## Elements of Geometry and Trigonometry |

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Page 69

Parallelograms which have 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

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 altitude AD : they are to each other as their

Let ABCD , AEFD , be two rectan- D gles having the common altitude AD : they are to each other as their

**bases**. AB , AE . ... AE will contain 4 of those parts : at each point of division erect a perpendicular to the**base**; seven partial ... Page 72

Hence , whatever be the ratio of the

Hence , whatever be the ratio of the

**bases**, two rectangles ABCD , AEFD , of the same altitude , are to each other as their**bases**AB , AE . PROPOSITION IV . THEOREM . Any two rectangles are to each other as the products of their**bases**... Page 73

For example , if the

For example , if the

**base**of the rectangle A contains three units , and its altitude ten , that rectangle will be represented by the number 3 × 10 , or 30 , a number which signifies nothing while thus isolated ; but if there is a second ...### 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