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" EG, let fall from a point in the circumference upon the diameter, is a mean proportional between the two segments of the diameter DS, EF (p. "
A Royal Road to Geometry: Or, an Easy and Familiar Introduction to the ... - Page 279
by Thomas Malton - 1774 - 440 pages
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1858 - 256 pages
...proportional required. For the perpendicular BD, le*. fall from a point in the circumference upon the diameter, is a mean proportional between the two segments of the diameter AB, BC (Prop. XXII., Cor., B. IV.) ; and these segments are equal to the wo given lines. B PROBLEM...
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Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ...

George Roberts Perkins - Geometry - 1860 - 474 pages
...diameter, is called an ordinate to this diameter. Hence, we have this condition : In a circle any ordinate to a diameter is a mean proportional between the two segments of this diameter. We can show that this property is one of the consequences of the properties of right-angled...
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Elements of Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1862 - 532 pages
...proportional required. For the perpendicular С D, drawn from a point in the circumference to a point in the diameter, is a mean proportional between the two segments of the diameter AC, С D (Prop. ХХХП. Cor., Bk. IV.) ; and these segments are equal to the given lines. PROBLEM...
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Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - Geometry - 1866 - 328 pages
...proportional required. For the perpendicular CD, drawn from a point in the circumference to a point in the diameter, is a mean proportional between the two segments of the diameter AC, CB (Prop. XXXII. Cor., Bk. IV.) ; and these segments are,equal to the given lines. PROBLEM XXVII....
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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - Geometry - 1871 - 302 pages
...proportional required. For the perpendicular BD, le*. fall from a point in the circumference upon the diameter, is a mean proportional between the two segments of the diameter AB, BC (Prop. XXII., Cor., B. IV.) ; and these segments are equal to th< wo given lines, PROBLEM XX....
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Catalogue - Harvard University

Harvard University - 1874 - 668 pages
...equivalent triangle. t). Prove that the perpendicular from any point in the circumference of a circle upon a diameter is a mean proportional between the two segments of the diameter. 7. An equilateral triangle is inscribed in a circle. Prove that the ratio of its side to the radius...
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Notes on Rankine's Applied Mechanics

George Ira Alden - Mechanical engineering - 1877 - 112 pages
...of Mechanism, Article 513.) ARTICLE 507. Equations (3). — The square of the perpendicular, drawn from any point in the circumference of a circle to a diameter, is equal to the product of the segments into which the foot of the perpendicular divides the diameter...
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First B.A. Examination, University of London: A Hand-book to the Study of ...

J. G - 1878 - 408 pages
...proportional form x : y '.'. y : 2c — x, we may infer the geometrical property of the circle that a perpendicular from any point in the circumference...a diameter is a mean proportional between the two parts into which the perpendicular divides the diameter (9) By writing it in the form yf + y2 = Zex,...
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Elements of Geometry, After Legendre, with a Selection of Geometrical ...

Charles Scott Venable - 1881 - 380 pages
...mean proportional sought. For, the perpendicular GE, let fall from a point of the circumference on the diameter, is a mean proportional between the two segments of the diameter DE, EF (Prop. XXV. , Cor. ) ; now, these segments are equal to the given lines A and B. PROBLEM IV....
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Metrical Geometry: An Elementary Treatise on Mensuration

George Bruce Halsted - Measurement - 1881 - 258 pages
...1-4 meters shadow. 74-25 meters. Ans. 28. The perpendicular from any point on a circumference to the diameter is a mean proportional between the two segments of the diameter. 29. Every chord of a circle is a mean proportional between the diameter drawn from one of its extremities,...
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