## Elements of Geometry and Trigonometry |

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Page 68

The

The

**altitude**of a triangle is the per- pendicular let fall from the vertex of an angle on the opposite side , taken as a base . Thus , AD is the**altitude**of the triangle BAC B 6. The**altitude**of a parallelogram is the perpendicular ... Page 69

Parallelograms which have equal bases and equal

Parallelograms which have equal bases and equal

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

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

Hence these two parallelograms ABCD , ABEF , which have 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 . E Suppose , first , that the bases are A commensurable , and are to each other , for example , as the numbers 7 and ... 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 ... Any two rectangles are to each other as the products of their bases multiplied by their**altitudes**, Let ABCD ...### What people are saying - Write a review

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Elements of Geometry and Trigonometry from the Works of A. M. Legendre A. M. Legendre No preview available - 2017 |

### 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