## Elements of Geometry and Trigonometry |

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Page 13

... which expresses the distance between the points A and B. The expression Ax ( B + C - D ) represents the product of A by the quantity B + C - D . If A + B were to be

... which expresses the distance between the points A and B. The expression Ax ( B + C - D ) represents the product of A by the quantity B + C - D . If A + B were to be

**multiplied**by A - B + C , the product would be indicated thus ... Page 30

... are triangles in the figure ; in other words , as there are units in the number of sides diminished by two . Cor . 1. The sum of the angles in a quadrilateral is equal to two right angles

... are triangles in the figure ; in other words , as there are units in the number of sides diminished by two . Cor . 1. The sum of the angles in a quadrilateral is equal to two right angles

**multiplied**by 4-2 , which amounts to four ... Page 31

The sum of the angles of a pentagon is equal to two right angles

The sum of the angles of a pentagon is equal to two right angles

**multiplied**by 5-2 , which amounts to six right angles : hence , when a pentagon is equiangular , each angle is equal to the fifth part of six right angles , or to § of one ... Page 35

Equimultiples of two quantities are the products which arise from

Equimultiples of two quantities are the products which arise from

**multiplying**the quantities by the same number : thus , mx A , mx B , are equimultiples of A and B , the common multiplier being m . 10. Two quantities A and B are said to ... Page 38

P , by

P , by

**multiplying**both members of the equation by mxn . But m . M and n . Q , may be regarded as the two extremes , and n . N and m . P , as the means of a propor- tion ; hence , m . M : n . N :: m . P : n . Q. PROPOSITION IX .### What people are saying - Write a review

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### Common terms and phrases

ABCD adjacent altitude base become Book called centre chord circle circumference circumscribed common cone consequently construction contained corresponding cosine Cotang cylinder described diameter difference distance divided draw drawn equal equation equivalent evident expressed extremities fall figure follows formed formulas four frustum give given gles greater half hence homologous included inscribed intersection less likewise logarithm manner means measured meet middle multiplied opposite parallel parallelogram parallelopipedon pass perpendicular plane polygon prism PROBLEM Prop proportional PROPOSITION pyramid quantities radii radius ratio reason rectangle regular remaining right angles Scholium segment shown sides similar sine solid solid angle sphere spherical triangle square straight line Suppose surface taken tang tangent THEOREM third triangle triangle ABC vertex whole