## 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 pages |

### From inside the book

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**angle EDF**then shall the base BC be equal to the base EF ; and the triangle ABC to the tri- angle DEF ; and the A D other angles , to which the equal sides are op- B C E F * The three conclusions in this enunciation are more briefly ... Page 24

... angle BAC is equal to the

... angle BAC is equal to the

**angle EDF**; wherefore also the point C shall coincide with the point F , because AC is equal to DF : But the point B coincides with the point E ; wherefore the base BC shall coincide with the base EF ( cor ... Page 27

... angle BAC is equal to the

... angle BAC is equal to the

**angle EDF**. For , if the triangle ABC be applied to the triangle DEF , so that the point B be on E , and the straight line BC upon EF ; the point C shall also coincide with the point F , because BC is equal to ... Page 36

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**angle**FAG is made equal to the given rectilineal ,**angle**DCE . Which was to be done . PROP . XXIV . THEOR . If two ...**EDF**; the base BC is also greater than the base EF . Of the two sides DE , DF , let DE be the side which is not greater ... Page 37

... angle BAC is likewise greater than the

... angle BAC is likewise greater than the

**angle EDF**. Α D For , if it be not greater , it must either be equal to it , or less ; but the angle BAC is not equal to the**angle EDF**, because then the base , BC would be equal ( 4. 1. ) to EF ...### Other editions - View all

### Common terms and phrases

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

### Popular passages

Page 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...

Page 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.

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

Page 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...

Page 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.

Page 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.

Page 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.

Page 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.

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

Page 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.