## The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth. The Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected, and Some of Euclid's Demonstrations are Restored. Also, the Book of Euclid's Data, in Like Manner Corrected |

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Resultat 1-5 av 53

Side 119

... with the second , is to the second , as the third , together with the fourth , is to

the fourth . 18th . Prop . book 5 . XVI . Dividendo , by division ; when there are four

proportionals , and it is inferred , that the

... with the second , is to the second , as the third , together with the fourth , is to

the fourth . 18th . Prop . book 5 . XVI . Dividendo , by division ; when there are four

proportionals , and it is inferred , that the

**excess**of the first above the second ... Side 120

... Have Long Ago Vitiated These Books, are Corrected, and Some of Euclid's

Demonstrations are Restored. Also, the Book of Euclid's Data, in Like Manner Co

Euclid, Robert Simson. second , as the third to its

... Have Long Ago Vitiated These Books, are Corrected, and Some of Euclid's

Demonstrations are Restored. Also, the Book of Euclid's Data, in Like Manner Co

Euclid, Robert Simson. second , as the third to its

**excess**above the fourth . Prop . Side 142

If four magnitudes be proportionals , they are also pro' portionals by conversion ,

that is , the first is to its

the fourth . A с E Let AB be to BE , as CD to DF ; then BA is to AE , as DC to CF.

If four magnitudes be proportionals , they are also pro' portionals by conversion ,

that is , the first is to its

**excess**above the second , as the third to its**excess**abovethe fourth . A с E Let AB be to BE , as CD to DF ; then BA is to AE , as DC to CF.

Side 148

If the same hypothesis be made as in the proposition , the

fifth shall be to the second , as the

demonstration of this is the same with that of the proposition , if division be used ...

If the same hypothesis be made as in the proposition , the

**excess**of the first andfifth shall be to the second , as the

**excess**of the third and sixth to the fourth . Thedemonstration of this is the same with that of the proposition , if division be used ...

Side 184

the parallelogram KLMN equal to the

similarly situated to D ; but D is similar to EF , therefore ( 21. 6. ) also KM is similar

to EF ; let KL 1 TYL . See Note : be the homologous side to EG , and LM , 184 ...

the parallelogram KLMN equal to the

**excess**of EF above C , and similar andsimilarly situated to D ; but D is similar to EF , therefore ( 21. 6. ) also KM is similar

to EF ; let KL 1 TYL . See Note : be the homologous side to EG , and LM , 184 ...

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The Elements of Euclid: The Errors, by Which Theon, Or Others, Have Long Ago ... Robert Simson,Robert Euclid Ingen forhåndsvisning tilgjengelig - 2015 |

The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Robert Simson,Robert Euclid Ingen forhåndsvisning tilgjengelig - 2016 |

The Elements of Euclid: The Errors, by Which Theon, Or Others, Have Long Ago ... Robert Simson,Robert Euclid Ingen forhåndsvisning tilgjengelig - 2018 |

### Vanlige uttrykk og setninger

added altitude angle ABC angle BAC base BC is given centre circle circle ABCD circumference common cone contained cylinder definition demonstrated described diameter divided double draw drawn equal equal angles equiangular equimultiples excess fore four fourth given angle given in position given in species given magnitude given ratio given straight line greater Greek half join less likewise magnitude manner meet multiple Note opposite parallel parallelogram pass perpendicular plane prism produced PROP proportionals proposition pyramid Q. E. D. PROP radius reason rectangle rectangle contained remaining right angles segment shown sides similar sine solid solid angle sphere square square of AC taken THEOR third triangle ABC wherefore whole