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" The angle at the centre of a circle is double the angle at the circumference on the same arc. "
Elementary Plane Geometry: Inductive and Deductive - Página 86
por Alfred Baker - 1903 - 144 páginas
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 513 páginas
...; that is, the centre is in C A. Therefore, " if a straight line" &c. QED PROP. XX. THEOR. S«e N. The angle at the centre of a circle is double the angle at the circumference upon the same base, that is, upon the same part of the circumference. B a 5. 1. b 32. 1. Let ABC be...
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The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

1836 - 472 páginas
...straight line be drawn at right angles to the touching line, the centre of the circle is in that line. XX. The angle at the centre of a circle is double the angle at the circumference, upon the same base, that is, upon the same point of the circumference. XXI. The angles in the same...
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Lessons on Form: Or, An Introduction to Geometry, as Given in a Pestalozzian ...

Charles Reiner - 1837 - 215 páginas
...not equal to each other, and the lesser chord is farther from the centre than the greater chord. 11. The angle at the centre of a circle is double the angle at the circumference, upon the same arc. 12. At the circumference, an angle which stands upon a semi-circumference is a right...
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Transactions of the Royal Scottish Society of Arts, Volumen4

Royal Scottish Society of Arts - 1856
...apparatus I have termed a semi-revolving one. In Prop. XX., Book III., Euclid, it is demonstrated that the angle at. the centre of a circle is double the angle at the circumference upon the same base that is upon the same part of the circumference. Let ABCDEF be a circular frame...
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Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's ...

Dennis M'Curdy - 1846 - 138 páginas
...Therefore, if a straight line, <fec. QED Recite (a) p. 18, 3 ; (4) def. 10, 1 ; (c)ax. 10; (d)ax.9. 20 Th. The angle at the centre of a circle is double the angle at the circumference upon the same arc. The angles AEB, BEC, AEC are central: The angles ADB, BDC, ADC are at the circumference,...
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Elements of Geometry: With Practical Applications ...

George Roberts Perkins - 1847 - 308 páginas
...upon the same arc, are equal to each other ; for each is measured by half the same arc. Cor. 2. An angle at the centre of a circle is double the angle at the circumference, when both stand on the same arc. For the angle at the centre is (B. lll, Def. 12) measured by the whole...
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Notes and Queries

1891
...the angle be the ame ? Is GENERAL DRATSON acquainted with an obscure writer who long ago proved that the angle at the centre of a circle is double the angle at the circumference t But probably Euclid was a fossil geometer, as all who disagree with GENERAL. DRATSON are fossil astronomers....
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Elements of Geometry: With, Practical Applications

George Roberts Perkins - 1850 - 320 páginas
...subtended by the same arc, are equal to each other; for each is measured by half ihe same arc. Cor. 2. An angle at the centre of a circle is double the angle at the circumference, when both are subtended by the same arc. For the angle at the centre is (B. Ill, Def. 13,) measured...
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Papers for the schoolmaster, Volumen3

1867
...and the least straight lines that can be drawn touching the former, and terminated by the latter. 3. The angle at the centre of a circle is double the angle at the circumference upon the same base, ie, upon the same part of the circumference. If any three points ABE, be taken...
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Five Years in an English University, Volumen2

Charles Astor Bristed - 1852
...double the squares of the half-line and the line made up of the half-line and the part produced. 10. The angle at the centre of a circle is double the angle at the circumference, upon the same base. 11. The angle between a tangent and any chord, is equal to the angle in the alternate...
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