## Euclid's Elements [book 1-6] with corrections, by J.R. Young1838 |

### From inside the book

Page 184

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**sides may be described upon a given straight line similar to one given , and so on . Which was to be**done . PROP . XIX . THEOR . Similar triangles are to one another as the squares of their homologous sides . Let ABC , DEF be similar ...### Other editions - View all

### Common terms and phrases

ABCD angle ABC angle ACB angle BAC antecedent base base BC BC is equal bisected Book called centre circle circle ABC circumference common consequent Const contained demonstrated describe diameter difference divided double draw drawn equal angles equiangular equilateral equimultiples exterior angle extremity fall fore four Geometry given straight line greater half Hence inscribed join less Let ABC logarithm magnitudes manner measure meet multiple parallel parallelogram pass perpendicular PROB produced PROP proportion proposition proved radius reason rectangle rectangle contained rectilineal figure remaining angle right angles segment sides similar sine square square of AC taken THEOR third touches the circle triangle ABC wherefore whole

### Popular passages

Page 30 - IF two triangles have two sides of the one equal to two sides of the other, each to each, but the angle contained by the two sides of one of them greater than the angle contained by the two sides equal to them, of the other ; the base of that which has the greater angle shall be greater than the base of the other.

Page 105 - 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 50 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.

Page 61 - 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 on the line between the points of section, is equal to the square on half the line.

Page 65 - 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 70 - 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 of the other part.

Page 41 - 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 172 - 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 45 - TRIANGLES upon the same base, and between the same parallels, are equal to one another.

Page 38 - If a, straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another; and the exterior angle equal to the interior and opposite upon the same side; and likewise the two interior angles upon the same side together equal to two right angles.