 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...  A Treatise on Mensuration for the Use of Schools - Page 50by Commissioners of National Education in Ireland - 1837 - 262 pagesFull view - About this book
 | Euclides - 1858 - 248 pages
...another within a circle ; as Prop. 35, bk. iii. , "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. " 4. By this proposition the method may be demonstrated of finding the value of an Adfected Quadratic... | |
 | Euclides - 1860 - 288 pages
...circle ABC containing an angle equal to the given angle D. PBOPOSITION XXXV. THEOREM. If two chords in a circle cut one another, the rectangle contained...rectangle contained by the segments of the other. Given the two chords AC and BD, within the circle ABCD, cutting one another in the point E ; to prove... | |
 | Robert Potts - Geometry, Plane - 1860 - 380 pages
...PROPOSITION XXXV. THEOREM. If two straight lines cut one another within a circle, the rectangle contained btf the segments of one of them, is equal to the rectangle contained by the si'gmrnh of the other. Let the two straight lines AC, BD, cut one another in the point E, within... | |
 | Euclides - 1861 - 464 pages
...BC. QE r. PBOP. 35. — THEOK. (Very Important.) If two st. lines eut one another within a circle, the rectangle contained by the segments of one of...rectangle contained by the segments of the other. Cox. 10, I. 12, I. 1, III. Pst. 1. DEM. Def. 15, I. 3, III. 47, I. Axs. 1, 2, 3, I. 36, 1. Parlms.... | |
 | Alexander Hadden Hutchinson - 1861 - 128 pages
...his army consist before the battle ? Euclid. 1. 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. 2. If a point be taken within a circle, from which there fall more than two equal straight lines to... | |
 | Euclides - 1862 - 172 pages
...// two straight lines within a circle cut one another ; then the rectangle contained by the segment? of one of them is equal to the rectangle contained by the segments of the other. (References — Prop. i. 12, 47; n. 5; in. 1, 3.) Let the two straight lines AC, BD, within the circle... | |
 | Euclides - 1862 - 140 pages
...containing an angle equal to the given angle DQEF PROPOSITION 35.— THEOREM. If two straight lines within a circle cut one another, the rectangle contained by the segments of one of them shall be equal to tlte rectangle contained by the segments of the other. (References— Prop. I. 12,... | |
 | Robert Potts - 1863 - 482 pages
...making any constant angle with AB and AC, the locus of P is a circle. 7. If two straight lines within a circle cut one another, the rectangle contained...rectangle contained by the segments of the other. With a point A in the circumference of a circle ABC as centre a circle PBC is described cutting the... | |
 | Architecture - 1863 - 300 pages
...EUCLID. — Book III. 1. Proposition 35. Theorem. 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. 2. A projected railway having been surveyed through an estate I ask the engineer where the line will... | |
 | Euclides - 1864 - 262 pages
...Or, in other words : — If the diagonals of a quadrilateral figure intersect one another, so that the rectangle contained by the segments of one of...the rectangle contained by the segments of the other ; then a circle may be described about the quadrilateral. Prop. xxxvi. The converse of the corollary... | |
| |
