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 ## A Treatise on Algebra: In Practice and Theory, ... with Notes and ..., Volume 2

John Bonnycastle - Algebra - 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... ## 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... ## 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... ## Geometrical Problems Deducible from the First Six Books of Euclid, Arranged ...

Miles Bland - 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... ## 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... ## 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... ## 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... ## 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... ## A Series on Elementary and Higher Geometry, Trigonometry, and Mensuration ...

...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... 