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The angle at the centre of a circle is double the angle at the circumference on the same arc.
The Elements of geometry [Euclid book 1-3] in general terms, with notes &c ... - Page 128
by Euclides - 1821

## The Elements of Euclid: viz. the first six books, together with the eleventh ...

Robert Simson - Trigonometry - 1835 - 513 pages
...CA, is the centre ; that is, the centre is in C A. Therefore, " if a straight line" &c. QED PROP. XX. THEOR. 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. a 5. 1. . l. Let ABC be a circle,...

## The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 540 pages
...; 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...

## The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

Mathematics - 1836 - 472 pages
...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...

## Lessons on Form: Or, An Introduction to Geometry, as Given in a Pestalozzian ...

Charles Reiner - Geometry - 1837 - 254 pages
...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...

## Transactions of the Royal Scottish Society of Arts, Volume 4

Royal Scottish Society of Arts - Industrial arts - 1856 - 860 pages
...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...

## Euclid's Elements of geometry, the first three books (the fourth, fifth, and ...

Euclides - 1846 - 272 pages
...AB, is the centre. PROPOSITION XX. THEOREM. The angle (ACD) at the centre of a circle, is double of the angle at the circumference, when they have the same part of the circumference for their base. Firstly — Let either leg of the angle at the periphery pass through the centre; and because in the...

## Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's ...

Dennis M'Curdy - Geometry - 1846 - 138 pages
...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,...

## Elements of Geometry: With Practical Applications ...

George Roberts Perkins - Geometry - 1847 - 308 pages
...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...

## Notes and Queries

Electronic journals - 1891 - 670 pages
...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....

## Elements of Geometry: With, Practical Applications

George Roberts Perkins - Geometry - 1850 - 332 pages
...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 by the...