## Elements of Geometry: Containing the First Six Books of Euclid: With a Supplement on the Quadrature of the Circle and the Geometry of Solids ...J. Eastburn & Company, 1819 - 317 sider |

### Inni boken

Resultat 1-5 av 28

Side 19

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**semicircle**is the figure contained by a diameter and the part of the circumference cut off by the diameter . XV . Rectilineal figures are those which are contained by straight lines . XVI . Trilateral figures , or triangles , by three ... Side 63

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**semicircle**BHF and produce DE to H , and join GH . Therefore , because the straight line BF is divided into two equal parts in the point G , and into two unequal in the point E , the rect- angle BE.EF , together with the square of EG ... Side 80

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**semicircle**, and join BF , FD : And because the angle BFD is at the cen- tre , and the angle BAD at the circumfer- ence , both having the same part of the circumference , viz . BCD , for their base ; therefore the angle BFD is double ... Side 81

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**semicircle**; and the angles in it BAC , BEC are equal , by the first case : For the same reason , because CBED is greater than a**semicir**- cle , the angles CAD , CED are equal : Therefore the whole angle BAD is equal D F to the whole ... Side 82

... the segment ABC is a

... the segment ABC is a

**semicircle**. Next let the angles ABD , BAD be unequal ; at the point A , in the straight line AB make ( 23 . 1. ) the angle BAE equal to the angle ABD , and produce BD if neces- : B B B D E A A D C E 82 ELEMENTS.### Andre utgaver - Vis alle

Elements of Geometry: Containing the First Six Books of Euclid : with a ... John Playfair Uten tilgangsbegrensning - 1837 |

Elements of Geometry: Containing the First Six Books of Euclid, with a ... John Playfair Uten tilgangsbegrensning - 1824 |

Elements of Geometry: Containing the First Six Books of Euclid, with a ... John Playfair Uten tilgangsbegrensning - 1819 |

### Vanlige uttrykk og setninger

ABC is equal ABCD altitude angle ABC angle ACB angle BAC angle EDF arch AC base BC bisected centre circle ABC circumference common section cosine cylinder demonstrated diameter draw drawn equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater hypotenuse inscribed join less Let ABC Let the straight line BC magnitudes meet opposite angle parallel parallelepipeds parallelogram perpendicular polygon prism PROB produced proportionals proposition Q. E. D. COR Q. E. D. PROP radius ratio rectangle contained rectilineal figure remaining angle segment semicircle shewn side BC sine solid angle solid parallelepipeds spherical angle spherical triangle straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore

### Populære avsnitt

Side 153 - If from the vertical angle of a triangle a straight line be drawn perpendicular to the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the perpendicular and the diameter of the circle...

Side 19 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.

Side 33 - THE greater angle of every triangle is subtended by the greater side, or has the greater side opposite to it.

Side 292 - If a straight line meet two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...

Side 308 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.

Side 36 - IF two triangles have two sides of the one equal to two sides of the other, each to each, but the angle contained by the two sides of one of them greater than the angle contained by the two sides equal to them, of the other ; the base of that which has the greater angle shall be greater than the base of the other.

Side 18 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.

Side 78 - To draw a straight line from a given point, either without or in the circumference, which shall touch a given circle. First, let A be a given point without the given circle BCD : it is required to draw a straight line from A which shall touch the circle.

Side 77 - THE straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle...

Side 39 - If a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another ; and the exterior angle equal to the interior and opposite upon the same side ; and likewise the too interior angles upon the same side together equal to two right angles.