## 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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Side 317

B. V. of this there is

the Elements . tudes and

demonstration of this proposition , because that which is in the Greek and Latin ...

B. V. of this there is

**given**a more explicit demonstration than that which is now inthe Elements . tudes and

**ratios**, PROP . X. B. V. It was necessary to**give**anotherdemonstration of this proposition , because that which is in the Greek and Latin ...

Side 318

this ; if A had to C the same

whatever of A and B be taken , and any ... And it seems that he who has

demonstration of the 10th proposition as we now have it , instead of that which ...

this ; if A had to C the same

**ratio**that B has to C ; then if any equimultipleswhatever of A and B be taken , and any ... And it seems that he who has

**given**thedemonstration of the 10th proposition as we now have it , instead of that which ...

Side 327

of the

is quite useless and absurd : for that Theon brought it into the Elements can

scarce be doubted ; as it is to be found in his commentary ...

of the

**ratio**of K to L , and of the**ratio**of L to M. ” This defidition therefore of Theonis quite useless and absurd : for that Theon brought it into the Elements can

scarce be doubted ; as it is to be found in his commentary ...

**ratio**are**given**; viz . Side 328

... is compounded of the

to Z : and , by def . 5. book 6. and the explication

commentators , the

is the

... is compounded of the

**ratios**of their sides ; that is , of the**ratios**of C to E , and Dto Z : and , by def . 5. book 6. and the explication

**given**of it by all thecommentators , the

**ratio**which is compounded of the**ratios**of C to E , and D to Z ,is the

**ratio**... Side 330

1 like cases , how to find the ratio which is compounded of two or more

whatever of the same kind A , B , C , D , & c . the ratio compounded of the ratios of

the ...

1 like cases , how to find the ratio which is compounded of two or more

**given****ratios**. From what has been said , it may be observed , that in any magnitudeswhatever of the same kind A , B , C , D , & c . the ratio compounded of the ratios of

the ...

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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Euclid Uten tilgangsbegrensning - 1810 |

The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... Robert Simson,Euclid 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