## The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh and Twelfth ; the Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected, and Some of Euclid's Demonstrations are Restored ; Also the Book of Euclid's Data, in Like Manner Corrected |

### From inside the book

Results 11-15 of 62

Page 58

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**squares of AC**, CD : and the square of AF is equal ( 47. 1. ) to the squares of AE , EF , because AEF is a right angle ; therefore the square of AF is double of the**squares of AC**, CD : but the squares of AD , DF are equal to the square ... Page 59

... square of EC is equal to the square of CA ; therefore the squares of EC , CA are double of the square of CA : but the square of EA is equal ( 47. 1. ) to the squares of EC , CA ; therefore the square of EA is double of the

... square of EC is equal to the square of CA ; therefore the squares of EC , CA are double of the square of CA : but the square of EA is equal ( 47. 1. ) to the squares of EC , CA ; therefore the square of EA is double of the

**square of AC**... Page 60

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**square**ABDC ; bisect ( 10. 1. )**AC**in E , and join BE ; produce CA to F , and make ( 3. 1. ) EF equal to EB , and upon AF describe ( 46. 1. ) the**square**FGHA ; AB is divided in H , so that the rectangle AB , BH is equal to the**square**of ... Page 61

... square of AB is greater than the

... square of AB is greater than the

**squares of AC**, CB by twice the rectangle BC , CD . A Because the straight line BD is divided into two parts in the point C , the square of BD is equal ( 4. 2. ) to the squares of BC , CD , and twice the ... Page 62

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**square of AC**, opposite to the angle B , is less than the squares of CB , BA , by twice the rectangle CB , BD . A First , Let AD fall within the triangle ABC ; and because the straight line CD is divided into two parts in the point D ...### Other editions - View all

The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... Robert Simson,Euclid Euclid No preview available - 2018 |

### Common terms and phrases

altitude angle ABC angle BAC base BC BC is equal BC is given bisected centre circle ABCD circumference co-sine cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid ex æquali excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gnomon greater join less Let ABC multiple parallel parallelogram parallelogram AC perpendicular point F polygon prism proportionals proposition Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar sine solid angle solid parallelopipeds square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore

### Popular passages

Page 9 - Let it be granted that a straight line may be drawn from any one point to any other point.

Page 81 - The angles in the same segment of a circle are equal to one another.

Page 315 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.

Page 33 - 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 49 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.

Page 96 - If from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.

Page 155 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.

Page 22 - ANY two angles of a triangle are together less than two right angles.

Page 25 - Let A, B, C be the three given straight lines, of which any two whatever are greater than the third, viz.

Page 24 - Any two sides of a triangle are together greater than the third side.