## Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes; together with a selection of geometrical exercises. To which is prefixed an intr., containing a brief outline of the history of geometry. By R. Potts. [With] Appendix1845 |

### From inside the book

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**trapezium**ABCF take the triangle FDC , and from the same**trapezium**take the triangle EAB , and the remainders are equal , ( ax . 3. ) therefore the parallelogram ABCD is equal to the parallelogram EBCF . Therefore parallelograms upon ... Page 43

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**trapezium**, fall under the general idea of a parallelogram ; but as Euclid has defined parallel straight lines after he had defined four - sided figures , no other arrangement could be adopted than the one he has followed ; and for ... Page 51

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**trapezium**, which would appear to be impossible , if the sense in which Euclid applies the third axiom , is to be retained here . It may be observed , that the two parallelograms exhibited in fig . 2 partially lie on one another , and ... Page 298

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**trapezium**( 1 ) by a line drawn from one of its angular points : ( 2 ) by a line drawn from a given point in one side . 39. Divide a triangle into three equal parts , ( 1 ) by lines drawn from a point in one of the sides : ( 2 ) by ... Page 299

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**trapezium**is such , that the perpendiculars let fall on a diagonal from the opposite angles are equal . Divide the**trapezium**into four equal triangles , by straight lines drawn to the angles from a point within it . 48. Given one side ...### Other editions - View all

Euclid's Elements of Geometry [Book 1-6, 11,12] with Explanatory Notes ... Euclides No preview available - 2016 |

### Common terms and phrases

AC is equal altitude angle ABC angle BAC angle equal base BC chord circle ABCD circumference cone cylinder describe a circle diagonals diameter divided draw EFGH equal angles equiangular equilateral triangle equimultiples Euclid Euclid's Elements Geometry given angle given circle given line given point given straight line given triangle gnomon greater hypothenuse inscribed interior angles intersection isosceles triangle less Let ABC lines be drawn magnitudes meet the circumference multiple opposite sides parallel parallelogram pentagon perpendicular polygon prism problem Proclus produced Prop proportional proved pyramid Q.E.D. PROPOSITION radius rectangle contained rectilineal figure remaining angle right angles right-angled triangle segment semicircle shew shewn similar triangles solid angle solid parallelopipeds square of AC tangent THEOREM touches the circle trapezium triangle ABC vertex vertical angle wherefore

### Popular passages

Page 56 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.

Page 29 - THE straight lines which join the extremities of two equal and parallel straight lines, towards the same parts, are also themselves equal and parallel.

Page 26 - Wherefore, if a straight line, &c. QED PROPOSITION XXIX. THEOREM. Jf a straight line fall upon two parallel straight lines, it makes the alternate angles equal...

Page 99 - The angle in a semicircle is a right angle ; the angle in a segment greater than a semicircle is less than a right angle ; and the angle in a segment less than a semicircle is greater than a right angle.

Page 15 - The angles which one straight line makes with another upon one side of it, are either two right angles, or are together equal to two right angles. Let the straight line AB make with CD, upon one side of it, the angles CBA, ABD : these shall either be two right angles, or shall together be equal to two right angles. For...

Page 58 - If the vertical angle of a triangle be bisected by a straight line which also cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.

Page 22 - IF two triangles have two sides of the one equal to two sides of the...

Page vi - The sluggard is wiser in his own conceit than seven men that can render a reason.

Page 54 - If there be imo straight lines, one of which is divided into any number of parts; the rectangle contained by the two straight lines, is equal to the rectangles contained by the undivided line, and the several parts of the divided line.

Page 26 - That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.