 | Mathematics - 1836 - 488 pages
...which touches the circle, shall be equal to the angles in the alternate segments of the circle. XXXIV. If two straight lines within a circle cut one another,...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 Playfair - Euclid's Elements - 1836 - 488 pages
...circle ABC containing an angle equal to the given angle D. Which was to be done.PROP. XXXV. THEOR. If two straight lines within a circle cut one another,...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... | |
 | John Martin Frederick Wright - Mathematics - 1836 - 776 pages
...double of the square of half the line, and of the square of the line between the points 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.... | |
 | John Playfair - Euclid's Elements - 1837 - 332 pages
...out off from the given circle ABC containing an angle equal to the given angle D. PROP. XXXV. THEOR. If two straight lines within a circle cut one another,...rectangle contained by the segments of the other. Let the two straight lines AC, BD, within the circle ABCD, cut one another in the point E ; the rectangle... | |
 | Euclid, James Thomson - Geometry - 1837 - 410 pages
...complement of the given angle C ; that is, the difference between it and a right angle. IF two chords of a circle cut one another, the rectangle contained...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 - Measurement - 1837 - 290 pages
...X 45-36 = 30-24 ; then = -36571 ; hence 30-24 + -36571 = 30-60571 the area. Note. If two chords of a circle cut one another, the rectangle contained...rectangle contained by the segments of the other. This is the 35th Proposition of the III. Book of Euclid. 4. Required the area of the segment AGFB whose... | |
 | Andrew Bell - Euclid's Elements - 1837 - 290 pages
...circle ABC containing an angle equal to the given angle D. PROPOSITION XXXV. THEOREM. If two chords in a circle cut one another, the rectangle contained...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 - Euclid's Elements - 1837 - 112 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 one 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... | |
 | Robert Simson - Geometry - 1838 - 434 pages
...circle ABC containing an angle equal to the given angle D. Which was to be done. PROP. XXXV. THEOR. B C IF two straight lines within a circle cut one another,...rectangle contained by the segments of the other.* Let the two straight lines AC BD, within the circle ABCD, cut one another in the point E : the rectangle... | |
 | Euclides - 1838 - 264 pages
...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...rectangle contained by the segments of the other. Let the two straight lines AC, BD, cut one another In the point E within the circle ABCD: the rectangle... | |
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BAC is cut off from the given circle ABC containing an angle equal to the given 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... 
