## A Text-book of Geometrical Deductions: Book I [-II] Corresponding to Euclid, Book I [-II], Book 2 |

### From inside the book

Page 180

If there be two straight lines , one of which is divided into any number of parts , the rectangle contained by the two lines is equal to the sum of

If there be two straight lines , one of which is divided into any number of parts , the rectangle contained by the two lines is equal to the sum of

**the rectangles contained by the undivided line and the several parts of the divided line**...### What people are saying - Write a review

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A Text-Book of Geometrical Deductions: Book I [-II] Corresponding to Euclid ... William Thomson No preview available - 2016 |

### Common terms and phrases

AB=AC ABCD adjacent altitude angle angle is equal Apply Ex base base BC BC produced bisected bisector Book Bookwork College Compare concurrent Consider constant Construct Construct a rectangle DEDUCTIONS described diagonals difference distances drawn equal to twice equilateral EUCLID externally falls figure find the locus four points given points given square given straight line greater hence hypotenuse internally isosceles triangle length line be divided lines is equal means medians mid-point of AB mid-points of BC Observe obtuse angle opposite sides parallel straight lines parallelogram perimeter point in BC point of intersection points in order projection proof prove quadrilateral rectangle contained right-angled triangle School segments square on half Standard Theorem taken twice the rectangle twice the square vertex vertices whole line

### Popular passages

Page 180 - 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 181 - IF a straight line be bisected, and produced to any point: the rectangle contained by the whole line thus produced, and the part of it produced, together with the square of half the line bisected, is equal to the square of the straight line which is made up of the half and the part produced.

Page 181 - 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 180 - If there be two 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. Let...

Page 169 - In every triangle, the square on the side subtending either of the acute angles, is less than the squares on the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the...

Page 181 - To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts, shall be equal to the square on the other part.

Page 181 - In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square on the side subtending the obtuse angle is greater than the squares on the sides containing the obtuse angle, by twice the rectangle contained by the side...

Page 168 - In any obtuse triangle, the square of the side opposite the obtuse angle is equal to the sum of the squares of the other two sides, increased by twice the product of one of these sides and the projection of the other side upon it.

Page 171 - AB into two parts, so that the rectangle contained by the whole line and one of the parts, shall be equal to the square on the other part.

Page 162 - In any triangle the sum of the squares on two sides is equal to twice the square on half the third side together with twice the square on the median which bisects the third side.