 | Mathematics - 1836 - 488 pages
...circle there be drawn two straight lines, one of which cuts the circle, and the other meets it ; if the rectangle contained by the whole line, which cuts the circle, and the part of it without a circle, be equal to the line which meets it, the line which meets shall touch the circle. BOOK iv.... | |
 | Euclid, James Thomson - Geometry - 1837 - 410 pages
...AE.EC is equal to the rectangle BE.ED. If, therefore, two chords of a circle, &c. PROP. XXXVI. THEOR. IF from any point without a circle two straight lines...the circle, and the part of it without the circle, is equal to the square of the line which touches it. Let D be any point without the circle ABC, and... | |
 | Euclides - Euclid's Elements - 1837 - 112 pages
...showing that AE x EC and BE x ED are each = GE x EH, and .'. = each other. PROPOSITION XXXVI. Theorem. If from any point without a circle two straight lines...the circle, and the other touches it, the rectangle B/ contained by the whole line which cuts the circle, and the part of it without the circle, shall... | |
 | Mrs. L. H. Tyler - Astronomy - 1837 - 302 pages
...less is the polar than the equatorial di ameter ? What is the curvature of the earth for one mile ? rectangle* contained by the whole line which cuts the circle, and the part of it without the circle is equal to the square of the line which touches it, ie the distance cn multipled into nb, equals the... | |
 | Euclides - 1838 - 264 pages
...circle there be drawn two straight lines, one of which cuts the circle, and the other meets it; and if the rectangle contained by the whole line which cuts...the circle, and the part of it without the circle, be equal to the square of the line which meets it, the line which meets shall touch the circle. Let... | |
 | Euclides - Geometry - 1841 - 378 pages
...circle there be drawn two straight lines, one of which cuts the circle, and the other meets it; if the rectangle contained by the whole line which cuts...the circle, and the part of it without the circle, be equal to the square of the line which meets it, the line which meeti shall touch the circle. Let... | |
 | John Playfair - Euclid's Elements - 1842 - 332 pages
...because, as has been shown, AE.EC = GE.EH, and BE.ED=GE.EH; therefore AE.EC=BE. ED. PROP. XXXVI. THEOR. If from any point without a circle two straight lines...the circle, and the part of it without the circle, is equal to the square of the line which touches it. Let D be any point without the circle ABC, and... | |
 | Euclides - 1842 - 320 pages
...Wherefore, if two straight lines, &c. QED PROP. XXXVI. THEOR. IF from any point on the exterior of a circle two straight lines be drawn, one of which...whole line which cuts the circle, and the part of it which is on the exterior of the circle, shall be equivalent to the square of the line which touches... | |
 | Euclid, James Thomson - Geometry - 1845 - 380 pages
...proposition and the following. See the Notes at the end of tb" »«i"—•< PROP. XXXVI. THEOR. — If from any point without a circle two straight lines...the circle, and the part of it without the circle, is equal to the square of the line which touches it. Let D be any point without the circle ABC, and... | |
 | Euclid - Geometry - 1845 - 218 pages
...circle there be draimi two straight lines, one of which cuts the circle, and the other meets it ; if the rectangle contained by the whole line which cuts the circle, and the part of it withmit the circle be equal to the square of the line which, meets it, the line which meets shall touch... | |
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If from any point without a circle two straight lines be drawn, one of -which cuts the circle, and the other touches it; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square... 
