Elements of Geometry;: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle and the Geometry of Solids; to which are Added, Elements of Plane and Spherical TrigonometryBell & Bradfute, 1804 - 440 Seiten |
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Seite 209
... polygons , of the fame number of fides , infcribed in circles , are fimilar , and are to one another as the fquares of the diameters of the circles . Let ABCDEF and GHIKLM be two equilateral polygons of the fame number of fides ...
... polygons , of the fame number of fides , infcribed in circles , are fimilar , and are to one another as the fquares of the diameters of the circles . Let ABCDEF and GHIKLM be two equilateral polygons of the fame number of fides ...
Seite 210
... polygon d 1. def . 6. ABCD is therefore fimilar to the polygon GHIKLM d . And because fimilar polygons are as the fquares of their homolo- e 20. 6. gous fidese , the polygon ABCDEF is to the polygon GHIKLM as the fquare of AB to the ...
... polygon d 1. def . 6. ABCD is therefore fimilar to the polygon GHIKLM d . And because fimilar polygons are as the fquares of their homolo- e 20. 6. gous fidese , the polygon ABCDEF is to the polygon GHIKLM as the fquare of AB to the ...
Seite 211
... polygon infcribed in a circle being given , to find the fide of a poly- gon of the fame number of fides defcribed about the circle . Let ABCDEF be an equilateral polygon infcribed in the circle ABD ; it is required to find the fide of ...
... polygon infcribed in a circle being given , to find the fide of a poly- gon of the fame number of fides defcribed about the circle . Let ABCDEF be an equilateral polygon infcribed in the circle ABD ; it is required to find the fide of ...
Seite 212
... polygon , an equilateral polygon may be defcribed about the circle , the fides of which will each be equal to KL , and will be equal in number to the fides of the infcribed polygon . Therefore , KL is the fide of an equilate- ral polygon ...
... polygon , an equilateral polygon may be defcribed about the circle , the fides of which will each be equal to KL , and will be equal in number to the fides of the infcribed polygon . Therefore , KL is the fide of an equilate- ral polygon ...
Seite 213
... polygon , of the fame number of fides , defcribed about ABC d . Let the polygon de- fcribed about the circle be called M , and the polygon infcribed be called N ; then , because thefe polygons are fimilare , they are as the fquares of ...
... polygon , of the fame number of fides , defcribed about ABC d . Let the polygon de- fcribed about the circle be called M , and the polygon infcribed be called N ; then , because thefe polygons are fimilare , they are as the fquares of ...
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Häufige Begriffe und Wortgruppen
ABC is equal ABCD alfo alſo angle ABC angle ACB angle BAC arch bafe baſe becauſe the angle bifected Book cafe centre circle ABC circumference co-fine cof BC cylinder defcribed demonftrated diameter draw drawn equal angles equiangular equilateral polygon equimultiples Euclid exterior angle faid fame altitude fame manner fame plane fame ratio fame reaſon fecond fection fegment femicircle fhall fhewn fide BC fides fince firft firſt folid fore fquare fuch given ftraight line greater infcribed interfect join lefs leſs Let ABC line BC magnitudes muſt oppofite angle parallel parallelepipeds parallelogram perpendicular polygon prifm propofition proportionals Q. E. D. PROP radius reafon rectangle contained rectilineal figure remaining angle ſpherical triangle ſquare tangent THEOR theſe thofe thoſe triangle ABC uſe wherefore
Beliebte Passagen
Seite 27 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...
Seite 172 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Seite 42 - The complements of the parallelograms, which are about the diameter of any parallelogram, are equal to one another.
Seite 84 - The diameter is the greatest straight line in a circle; and of all others, that which is nearer to the centre is always greater than one more remote; and the greater is nearer to the centre than the less. Let ABCD be a circle, of which...
Seite 106 - IF from a point without a circle there be drawn two straight lines, one of which cuts the circle, and the other meets it ; if the rectangle contained by the whole line which cuts the circle, and the part of it without the circle be equal to the square of the line which meets it, the line which meets shall touch the circle.
Seite 22 - THE greater angle of every triangle is subtended by the greater side, or has the greater side opposite to it. Let ABC be a triangle, of which the angle ABC is greater than the angle BCA : the side AC is likewise greater than the side AB. For, if it be not greater, AC must...
Seite 64 - If then the sides of it, BE, ED are equal to one another, it is a square, and what was required is now done: But if they are not equal, produce one of them BE to F, and make EF equal to ED, and bisect BF in G : and from the centre G, at the distance GB, or GF, describe the semicircle...
Seite 166 - IN a right angled triangle, if a perpendicular be drawn from the right angle to the base, the triangles on each side of it are similar to the whole triangle, and to one another. Let ABC be a right angled triangle, having the right angle BAC ; and from the point A let AD be drawn perpendicular to the base BC : the triangles ABD, ADC are similar to the whole triangle ABC, and to one another.
Seite 54 - If a straight line be bisected, and produced to any point ; the rectangle contained by the whole line thus produced, and the part of it produced...
Seite 2 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle; and the straight line which stands on the other is called a perpendicular to it.