 | Euclides - 1874 - 342 σελίδες
...ABD, ACD, are equiangular and similar to each other. Therefore, in a right-angled, &c. QED Cor. From this it is manifest, that the perpendicular drawn...the right angle of a right-angled triangle to the base, is a mean proportional between the segments of the base ; and also that each of the sides is... | |
 | William Alexander Myers - 1874 - 207 σελίδες
...right-angle of a right-angled triangle to the base, is a mean proportional between the segments of the base, and also that each of the sides is a mean proportional between the base and the segment of the base adjacent to that side. For in the triangles BAD, BDC, AB is to BD... | |
 | Robert Potts - 1876 - 446 σελίδες
...angle of a right-anglea triangle to the base, is a mean proportional between the segments of the base; and also that each of the sides is a mean proportional between the base, and the segment of it adjacent to that side : because in the triangles BDA, ADQ; BD is to DA,... | |
 | George Albert Wentworth - 1877 - 416 σελίδες
...to the hypotenuse. .-.AC : CH : : С H : С B, §289 (the ± let fall from the vertex of the rt. Z to the hypotenuse is a mean proportional between the segments of the hypotenuse). Substitute for A С and С B their equals m and n. Then m : С H : : С H : п. QEF 307. COROLLARY.... | |
 | Isaac Sharpless - 1879 - 282 σελίδες
...sum of the squares of the two sides is equal to the square of the diameter (II. 9). 10. The square on the perpendicular, drawn from the right angle of a right-angled triangle to the base, is equal to the rectangle contained by the segments of the base. BOOK III. CIRCLES. DEFINITIONS.... | |
 | Isaac Todhunter - 1880 - 426 σελίδες
...triangle ABC, are similar to each other. Wherefore, in a right-angled triangle &c. QED COROLLARY. From this it is manifest, that the perpendicular drawn...the right angle of a right-angled triangle to the base, is a mean proportional between the segments of the base, and also that each of the sides is a... | |
 | George Albert Wentworth - 1879 - 262 σελίδες
...rt. Z to the hypotenuse. .'.AC : CH :: CH : CB, §289 (the J. let fall from 1he vertex of the rt. Z to the hypotenuse is a mean proportional between the segments of the hypotcmise). Substitute for AC and CB their equals m and n. Then ' m : CII : : CH : n. QEF 307. COROLLARY.... | |
 | Euclid, Isaac Todhunter - 1883 - 428 σελίδες
...triangle ABC, are similar to each other. Wherefore, in a right-angled triangle &c. QED COROLLARY. Prom this it is manifest, that the perpendicular drawn...the right angle of a right-angled triangle to the base, is a mean proportional between the segments of the base, and also that each of the sides is a... | |
 | Euclid - 1890 - 442 σελίδες
...other : (j3) the perpendicular is a mean proportional between the segments of the hypotenuse : (y) each of the sides is a mean proportional between the hypotenuse and its segment adjacent to that side. A Let ABC be a A, having C right. Draw CN J_ to AB. Then (a) in... | |
 | Seth Thayer Stewart - 1891 - 428 σελίδες
...angle to the hypotenuse. PROP. X. In any right-angled triangle, the perpendicular from the right angle to the hypotenuse is a mean proportional between the segments of the hypotenuse. 3. MISCELLANEOUS EXERCISES. SECTION III.— POLYGONS. 3§6. i. DEFINITIONS. 2. PROPOSITIONS. PROP.... | |
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From this it is manifest, that the perpendicular drawn from the right angle of a right-angled triangle to the base, is a mean proportional between the segments of the base; and also that each of the sides is a mean proportional between the base, and... 
