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" The areas or spaces of circles are to each other as the squares of their diameters, or of their radii. "
Elementary Course of Geometry ... - Pągina 70
per Charles William Hackley - 1847 - 103 pągines
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1806 - 311 pągines
...same number of sides, inscribed in the circles ABD and GHK ; ABCDEF and GHIKLM are similar, and are to each other as the squares of the diameters of the circles ABD, GHK. Find N, O the centres of the circles ; join AN and BN, and GO and HO ; and produce AN and...
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A Course of Mathematics ...: Composed for the Use of the Royal Military ...

Charles Hutton - 1811
...and then it follows, that the spaces of the circles, which are the same as of the polygons, will be to each other as the squares of the diameters of the circles, c^. ED Corol. The spaces of circles are also to each other as the squares of the circumferences ; since...
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A Course of Mathematics: For the Use of Academies as Well as Private Tuition

Charles Hutton - 1812
...: FO + GH +HI, &t :: the diam. AL : the diam. KM (th. 72). (). E. 1). THEOREM XCI. Similar Figures Inscribed in Circles, are to each other as the Squares of the Diameters of those Circles. LET ABCDE, FCHIK, be two similar figures inscribed in the circles •whose diameters...
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A Practical Application of the Principles of Geometry to the Mensuration of ...

Jeremiah Day - 1815 - 96 pągines
...the latter is found in the table ; and, from the properties of similar figures, the two segments are to each other, as the squares of the diameters of the circles. We have then the following rule ; To find the area of a circular SEGMENT by the TABLE. Divide the height...
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A Course of Mathematics: In Two Volumes : for the Use of Academies ..., Volum 1

Charles Hutton - 1816
...or spaces of two circles, and D, dineir diameters ; then A : a •. -. o* : d1. For (by theorem 91) similar polygons inscribed in circles are to each...polygons to be increased more and more, or the length of thesides to become less and less, the polygon approaches nearer and nearer to the circle, till at length,...
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A Course of Mathematics: For the Use of Academies, as Well as Private Tuition

Charles Hutton - 1818
...or spaces of two circles, and D, tl their diameters ; then A : a : : oa : rf3. For (by theorem 91'i similar polygons inscribed in circles are to each...and less, the polygon approaches nearer and nearer lo the circle, till at length, by an infinite approach, coincide, and become in effect equal ; and...
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A Course of Mathematics: For the Use of Academies, as Well as Private ...

Charles Hutton - 1822
...&c. : FO + OH + HI, &c. : : the diam. AL : the diam. FM (th. 72). 4. ED THEOREM XCI. Similar Figures Inscribed in Circles, are to each other as the Squares of the Diameters of those Circles: Let ABCDE, FGH1K, be two similar figures inscribed in the circles whose diameters are...
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The Second [-fifth and Sixth] Part of A Course of Mathematics: Adapted to ...

Jeremiah Day - 1824
...the latter is found in the table ; and from the properties of similar figures, the two segments are to each other, as the squares of the diameters of the circles. We have then the following rule: To find the area of a circular SEGMENT by the TABLE. Divide the height...
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A Course of Mathematics for the Use of Academies: As Well as ..., Volum 1

Charles Hutton - 1825
...areas or spaces of two circles, and D d, their diameters ; then A : a : : oa : d*. For (by theorem 91) similar polygons inscribed in circles are to each...the circle, till at length, by an infinite approach, coincide, and become in effect equal ; and then it follows that the spaces of the circles, which are...
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Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry

John Playfair - 1829 - 186 pągines
...polygons of the same number of sides, inscribed in the circles ABO, UHK.; they are similar, and are to each other as the squares of the diameters of the circles. 1. Find N, O the centres of the circles; join AN, BN, and GO, HO; produce AN and GO till they meet...
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