 | John Bonnycastle - 1813 - عدد الصفحات: 444
...difference between the other two sides (7), to find these sides(y). Ans. 5 and 12 PROBLEM III. To find the side of an equilateral triangle, inscribed in a circle, whose diameter is d; and that of another circumscribed about the same circle. Ans. dV3, and PROBLEM IV. To find the side... | |
 | John Bonnycastle - 1818 - عدد الصفحات: 284
...difference between the other two sides (7), to find these sides (/). Ans. 5 and 12 PROBLEM III. To find the side of an equilateral triangle, inscribed in a circle, whose diameter is d ; and that of another circumscribed about the same circle Ans. i^v/3, and d^/3 PROBLEM IV. To find... | |
 | Miles Bland - 1819 - عدد الصفحات: 444
...the side opposite to the bisected angle, and from the centre of a circle inscribed in the triangle. 24. The perpendicular from the vertex on the base...inscribed in a circle whose diameter is the base. 25. If an equilateral triangle be inscribed in a circle, and the adjacent arcs cut off by two of its... | |
 | Miles Bland - 1821 - عدد الصفحات: 898
...these add the angle CBO or its equal ABO ; and thé whole angle OBD is equal to the two ABO, OAB, ie to BOD (Eucl. i. 32.) ; and .-. OD = DB. (24.) The...an equilateral triangle is equal to the side of an equi~ lateral triangle inscribed in a circle, whose diameter is the base. From С the vertex, let CO... | |
 | Miles Bland - 1827 - عدد الصفحات: 462
...these add the angle CBO or its equal^ ABO ; and the whole angle OBD is equal to the two ABO, OAB, ie to BOD (Eucl. i. 32.) ; and .-. OD = DB. (24.) The...in it; CO will be equal to a side of this triangle. each equal to half the angle of an equilateral triangle, are equal to each other, and AOC=DEG, each... | |
 | John Radford Young - 1833 - عدد الصفحات: 310
...consequently x — a + i6 ± % V (62— 4a6 -4a2), and y = a+ *b T i V (62— 4a6-4a2). PROBLEM LXIV. To find the side of an equilateral triangle, inscribed in a circle, whose diameter is d ; and that of another circumscribed about the same circle. Let AFGC be the given circle, and ABC... | |
 | John Radford Young - 1835 - عدد الصفحات: 298
...consequently x = a + |6 ± |V (&2 — 4o6— 4a2),andi/=a+J& :p|V (b2—4ab-4a?). PROBLEM LXIV. To find the side of an equilateral triangle, inscribed in a circle, whose diameter is d ; and that of another circumscribed about the same circle. Let AFGC be the given circle, and ABC... | |
 | Euclides - 1845 - عدد الصفحات: 546
...circle, any of* sides will cut off one-fourth part of the diameter drawn through tie opposite angle. 13. The perpendicular from the vertex on the base of an...equal to the side of an equilateral triangle inscribed m a circle whose diameter is the base. Required proof. 14. If a circle be inscribed in a right-angled... | |
 | Nathan Scholfield - 1845 - عدد الصفحات: 542
...a square, inscribed in a given semicircle, whose diameter is d. 1 Ans. —a •/ 5 5 Ex. 2. To find the side of an equilateral triangle inscribed in a circle whose diameter is d ; and that of another circumscribed about the same circle. Ans. ^d^/3, and d^/3 Ex. 3. To find the... | |
 | Nathan Scholfield - 1845 - عدد الصفحات: 506
...of a square, inscribed in a given semicircle, whose diameter is A . 1 , Ans. -rav/5 D Ex. 2. To find the side of an equilateral triangle inscribed in a circle whose diameter is d ; and that of another circumscribed about the same circle. Ans. ?d</3, and d^/3 Ex. 3. To find the... | |
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The perpendicular from the vertex on the base of an equilateral triangle is equal to the side of an equilateral triangle inscribed in a circle, whose diameter is the base. 
