## The Elements of Euclid. Books I.-VI.; XI. 1-21 XII. 1-2. A New Text, Based on that of Simson. Edited by H. J. Hose, Book 1 |

### From inside the book

Page 47

... and things that are equal to the same thing are equal to one another ( Ax . 1 ) : therefore all the angles of the polygon ABCDE ,

... and things that are equal to the same thing are equal to one another ( Ax . 1 ) : therefore all the angles of the polygon ABCDE ,

**together with four right angles are equal to twice as many right angles as the**polygon has sides . Page 287

But all the angles of the polygon GHKLM

But all the angles of the polygon GHKLM

**together with four right angles are equal to twice as many right angles as the**polygon has sides ( i . 32 . Cor . 1 ) , that is , as there are plane angles constituting the solid angle at A ...### What people are saying - Write a review

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The Elements of Euclid, Books I-VI: XI. 1-21; XII. 1,2; Ed. by H.J. Hose Euclides No preview available - 2016 |

### Common terms and phrases

ABCD according adjacent angle ACB angle bac angles ABC angular points base bisected centre circle ABC circumference cloth coincide common const defn described diagonal divided double draw drawn edition equal angles equal Ax equimultiples exterior angle extremities fall figure fore four magnitudes fourth given given straight line greater half Hence homologous hyps included angle interior join less Let ABC magnitudes manner meet multiple opposite sides pair parallel parallelogram pass perpendicular plane polygon produced PROP proportional proved radius ratio rectangle respectively equal right angles segment shewn sides sides BC similar square square of ac taken THEOR thing are equal third triangle ABC unequal whole

### Popular passages

Page 39 - To draw a straight line through a given point parallel to a given straight line. Let A be the given point, and BC the given straight line...

Page 52 - 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 16 - To draw a straight line at right angles to a given straight line, from a given point in the same.

Page 5 - From a given point to draw a straight line equal to a given straight line. Let A be the given point, and BC the given straight line ; it is required to draw, from the point A, a straight line equal to BC.

Page 11 - Upon the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of' the base, equal to one another, and likewise those which are terminated in the other extremity.

Page 105 - If a straight line touch a circle, and from the point of contact a straight line be drawn cutting the circle ; the angles which this line makes with the line touching the circle, shall be equal to the angles which are in the alternate segments of the circle.

Page 118 - IF a straight line touch a circle, and from the point of contact a straight line be drawn at right angles to the touching line, the centre of the circle shall be in that line.

Page 66 - 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 6 - From the greater of two given straight lines to cut off a part equal to the less. Let AB and C be the two given straight lines, whereof AB is the greater.

Page 119 - Upon a given straight line to describe a segment of a circle, which shall contain an angle equal to a given rectilineal angle.