## 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

Results 6-10 of 71

Page 93

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**semicircle**. B A E D C Draw AF to the centre , and produce it to C , and join CE . Therefore the segment BADC is greater than a**semicircle**; and the angles in it BAC , BEC are equal , by the first case : for the same reason , because ... Page 95

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**semicircle**. But if the angles ABD , BAD are not equal to one another . B D C E B E A D C At the point A , in the straight line AB , make the angle BAE equal to the angle ABD , ( 1.23 . ) and produce BD , if necessary , to meet AE in E ... Page 96

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**semicircle**: but if the angle ABD be less than BAD , the centre E falls within the segment ABC , which is therefore greater than a**semicircle**. Wherefore a segment of a circle being given , the circle is described of which it is a ... Page 99

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**semicircle**; because DC passes through the centre : ( III . 1. Cor . ) therefore the circumference AD is equal to ...**semicircle**is a right angle ; but the angle in a segment greater than a**semicircle**is less than a right angle ... Page 100

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**semicircle**is a right angle : ( 111. 31. ) and consequently the other two angles BAD , ABD , are equal to a right angle ; ( 1. 32. ) but ABF is likewise a right angle ; ( constr . ) ( ax . 1. ) therefore the angle ABF is equal to the ...### 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.