## Elements of Geometry and Trigonometry |

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Page 68

The

The

**altitude**of a parallelogram is the perpendicular which measures the distance between two opposite sides taken as bases . Thus , EF is the**altitude**of the parallelo- Á gram DB . 7. The**altitude**of a trapezoid is the perpendicular ... Page 69

Parallelograms which have equal bases and equal

Parallelograms which have equal bases and equal

**altitudes**, are equivalent . Let AB be the common base of D CF EDF CE the two parallelograms ABCD , ABEF : and since they are supposed to have the same**altitude**, their upper bases DC ... Page 70

Hence these two parallelograms ABCD , ABEF , which havẽ the same base and

Hence these two parallelograms ABCD , ABEF , which havẽ the same base and

**altitude**, are equivalent Cor . Every parallelogram is equivalent to the rectangle which has the same base and the same**altitude**. PROPOSITION II . THEOREM . Page 71

Let ABCD , AEFD , be two rectan- D gles having the common

Let ABCD , AEFD , be two rectan- D gles having the common

**altitude**AD : they are to each other as their bases . AB , AE . A E Suppose , first , that the bases are commensurable , and are to each other , for example , as the numbers 7 ... Page 72

Hence , whatever be the ratio of the bases , two rectangles ABCD , AEFD , of the same

Hence , whatever be the ratio of the bases , two rectangles ABCD , AEFD , of the same

**altitude**, are to each other as their bases AB ... Any two rectangles are to each other as the products of their bases multiplied by their**altitudes**.### 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 contained Cosine Cotang cylinder described determine diameter difference distance divided draw drawn equal equations equivalent expressed extremities faces feet figure follows formed four frustum give given gles greater half hence homologous hypothenuse included inscribed intersection less let fall logarithm manner means measured meet middle multiplied number of sides opposite parallel parallelogram pass perpendicular plane polygon prism PROBLEM Prop proportional PROPOSITION pyramid quadrant quantities radii radius ratio reason rectangle regular remaining right angles Scholium segment sides similar Sine solid solid angle sphere spherical triangle square straight line suppose taken Tang tangent THEOREM third triangle triangle ABC unit vertex whole