euclid's Elements of plane geometry [book 1-6] with explanatory appendix ...

Euclides - 1840 - 192 pages
...Proposition is introduced for the sake of proving the Eighth. It amounts to this, that on the same straight line, and on the same side of it, there cannot be two isosceles triangles, having the vertex of each outside of the other. It is shown by the indirect method,...
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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - Geometry - 1841 - 378 pages
...angles. Therefore, the opposite angles, &c. QED 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 with one another. I 2 If it be possible, upon the same straight line AB, and upon the same side of it, let...
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Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842 - 316 pages
...to ADC by the proposition. Therefore, &c. 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 with one another. If it be possible, let the two similar segments of circles, viz. ACB, ADB be upon the...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1842 - 332 pages
...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 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, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1845 - 382 pages
...angles. Take away CBA, and there remains CBE equal to CDA. PROP. XXIII. THEOR. — 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. If it be possible, let the two similar segments of circles, viz. ACB, ADB, be upon the...
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845 - 546 pages
...Therefore, the opposite angles, &c. QED PROPOSITION 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, upon the same straight line AJi, and upon the same side of it, let...
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Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - Geometry - 1845 - 218 pages
...right angles. ' St. 1. t 11.3. PROPOSITION XXIII. THEOB. — 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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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - Euclid's Elements - 1846 - 334 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 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 Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846 - 292 pages
...Wherefore, The opposite angles S;c. Qi•..i>. 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 with one another, If it be possible, let two similar segments of circles, viz. ACB, ADB, be upon the same...
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The definitions, postulates, axioms, and enunciations of the propositions of ...

Euclides - 1848 - 52 pages
...are together equal to two right angles. 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. PROP. XXIV. THEOREM. Similar segments of circles upon equal straight lines, are equal...
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