## Elements of Geometry and Trigonometry |

### From inside the book

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Page 11

The

The

**rectangle**, which has its angles right an- gles , without having its sides equal . The parallelogram , or rhomboid , which has its opposite sides parallel . The rhombus , or lozenge , which has its sides equal , without having its ... Page 31

... each of them will be a right angle ; a conclusion which sanctions the seventeenth Definition , whère the four angles of a quadrilateral are asserted to be right angles , in the case of the

... each of them will be a right angle ; a conclusion which sanctions the seventeenth Definition , whère the four angles of a quadrilateral are asserted to be right angles , in the case of the

**rectangle**and the square . Cor . 2. Page 63

If the given angle is a right angle , the figure will be a

If the given angle is a right angle , the figure will be a

**rectangle**; if , in addition to this , the sides are equal , it will be a square . PROBLEM XIII . To find the centre of a given circle or arc . Page 70

Every parallelogram is equivalent to the

Every parallelogram is equivalent to the

**rectangle**which has the same base and the same altitude . · PROPOSITION II . THEOREM . Every triangle is half the parallelogram which has the same base and the same altitude . Page 71

The

The

**rectangle**ABCD will contain seven partial**rectangles**, while AEFD will contain four : hence the**rectangle**ABCD is to AEFD as 7 is to 4 , or as AB is to AE . The same reasoning may be applied to any other ratio equally with that of 7 ...### 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