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

### From inside the book

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Page 15

... triangles DAF , EAF ; the two sides DA , AF , are equal to the B F two sides EA , AF , each to each ; and the base DF , is equalt to the base EF ; there- 4 Const .

... triangles DAF , EAF ; the two sides DA , AF , are equal to the B F two sides EA , AF , each to each ; and the base DF , is equalt to the base EF ; there- 4 Const .

**fore**the angle DAF is equal * to the angle EAF : * 8 . Page 19

... there- * 1 Ax .

... there- * 1 Ax .

**fore**the angles CBE , EBD are equal to the angles DBA , ABC : but CBE , EBD are two right angles ; therefore DBA , ABC are together equalt to two right angles . Wherefore , when † 1 AX . a straight line , & c . Page 23

Because DA is equal to AC , the angle ADC is equal * B to ACD ; but the angle BCD is greatert than the angle ACD : there- 19 Ax .

Because DA is equal to AC , the angle ADC is equal * B to ACD ; but the angle BCD is greatert than the angle ACD : there- 19 Ax .

**fore**the angle BCD is greater than the angle ADC : and because the angle BCD of the triangle DCB is ... Page 29

1 . wherefore BC is not unequal to EF , that is , it is equal to it : and AB is equalf to DE ; therefore the f Hyp . two AB , BC are equal to the two DE , EF , each to and they contain t equal angles ; where- + Hyp .

1 . wherefore BC is not unequal to EF , that is , it is equal to it : and AB is equalf to DE ; therefore the f Hyp . two AB , BC are equal to the two DE , EF , each to and they contain t equal angles ; where- + Hyp .

**fore**the base AC is ... Page 31

... f1 Ax Take away the common angle BGH ; therefore the remaining angle AGH is equal † to the +3 Ax . remaining angle GHD : and they are alternate angles : therefore ABis parallelt to CD . Where- +27 . 1 .

... f1 Ax Take away the common angle BGH ; therefore the remaining angle AGH is equal † to the +3 Ax . remaining angle GHD : and they are alternate angles : therefore ABis parallelt to CD . Where- +27 . 1 .

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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