 | Euclides - 1816 - 588 ページ
...the centre ; that is, the centre is in CA. Therefore, if a straight line, &c. QED PROP. XX. THEOR. THE angle at the centre of a circle is double of the...that is, upon the same part of the circumference. Let ABC be a circle, and BEC an angle at the centre, Bo°* mand BAC an angle at the circumference,... | |
 | Sir John Leslie - 1817 - 456 ページ
...lines CA CD, and CB being all equal, the point C is the centre of the circle. PROP. XV. THEQR. . , The angle at the centre of a circle is double of the angle which, standing on the same arc, has its vertex in the circumference.. Let AB be an arc of a circle... | |
 | John Playfair - 1819 - 350 ページ
...the centre; thafris, the centre is in CA. Therefore, if* straight line, &c. QED r B PROP. XX. THEOR. The angle at the centre of a circle is double of the...that is, upon the same part of the circumference. . Let ABC be a circle, and BDC an angle at the centre, and BAC an angle at the circumference, which... | |
 | John Mason Good - 1819 - 800 ページ
...right angles to the touchingline, the centre of the circle shall be in that line. Prop. XX. Theor. The angle at the centre of a circle is double of the...that is, upon the same part of the circumference. Prop. XXI. Theor. The angle» in the same segment of a circle are equal lo one another. Prop. XXII.... | |
 | Dugald Stewart - 1822 - 572 ページ
...quantities, and the connexions which exist between d ¡i li wiit relations. When we demonstrate, that the angle at the centre of a circle is double of the anglt? at the circumference on the same base, we ascertain a relation between two quantities. When... | |
 | Peter Nicholson - 1823 - 210 ページ
...to AB, which is impossible : therefore the angle ACB is equal to DCE. THEOREM 34. 91. An angle, ACB, at the centre of a circle, is double of the angle at the cirumference, upon the same arc, AB. Draw DC, (fig. 1,) and produce it to E. First, let the angle at... | |
 | Peter Nicholson - 1825 - 1046 ページ
...centre ; that is, the centre is in CA. Therefore, if a straight line, &c. QED Proposition XX. Theorem. The angle at the centre of a circle is double of the angle at the circumference, upon the same*base, that is, upon the same part of the circumference. Let ABC be a circle, and BEC an angle... | |
 | Robert Simson - 1827 - 546 ページ
...centre; that is, the centre is in CA. Therefore, if a straight line, &c. QED PROP. XX. THEOR. See N. The angle at the centre of a circle is double of the...that is, upon the same part of the circumference. Let ABC be a circle, and BEC an angle at the centre, and BAC an angle at the circumference, which have... | |
 | Dugald Stewart - 1829 - 482 ページ
...different quantities, and the connexions which exist between different relations. When we demonstrate, that the angle at the centre of a circle is double of the angle at the circumference on the same base, we ascertain a relation between two quantities. When we demonstrate, that triangles... | |
 | John Playfair - 1829 - 210 ページ
...centre; that is, the centre is in CA. Therefore, if a straight line &c. QE 1). PROPOSITION XX. THEOREM. The angle at the centre of a circle is double of the angle at -the circumference, both standing on the same arch. Let ABC be a circle, and BDC an angle at the centre, and BAT an angle... | |
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The angle at the centre of a circle is double of the angle at the circumference upon the same base, that is, upon the same part of the circumference. 
