## Elements of Geometry and Trigonometry |

### From inside the book

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Page 28

and since CD is parallel to EF , PR will for a like

and since CD is parallel to EF , PR will for a like

**reason**be perpen - C dicular to CD . Hence AB and CD are . perpendicular to the same straight line ; hence they are parallel ( Prop . XVIII . ) . R Q P F D B PROPOSITION XXIII . Page 33

For a like

For a like

**reason**AB is parallel to CD therefore the quadrilateral ABCD is a parallelogram . PROPOSITION XXX . THEOREM . If two opposite sides of a quadrilateral are equal and parallel , the remaining sides will also be equal and ... Page 46

neither could it be out of the line FG , for a like

neither could it be out of the line FG , for a like

**reason**; therefore , it would be in both the lines DE , FG . But two straight lines cannot cut each other in more than one point ; hence there is but one circumference which can pass ... Page 53

It has been found more simple to measure them by arcs of a circle , on account of the facility with which arcs can be made equal to given arcs , and for various other

It has been found more simple to measure them by arcs of a circle , on account of the facility with which arcs can be made equal to given arcs , and for various other

**reasons**. At all events , if the measurement of angles ... Page 54

For a like

For a like

**reason**, the angle CAD will be measured by the half of ED ; hence BAC + CAD , or BAD will be measured by half of BE + ED , or of BED . Suppose , in the second place , that the centre Clies without the angle BAD .### 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 produced 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