## The Elements of Euclid for the Use of Schools and Colleges: Comprising the First Six Books and Portions of the Eleventh and Twelfth Books : with Notes, an Appendix, and Exercises |

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Page 66

To divide a given straight line into two parts , so

To divide a given straight line into two parts , so

**that the rectangle contained by the whole and one of the parts**may be equal to the square on the other part . Let AB be the given straight line : it is required to divide it into two ...### What people are saying - Write a review

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ABCD AC is equal angle ABC angle BAC Axiom base bisected Book centre chord circle ABC circumference common Construction Corollary Definition demonstration describe a circle described diameter divided double draw drawn equal equal angles equiangular equilateral equimultiples Euclid extremities fall figure fixed formed four fourth given circle given point given straight line greater half Hypothesis inscribed intersect join less Let ABC magnitudes manner meet multiple namely opposite sides parallel parallelogram pass perpendicular plane polygon PROBLEM produced proportionals PROPOSITION Q.E.D. PROPOSITION quadrilateral radius ratio reason rectangle contained rectilineal figure remaining respectively right angles segment shew shewn sides similar square straight line &c straight line drawn suppose Take taken THEOREM third triangle ABC twice Wherefore whole

### Popular passages

Page 264 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.

Page 73 - 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 264 - To draw a straight line at right angles to a given straight line, from a given point in the same. Let AB be...

Page 184 - 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 10 - THE angles at the base of an isosceles triangle are equal to one another : and, if the equal sides be produced, the angles upon the other side of the base shall be equal.

Page 300 - Describe a circle which shall pass through a given point and touch a given straight line and a given circle.

Page 60 - If a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.

Page 62 - If a straight line be divided into two equal, and also into two unequal parts, the squares on the two unequal parts are together double of the square on half the line, and of the square on the line between the points of section. Let the straight line AB be divided into two equal parts in the point C, and into two unequal parts in the point D ; The squares on AD and DB shall be together double of AD»+DB

Page 244 - Let AB and C be two unequal magnitudes, of which AB is the greater. If from AB there be taken more than its half, and from the remainder more than its half, and so on ; there shall at length remain a magnitude less than C. For C may be multiplied, so at length to become greater than AB.

Page 6 - Magnitudes which coincide with one another, that is, which exactly fill the same space, are equal to one another.