## The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |

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Page 9

Wherefore from the given point A a straight line AL has been drawn equal to the given straight line BC . Which was to be done . * 3 Ax , PROP . III . PROB . G * 2.1 . From the

Wherefore from the given point A a straight line AL has been drawn equal to the given straight line BC . Which was to be done . * 3 Ax , PROP . III . PROB . G * 2.1 . From the

**greater**of two given straight lines to cut off a part equal ... Page 12

For , if AB be not equal to AC , one of them is

For , if AB be not equal to AC , one of them is

**greater**than the other : let AB be the**greater**; and from it cut * off DB equal to AC , the less , and join DC : therefore , because in the triangles DBC , ACB , DB is equal to AC , and BC ... Page 13

... and the triangle DBC is equal to the triangle * ACB , the less to the D

... and the triangle DBC is equal to the triangle * ACB , the less to the D

**greater**, which is absurd . Therefore AB is not unequal to AC , that is , it is equal to it . Wherefore , if two angles , & c . Q. E. D. B * * 4.1 . с - Cor . Page 14

Again , because CB is Hyp . equalt to DB , the angle BDC is equal * to the angle BCD ; but BDC has been proved to be

Again , because CB is Hyp . equalt to DB , the angle BDC is equal * to the angle BCD ; but BDC has been proved to be

**greater**than the same BCD : which is impossible . The case in which the vertex of one triangle is upon a side of the ... Page 21

If one side of a triangle be produced , the exterior angle is

If one side of a triangle be produced , the exterior angle is

**greater**than either of the interior opposite angles .. Let ABC be a triangle , and let its side BC be produced to D : the exterior angle ACD shall be**greater**than either of ...### What people are saying - Write a review

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The Elements of Euclid: Viz. The First Six Books, Together With the Eleventh ... Euclid Euclid No preview available - 2018 |

### Common terms and phrases

altitude angle ABC angle BAC base base BC BC is equal centre circle ABCD circumference common cone Const contained cylinder demonstrated described diameter divided double draw drawn equal angles equiangular equilateral equimultiples extremities fall figure fore four fourth given given straight line greater half inscribed join less Let ABC likewise magnitudes manner meet multiple opposite parallel parallelogram pass perpendicular plane polygon prism PROB produced PROP proportionals proved pyramid ratio reason rectangle contained rectilineal figure remaining angle right angles segment shown sides similar solid solid angle solid parallelopiped sphere square taken THEOR third touches triangle ABC vertex wherefore whole