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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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Geometry Without Axioms; Or the First Book of Euclid's Elements. With ...

Thomas Perronet Thompson - Euclid's Elements - 1833 - 168 pages
...CB, CA, AB are all equal to one another. PROPOSITION VII. THEOREM. — Upon the same given straight line and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of it equal to one another, and...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 540 pages
...opposite angles," &c. QED PROP. XXIII. THEOR. Upon the same straight line, and upon the same See N. 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 Element of Geometry

John Playfair - Geometry - 1836 - 148 pages
...angles. Therefore, the opposite angles, &c. QED PROP. XV. THEOR. Upon the same straight line, and upon the same side of it, there cannot be two similar segments of circles, not coinciding with another. • If it be possible, let the two similar segments of circles, viz. ACB, ADB be upon the...
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The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

Mathematics - 1836 - 488 pages
...described in a circle, are together equal to two right angles. XXIII. 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. XXIV. Similar segments of circles upon equal straight lines are equal to one another....
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A companion to Euclid: being a help to the understanding and remembering of ...

Euclides - Euclid's Elements - 1837 - 112 pages
...Z s BAD + DCS = 2 rt. Z *. PROPOSITION XXIII. (Argument ad absurdum.) Theorem. On the same straight line, and on the same side of it, there cannot be...segments of circles not coinciding with each other. Steps of the Demonstration. Suppose that the segments ACB, ADB are similar, and on the same right line...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1837 - 410 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, A DB, be upon the...
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Elements of Plane Geometry According to Euclid

Andrew Bell - Euclid's Elements - 1837 - 290 pages
...to he equal to two right angles. i 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. because the circle ACB cuts the circle ADB in the two points A, B, they cannot cut one...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - Euclid's Elements - 1837 - 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 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 [book 1-6] with corrections, by J.R. Young

Euclides - 1838 - 264 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. If it be possible, upon the same straight line AB, and upon the same side of it, let there...
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The figures of Euclid with the enunciations, as printed in Euclid's Elements ...

Euclides - 1840 - 82 pages
...circle, are together equal to two right angles. 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 each other. PROP. XXIV. THEOR. Similar segments of circles upon equal straight fines are equal to each other. PROP....
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