...; 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...

...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...

...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...

...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...

...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,...

...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...

...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....

...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...

...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...

...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...