| Euclides - 1834
...be done. PROPOSITION XXXV. THEOR. — If two straight lines cut one another within a circle, See N. **the rectangle contained by the segments of one of...segments of the other. Let the two straight lines AC, BD** cut one another in the point E, within the circle ABCD : the rectangle contained by AE, EC, shall be... | |
| Euclid - 1835 - 513 pages
...Which was to be done. PROP. XXXV. THEOR. If two straight lines within a circle cut one another, See N. **the rectangle contained by the segments of one of...Let the two straight lines AC, BD within the circle** A BCD, cut one another in the point E : the rectangle contained by AE, EC is equal to the rectangle... | |
| Mathematics - 1836 - 472 pages
...the alternate segments of the circle. XXXIV. If two straight lines within a circle cut one another, **the rectangle contained by the segments of one of...rectangle contained by the segments of the other.** XXXVI. If from any point without a circle two straight lines be drawn, one of which cuts the circle,... | |
| John Martin Frederick Wright - Mathematics - 1836
...of section. 3. If two straight lines within a circle cut one another, the rectangle contained Ъу **the segments of one of them is equal to the rectangle contained by the segments of the other.** 4. Inscribe an equilateral and equiangular hexagon in a given circle. 5. If any number of magnitudes... | |
| John Playfair - Euclid's Elements - 1836 - 471 pages
...angle D. Which was to be done.PROP. XXXV. THEOR. If two straight lines within a circle cut one another, **the rectangle contained by the segments of one of them is equal to the rectangle contained by** me segments of the other. Let the two straight lines AC, BD, within the circle ABCD, cut one another... | |
| Euclides - Euclid's Elements - 1837 - 88 pages
...alternate segment BJC ~ ZD PROPOSITION XXXV. Theorem. If two straight lines within a circle cut each **other, the rectangle contained by the segments of...rectangle contained by the segments of the other.** • In case 1st, E is the centre of the 0, and evident that AE x EC = BE x ED. it is Steps of the Demonstration... | |
| Euclid, James Thomson - Geometry - 1837 - 390 pages
...; that is, the difference between it and a right angle. IF two chords of a circle cut one another, **the rectangle contained by the segments of one of...rectangle contained by the segments of the other.** In the circle ABCD, let the two chords AC, BD cut one another in the point E : the rectangle AE.EC... | |
| Commissioners of National Education in Ireland - 1837
...-36571 ; hence 30-24 + -36571 = 30-60571 the area. Note. If two chords of a circle cut one another, **the rectangle contained by the segments of one of...rectangle contained by the segments of the other.** This is the 35th Proposition of the IIL Book of Euclid. 4. Required the area of the segment AGFB whose... | |
| Andrew Bell - Euclid's Elements - 1837 - 240 pages
...angle equal to the given angle D. PROPOSITION XXXV. THEOREM. If two chords in a circle cut one another, **the rectangle contained by the segments of one of...rectangle contained by the segments of the other.** If AC, BD, pass each of them through the centre, so that E is the centre; it is evident that AE, EC,... | |
| Euclides - 1838
...D. Which was to be done. PROP. XXXV. THEOR. If two straight lines cut one another within a circle, **the rectangle contained by the segments of one of...segments of the other. Let the two straight lines AC, BD,** cut one another In the point E within the circle ABCD: the rectangle contained by AE, EC shall be equal... | |
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