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Books Books 1 - 10 of 31 on The perpendicular from the vertex on the base of an equilateral triangle is equal....
" 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. "
Geometrical problems deducible from the first six books of Euclid, arranged ... - Page 247
by Miles Bland - 1819 - 377 pages
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A treatise on algebra: in practice and theory, ... with notes and ..., Volume 2

John Bonnycastle - Mathematics - 1813
...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...
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An Introduction to Algebra: With Notes and Observations : Designed for the ...

John Bonnycastle - Algebra - 1818 - 260 pages
...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...
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Geometrical Problems Deducible from the First Six Books of Euclid: Arranged ...

Miles Bland - Geometry - 1819 - 377 pages
...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...
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Geometrical Problems Deducible from the First Six Books of Euclid, Arranged ...

Geometry - 1821 - 438 pages
...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...
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Geometrical Problems Deducible from the First Six Books of Euclid: Arranged ...

Miles Bland - Geometry - 1827 - 377 pages
...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...
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The Elements of Analytical Geometry ...

John Radford Young - Geometry, Analytic - 1833 - 288 pages
...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...
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The elements of analytical geometry ...

John Radford Young - Geometry, Analytic - 1835 - 288 pages
...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...
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Robert Potts - 1845
...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...
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A Series on Elementary and Higher Geometry, Trigonometry, and Mensuration ...

Conic sections - 1845
...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...
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Higher Geometry and Trigonometry: Being the Third Part of a Series on ...

Nathan Scholfield - Conic sections - 1845 - 232 pages
...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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