| Robert Simson - Trigonometry - 1806 - 518 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 - 740 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 - 513 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
...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 - 316 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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