## Elements of Geometry and Trigonometry |

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Page 69

Figures which have equal areas are called

Figures which have equal areas are called

**equivalent**. The term equal , when applied to figures , designates those which are equal in every respect , and which being applied to each other will coincide in all their parts ( Ax . 13. ) ... Page 70

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

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 74

For , the parallelogram ABCD is

For , the parallelogram ABCD is

**equivalent**F D to the rectangle ABEF , which has the same base AB , and the same altitude BE ( Prop . I. Cor . ) : but this rectangle is measured by AB × BE ( Prop . IV . Sch . ) ; therefore , ABX BE A is ... Page 75

therefore , the trapezoid ABCD is

therefore , the trapezoid ABCD is

**equivalent**to the parallelogram ADKL , and is measured by EFX AL . But we have AL - DK ; and since the triangles IBL and KCI are equal , the side BL - CK : hence , AB + CD = AL + DK = 2AL ; hence AL is ... Page 76

If a line is divided into two parts , the square described on the whole line is

If a line is divided into two parts , the square described on the whole line is

**equivalent**to the sum of the squares described on the parts , together with twice the rectangle contained by the parts . Let AC be the line , and B the ...### 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