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

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Page 10

AB to DE , and AC to DF ; CE F the angle BAC equal to the angle EDF , the

AB to DE , and AC to DF ; CE F the angle BAC equal to the angle EDF , the

**base**BC shall be equal to the**base**EF ; and the triangle ABC to the triangle DEF ; and the other angles to which the equal sides are opposite , shall be equal ... Page 11

Therefore , if two triangles have two sides of the one equal to two sides of the other , each to each , and have likewise the angles contained by those sides equal to one another , their

Therefore , if two triangles have two sides of the one equal to two sides of the other , each to each , and have likewise the angles contained by those sides equal to one another , their

**bases**shall likewise be equal , and the triangles ... Page 12

Therefore the angles at the

Therefore the angles at the

**base**; & c . Q. E. D. Corollary . — Hence every equilateral triangle is also equiangular . 3 PROP . VI . THEOR , If two angles of a triangle be egual to one another , the sides also which subtend or are ... Page 13

mon to both , the two sides , DB , BC are equal to the two AC , CB , each to each ; and the angle DBC is equal to the angle + ACB ; therefore the fIlyp .

mon to both , the two sides , DB , BC are equal to the two AC , CB , each to each ; and the angle DBC is equal to the angle + ACB ; therefore the fIlyp .

**base**DC is equal to the**base**AB , and the triangle DBC is equal to the triangle ... Page 14

But if one of the vertices , as D , be within the other triangle ACB ; produce AC , AD to E , F. + Hyp . therefore , because AC is equalt to AD in the triangle ACD , the E F angles ECD , FDC upon the other side of the

But if one of the vertices , as D , be within the other triangle ACB ; produce AC , AD to E , F. + Hyp . therefore , because AC is equalt to AD in the triangle ACD , the E F angles ECD , FDC upon the other side of the

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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