## Plane and Solid Geometry1901 |

### From inside the book

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**plane**figure is a geometrical figure , all of whose points lie in the same**plane**, as N. 14.**Plane**Geometry treats of**plane**figures only .**M N**FIG . 4 . 15. Solid Geometry treats of figures which are not**plane**. 16. When one figure can ... Page 54

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**MN**, VS = ST = TU . Proof . Draw Then WX = XY = YZ . WO , XP , YR || AB . WVSO , XSTP , YTUR are parallelograms , ( hyp . and con . ) . .. VS WO , ST XP , TU = YR , = ( opposite sides of parallelogram ) . But as VSST TU , = .. WO = XP ... Page 74

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**MN**. M chord B 166. A chord is a straight line joining any two points in the circumference ; as AB . 167. A central angle is an angle formed by two radii ; as A. 168. Circles having the same center are called concentric . PRELIMINARY ... Page 90

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**m n**+ 1 m The error in taking one of these approximate values as a ratio is less than 1 m As m may be made indefinitely large , the fraction may be made indefinitely small , or the value of B may be found with A any assigned degree of ... Page 119

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**mn**= = pq . m : p = q : n . Proof .**mn**= = pq . Dividing both members by np m q . n p Q.E.D. Ex . 519. If ab =**mn**, find all possible proportions consisting of a , b , m , and n . PROPOSITION III . THEOREM 266. A mean proportional ...### Other editions - View all

### Common terms and phrases

ABCD altitude angles are equal bisect bisector chord circumference circumscribed cone cylinder diagonals diagram for Prop diameter diedral angles divide draw drawn equiangular equiangular polygon equilateral triangle equivalent exterior angle face angles find a point Find the area Find the radius Find the volume frustum geometrical given circle given line given point given triangle Hence HINT homologous hypotenuse inches inscribed intersecting isosceles triangle joining the midpoints lateral area lateral edges line joining mean proportional median opposite sides parallel lines parallelogram parallelopiped perimeter perpendicular plane MN point equidistant polyedral angle polyedron PROPOSITION prove Proof quadrilateral radii ratio rectangle regular polygon respectively equal rhombus right angles right triangle SCHOLIUM segments similar triangles sphere spherical polygon spherical triangle square straight angle straight line surface tangent THEOREM trapezoid triangle ABC triangle are equal triedral vertex

### Popular passages

Page 144 - If two chords intersect within a circle, the product of the segments of one is equal to the product of the segments of the other.

Page 145 - If, from a jwint without a circle, a tangent and a secant be drawn, the tangent is the mean proportional between the secant and UK external segment.

Page 41 - If two triangles have two sides of one equal respectively to two sides of the other, but the included angle of the first triangle greater than the included angle of the second, then the third side of the first is greater than the third side of the second.

Page 301 - A cylinder is a solid bounded by a cylindrical surface and two parallel planes; the bases of a cylinder are the parallel planes; and the lateral surface is the cylindrical surface.

Page 176 - Two triangles having an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles.

Page 27 - The median to the base of an isosceles triangle is perpendicular to the base.

Page 149 - In any obtuse triangle, the square of the side opposite the obtuse angle is equal to the sum of the squares of the other two sides, increased by twice the product of one of these sides and the projection of the other side upon it.

Page 333 - A spherical polygon is a portion of the surface of a sphere bounded by three or more arcs of great circles. The bounding arcs are the sides of the polygon ; the...

Page 123 - If a line parallel to one side of a triangle intersects the other two sides, either side is to one of its segments as the other side is to its corresponding segment. For AD:DB = AE : EC.

Page 308 - The lateral areas, or the total areas, of similar cylinders of revolution are to each other as the squares of their altitudes, or as the squares of their radii ; and their volumes are to each other as the cubes of their altitudes, or as the cubes of their radii. Let S, S' denote the lateral areas, T, T...