## 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 100

Side 4

Equal and similar solid figures are those which are contained by similar planes of

the same number and

Definition ; because the equality of figures of any kind must be demonstrated ,

and ...

Equal and similar solid figures are those which are contained by similar planes of

the same number and

**magnitude**. ” Now this Proposition is a Theorem , not aDefinition ; because the equality of figures of any kind must be demonstrated ,

and ...

Side 117

THE The first of four

equal to that of the second , the multiple of the third ELEMENTS OF EUCLID .

BOOK V. DEFINITIONS . I. A LESS

THE The first of four

**magnitudes**is said to have the same ratio to the of the first beequal to that of the second , the multiple of the third ELEMENTS OF EUCLID .

BOOK V. DEFINITIONS . I. A LESS

**magnitude**is said to be a part of a greater ... Side 118

N. B. “ When four

, the first is to the second , as the third ... than the multiple of the fourth ; then the

first is said to have to the second a greater ratio than the third

N. B. “ When four

**magnitudes**are proportionals , it is usually expressed by saying, the first is to the second , as the third ... than the multiple of the fourth ; then the

first is said to have to the second a greater ratio than the third

**magnitude**has to ... Side 120

Ex æquali ( sc . distantia ) , or ex æquo , from equality of distance when there is

any number of

is used simply by itself , when the first

...

Ex æquali ( sc . distantia ) , or ex æquo , from equality of distance when there is

any number of

**magnitudes**more than two ... Ex æquali , from equality ; this termis used simply by itself , when the first

**magnitude**is to the second of the first rank...

Side 121

1 1 ber therefore of the

and CH to F , reason , because GB is equal to E , and HD to F ... That

of which a multiple is greater than the same multiple of another , is greater than ...

1 1 ber therefore of the

**magnitudes**CH , HD shall and because AG is equal to E ,and CH to F , reason , because GB is equal to E , and HD to F ... That

**magnitude**of which a multiple is greater than the same multiple of another , is greater than ...

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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