## A Text-book of Geometrical Deductions: Corresponding to Euclid, book II, with miscellaneous deductions from books I and II., Book 2Longmans, Green and Company, 1892 |

### Common terms and phrases

AB-AC AB=AC AB=BC ABē ABCD altitude angle is equal Apply Euc Apply Ex base BC BC meets BC produced bisector Bookwork Construct a rectangle Construct a triangle difference distances divided externally drawn 1 BC equal to twice EUCLID exterior angle externally at H figure find a point find the locus four points geometrical construction given points given square given straight line given the base half the line hypotenuse isosceles triangle James Thin joining the mid-points line be divided line be drawn lines is equal medial section medians meet AC mid-point of AB mid-points of BC obtuse angle parallel straight lines parallelogram perimeter perpendicular drawn point in AB point in BC point of intersection points in order previous Ex quadrilateral rectangle contained rhombus right-angled triangle segments square on half Standard Theorem trapezium twice the rectangle twice the square vertex 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 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 180 - 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 on the other...

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.