 | Robert Simson - Trigonometry - 1806 - 546 pages
...shown to be equal to two right angles. Book III. Therefore, the opposite angles, Sec. QE I). *— y~* 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.... | |
 | John Mason Good - 1819 - 800 pages
...equal lo one another. Prop. XXII. Theor. The opposite angles of any quadrilateral figure described in a circle, are together equal to two right angles. Prop. XXIII. Theor. Upon the same straight Ime, and upon the same side of it, there cannot be two similar segments of circles, not coinciding... | |
 | Euclid, Robert Simson - Geometry - 1821 - 514 pages
...angles BAD, DCB may be shown to be equal to two right angles. Therefore the opposite angles, &c- QED PROP. XXIII. THEOR. UPON the same straight line, and upon the same side x>f it, there cannot be two similar segments ofcircles, not coinciding with another.* Ifitbe possible,... | |
 | Robert Simson - Trigonometry - 1827 - 546 pages
...angle BAD is equalf t2Ax. to the whole angle BED. Wherefore the angles in the same segment, &c. QED PROP. XXII. THEOR. The opposite angles of any quadrilateral...a circle, are together equal to two right angles. 1 20. 3. Let ABCD be a quadrilateral figure in the circle ABCD; any two of its opposite angles shall... | |
 | Physics - 1828 - 524 pages
...the solidity. 10 70. Parallelograms upon equal bases and between the same parallels are equal. 80. The opposite angles of any quadrilateral figure, inscribed...a circle, are together equal to two right angles. 81. If two triangles have one angle in one equal to one angle in the other, and the sides about the... | |
 | University of Cambridge - 1831 - 552 pages
...Caius. FRIDAY MORNING, January 14, 1831. 9 o'clock, to 11. First, Second, Third and Fourth Classes. 1. THE opposite angles of any quadrilateral figure inscribed...in a circle are together equal to two right angles. 2. Describe an equilateral and equiangular pentagon about a given circle. 3. What sum must be paid... | |
 | John Playfair - Euclid's Elements - 1835 - 336 pages
...semicircle, the angles CAD, CED are equal ; Therefore the whole angle BAD is equal to the whole angle BED. PROP. XXII. THEOR. The opposite angles of any quadrilateral...a circle, are together equal to two right angles. Let ABCD be a quadrilateral figure in the circle ABCD ; any two of its opposite angles are together... | |
 | Euclid - 1835 - 540 pages
...DCB, ^ v""' may be shown to be equal to two right angles. Therefore, " the 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.... | |
 | Mathematics - 1836 - 366 pages
...two, the plane which passes through them, is parallel to the plane passing through the others. 1831 9. The opposite angles of any quadrilateral figure inscribed...in a circle are together equal to two right angles. 10. Describe an equilateral and equiangular pentagon about a given circle. 11. Triangles and parallelograms... | |
 | George Darley - Euclid's Elements - 1836 - 172 pages
...situated in the circumference of that circle. ART. 69. The opposite angles of a four-sided rectilineal figure inscribed in a circle, are together equal to two right angles. Let ABCD be a four-sided rectilineal figure inscribed in the circle ACD. Then the angles ABC, ADC,... | |
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The opposite angles of any quadrilateral figure inscribed in a circle, are together equal to two right angles. 
