## An Elementary Geometry |

### From inside the book

Results 6-10 of 14

Page 32

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**divided**into any number of equal parts , A E , EF , AH , HI , & c . , and through the points of division , lines E L , FM , HO , IP , & c . be drawn parallel to the sides of the rectangle ; then the rectangle will be**divided**into ... Page 37

... ; the triangle AGH or DEF , and the angle A GHE ( I. 40 ) . By hypothesis AB : DE AC : DF AB : AGAC : AH that is , the sides A B , A C are

... ; the triangle AGH or DEF , and the angle A GHE ( I. 40 ) . By hypothesis AB : DE AC : DF AB : AGAC : AH that is , the sides A B , A C are

**divided**proportionally by the line GH ; therefore G H is parallel to BC BOOK II . 37. Page 40

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**divided**into the same number of similar triangles . Let ABCDEF and GHIKLM be similar poly- B H I D G K M L F E gons ; they can be**divided**into the same number of sim- ilar triangles . From the homologous angles A and G draw the ... Page 41

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**divided**into the same number of similar triangles ( 30 ) ; therefore ( 29 ) 2 2 ABC : GHIAC2 : GI2 2 and ACD : GIK AC2 : GI2 Therefore ABC : GHI ACD : GIK In like manner ACD GIK : ADE : GKL and Hence ( Pn . 23 ) ADE : GKL AEF : GLM ABC ... Page 42

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**divided**by the number of angles which is the same . The homologous sides are proportional ; for as the polygons are regular , A B = BC = CD , & c . , and G H = HI = IK , & c . , therefore AB : GH BC : HI = CD : IK , & c . = THEOREM XVII ...### Other editions - View all

### Common terms and phrases

A B C ABCD adjacent altitude angle ABC apothem arcs A B base and altitude bisect centre chord circ circumference cone construct the triangle convex surface Corollary cube cylinder diagonals diameter distance divided dodecagon EATON'S equal altitudes equally distant equiangular equilateral feet frustum given angle given circle given line given point given side given square half the arc hexagon homologous sides hypothenuse included angle infinite number inscribed internal angles intersection isosceles triangle Let ABCDEF line joining lines A B measured by half number of sides opposite sides parallel planes parallelogram parallelopiped perimeter perpendicular plane parallel quadrilateral radii radius ratio rectangle regular polygon respectively equal rhombus right angles right prism right pyramid right triangle Scholium secant segment similar triangles slant height sphere tangent THEOREM VII trapezoid triangle ABC vertex

### Popular passages

Page 25 - Four quantities are in proportion when the ratio of the first to the second is equal to the ratio of the third to the fourth.

Page 30 - If any number of quantities are proportional, any antecedent is to its consequent as the sum of all the antecedents is to the sum of all the consequents. Let a : b = c : d = e :f Now ab = ab (1) and by Theorem I.

Page 27 - If the product of two quantities is equal to the product of two others, the...

Page 43 - The area of a regular polygon is equal to half the product of its perimeter and apothem.

Page 11 - If two triangles have two sides, and the included angle of the one equal to two sides and the included angle of the other, each to each, the two triangles are equal in all respects.

Page 23 - If two triangles have two sides of one respectively equal to two sides of the other, but the third sides unequal...

Page 20 - ... polygon, is equal to twice as many right angles as the polygon has sides minus two.

Page 49 - A Circle is a plane figure bounded by a curved line every point of which is equally distant from a point within called the center.

Page 70 - A right cylinder is a solid described by the revolution of a rectangle about one of its sides.

Page 64 - DEFINITIONS. 1 . A straight line is perpendicular to a plane, when it is perpendicular to every straight line of the plane which it meets.