 | Abram Robertson - 1818 - 196 pages
...the ellipse, and therefore (15. v.) the circle AFBG: the ellipse ADBE :: CF: CD :: AB : D E. 313. An ellipse is equal to a circle, whose diameter is a mean proportional between its axes. For the rest * As the hyperbola and its asymptotes may be indefinitely extended, it is evident... | |
 | John Farrar - Logarithms - 1822 - 270 pages
...stated thus, This figure being a mean proportional between its circumscribed and inscribed circles, that is, equal to a circle whose diameter is a mean proportional between the axes of the ellipse, we nay consider the product of the two axes of any ellipse is the square of the... | |
 | John Farrar - Logarithms - 1822 - 244 pages
...stated thus, This figure being a mean proportional between its circumscribed and inscribed circles, that is, equal to a circle whose diameter is a mean proportional between the axes of the ellipse, we may consider the product of the two axes of any ellipse is the square of the... | |
 | Thomas Curtis - Aeronautics - 1829 - 828 pages
...ellipse as the transverse axis is to the conjugate. COR. 2. The area of an ellipse is equal to that of a circle whose diameter is a mean proportional between the two axes. COR. 3. The areas of two ellipses are to each other as the rectangles under their axes. INDEX то... | |
 | John Farrar - Trigonometry - 1833 - 276 pages
...transverse. This figure being a mean proportional between its circumscribed and inscribed circles, that is, equal to a circle whose diameter is a mean proportional between the axes of the ellipse, we may consider the product of the two axes of any ellipse is the square of the... | |
 | John Farrar - Trigonometry - 1833 - 274 pages
...thus, "*• This figure being a mean proportional between its circumscribed and inscribed circles, that is, equal to a circle whose diameter is a mean proportional between the axes of the ellipse, we may consider the product of the two axes of any ellipse is the square of the... | |
 | John Bonnycastle - Measurement - 1835 - 308 pages
...c and then the fluent of— Xx^tx — x2 will be =yx A> from whence the rule is derived. QEI Carol. The ellipse is equal to a circle whose diameter is a mean proportional between the two axes, and from hence the rule is formed for the whole ellipse. 2. Multiply the segment thus found, and the two... | |
 | John Bonnycastle - Geometry - 1848 - 320 pages
...and then the fluent of— XxVtx — ar* will be ='rX A, from whence the rule is derived. QEI Carol. The ellipse is equal to a circle whose diameter is a mean proportional between the two axes, and from hence the rule is formed for the whole ellipse. COJUC SECTIONS. 101 2. Multiply the segment thus... | |
 | Alfred Hiley - 1871 - 184 pages
...and the other diameter are given. — Divide ^f °f the area by the given diameter. Note 3. — An ellipse is equal to a circle whose diameter is a mean proportional between the two diameters ; that is, the area of the ellipse ACBD is equal to the area of a circle whose diameter is... | |
 | Benjamin Hallowell - Geometry - 1872 - 286 pages
...the ellipse multiplied by the area of a circle whose diameter is unity, or it is equal to the area of a circle whose diameter is a mean proportional between the two axes, = \/4ab. PROBLEM IY. — To construct the ellipse from its equation y2 = 7,2 . . - V a2 — x'2, or... | |
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This figure being a mean proportional between its circumscribed and inscribed circles, that is, equal to a circle whose diameter is a mean proportional between the axes of the ellipse, we... 
