## The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With the Elements of Plane Trigonometry, and an Appendix in Four Books : With Notes and Illustrations |

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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ... James Thomson, gen,James Euclides No preview available - 2016 |

### Common terms and phrases

ABCD altitude base bisected called centre chord circle circumference coincide common cone consequently const construction contained continuation cylinder demonstrated described diagonal diameter difference divided double draw equal equal angles equiangular extremities figure fore four fourth given given circle given straight line greater half Hence inscribed join less magnitudes manner means meet multiple opposite parallel parallelepiped parallelogram pass perpendicular plane polygon prism produced proof PROP proportional proposition proved pyramid radius ratio reason rectangle remaining respectively right angles Schol segments shown sides similar solid angle square straight line taken THEOR third touching triangle triangle ABC twice wherefore whole

### Popular passages

Page 132 - 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 47 - 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 on half the line bisected, is equal to the square on the straight line which is made up of the half and the part produced.

Page 4 - A rhombus is that which has all its sides equal, but its angles are not right angles.

Page 52 - 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.

Page 40 - In any right-angled triangle, the square which is described upon the side subtending the right angle, is equal to the squares described upon the sides which contain the right angle.

Page 9 - If two triangles have two sides of the one equal to two sides of the...

Page 29 - 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 29 - If a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles ; and the three interior angles of every triangle are equal to two right angles.

Page 17 - If, at a point in a straight line, two other straight lines, upon the opposite sides of it, make the adjacent angles together equal to two right angles, these two straight lines shall be in one and the same straight line.

Page 38 - To describe a parallelogram equal to a given rectilineal figure, and having an angle equal to a given rectilineal angle. Let ABCD be the given rectilineal figure, and E the given rectilineal angle. It is required to describe a parallelogram equal to ABCD, and having an angle equal to E.