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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 Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - Geometry, Plane - 1860 - 380 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 AB, and upon the same side of it, let there...
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Euclid's Elements of geometry, books i. ii. iii. iv

Euclides - 1862 - 140 pages
...BAD, BCD, are together equal to two right 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 one another, (References— Prop. I. 16; III. 10; def. 11.) Hypothesis. — If it be possible, on the...
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The elements of plane geometry; or, The first six books of Euclid, ed. by W ...

Euclides - 1863 - 122 pages
...ACI) 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 ccincide. QED the point A may be on the point C. and the straight line AB upon the THOP....
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Euclid's Elements of geometry, the first four books, by R. Potts. Corrected ...

Euclides - 1864 - 262 pages
...Therefore, the opposite angles, &c. QED PROPOSITION XXIII. THEOREM. Upon the tame 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 AB, and upon the same side of it, let there...
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The College Euclid: Comprising the First Six and the Parts of the Eleventh ...

Euclides - 1865 - 402 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. (References — Prop. i. 16 ; in. 10, def. 11.) If it be possible, let the two similar...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 424 pages
...right angles. Wherefore, tlie opposite angles &c. QKD 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 for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...right angles. Wherefore, the opposite angles &c. QED PKOPOSITION 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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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1868 - 434 pages
...Therefore, the opposite angles, &c. OED PROPOSITION XXIII. THEOREM. Upon the tame 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 AB, and upon the same side of it, let there...
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Elements of geometry, containing the first two (third and fourth ..., Part 2

Euclides - 1872 - 102 pages
...which contain equal angles. BOOK III. 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 each other. If it be possible, on the same base AB, and on the same side of it, let there be two similar segments...
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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - Geometry - 1872 - 376 pages
...equal, or which contain equal angles. 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 each other. If It be possible, on the same base AB, and on the same side of it, let there be two similar segments...
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